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#include <bits/stdc++.h> using namespace std; const long long mod = 1e9 + 7; long long dx[] = {-1, 0, 1, 0}; long long dy[] = {0, -1, 0, 1}; int32_t main() { ios::sync_with_stdio(false); cin.tie(0); cout.tie(0); long long n, a, b, c; cin >> n >> a >> b >> c; long long ans = 0; for (long long i = 0; i <= a; i += 2) { for (long long j = 0; j <= c; j++) { long long k = n - i / 2 - 2 * j; if (k < 0 || k > b) continue; ans++; } } cout << ans << "\n"; }
#include <bits/stdc++.h> using namespace std; const int INF = 0x3f3f3f3f; int main() { int i, j, k; int n, m; int a, b, c; cin >> n >> a >> b >> c; if (a / 2 + b + c * 2 < n) { cout << 0 << endl; return 0; } long long cou = 0; for (i = 0; i <= a; i += 2) for (j = 0; j <= b; j++) { k = n - (i / 2 + j); if (k < 0) continue; if (k % 2 == 0 && k <= c * 2) cou++; } cout << cou << endl; return 0; }
#include <bits/stdc++.h> using namespace std; int n, a, b, c; int input(void) { scanf("%d%d%d%d", &n, &a, &b, &c); return 0; } int solve(void) { int x, ans = 0; for (register int y = 0; y <= b; y++) { for (register int z = 0; z <= c; z++) { x = (n - y - (z << 1)) << 1; if (0 <= x && x <= a) ans++; } } printf("%d\n", ans); return 0; } int main(void) { input(); solve(); return 0; }
#include <bits/stdc++.h> using namespace std; inline int read() { static int r, sign; static char c; r = 0, sign = 1; do c = getchar(); while (c != '-' && (c < '0' || c > '9')); if (c == '-') sign = -1, c = getchar(); while (c >= '0' && c <= '9') r = r * 10 + (int)(c - '0'), c = getchar(); return sign * r; } template <typename T> inline void print(T *a, int n) { for (int i = 1; i < n; ++i) cout << a[i] << " "; cout << a[n] << endl; } const int mod = (int)1e9 + 7; struct hashInt { int x; hashInt() {} hashInt(int _x) : x(_x) {} inline hashInt operator+(const hashInt &y) const { int z = x + y.x; if (z >= mod) z -= mod; if (z < 0) z += mod; return hashInt(z); } inline hashInt operator-(const hashInt &y) const { int z = x - y.x; if (z >= mod) z -= mod; if (z < 0) z += mod; return hashInt(z); } inline hashInt operator*(const hashInt &y) const { return hashInt((long long)x * y.x % mod); } }; struct edge { int next, node; hashInt w; } e[100100 << 1 | 1]; int head[100100 + 1], tot = 0; inline void addedge(int a, int b, int w) { e[++tot].next = head[a]; head[a] = tot, e[tot].node = b, e[tot].w = w; } struct DP { hashInt sum, sqr; DP() {} DP(int _s, int _q) : sum(_s), sqr(_q) {} DP(hashInt _s, hashInt _q) : sum(_s), sqr(_q) {} } up[100100 + 1], down[100100 + 1], downex[100100 + 1]; int n, size[100100 + 1]; inline hashInt delta(const DP &x, int n, hashInt b) { return x.sqr + b * b * n + b * 2 * x.sum; } void preUp(int x, int f) { size[x] = 1, up[x].sum = up[x].sqr = 0; for (int i = head[x]; i; i = e[i].next) { int node = e[i].node; if (node == f) continue; preUp(node, x); size[x] += size[node]; up[x].sum = up[x].sum + up[node].sum + e[i].w * size[node]; up[x].sqr = up[x].sqr + delta(up[node], size[node], e[i].w); } } void preDown(int x, int f) { for (int i = head[x]; i; i = e[i].next) { int node = e[i].node; if (node == f) continue; DP cur; cur.sum = down[x].sum + up[x].sum - up[node].sum - e[i].w * size[node]; cur.sqr = down[x].sqr + up[x].sqr - delta(up[node], size[node], e[i].w); downex[node] = cur; down[node].sum = cur.sum + e[i].w * (n - size[node]); down[node].sqr = delta(cur, n - size[node], e[i].w); preDown(node, x); } } int p[18 + 1][100100 + 1], logn, dep[100100 + 1]; hashInt dis[100100 + 1], dissum[100100 + 1], dissqr[100100 + 1]; void preDA(int x, int f) { p[0][x] = f; for (int i = head[x]; i; i = e[i].next) { int node = e[i].node; if (node == f) continue; dep[node] = dep[x] + 1; dis[node] = dis[x] + e[i].w; dissum[node] = dissum[x] + dis[node]; dissqr[node] = dissqr[x] + dis[node] * dis[node]; preDA(node, x); } } inline int LCA(int x, int y) { if (dep[x] > dep[y]) swap(x, y); for (int i = logn; i >= 0; --i) if (dep[x] <= dep[p[i][y]]) y = p[i][y]; if (x == y) return x; for (int i = logn; i >= 0; --i) if (p[i][x] != p[i][y]) x = p[i][x], y = p[i][y]; return p[0][x]; } inline int LCA2(int x, int y) { for (int i = logn; i >= 0; --i) if (dep[x] < dep[p[i][y]]) y = p[i][y]; return y; } vector<pair<int, int> > Q[100100 + 1]; int q, ans[100100 + 1], seq[100100 + 1], cnt = 0; DP pre[100100 + 1], suf[100100 + 1]; struct BIT { hashInt a[100100 + 1]; inline void modify(int x, hashInt w) { for (; x <= n; x += x & -x) a[x] = a[x] + w; } inline hashInt query(int x) { hashInt r = 0; for (; x > 0; x -= x & -x) r = r + a[x]; return r; } } sufsum, sufsqr; void dfs(int x, int f) { for (int i = 0; i < Q[x].size(); ++i) { int node = Q[x][i].first, id = Q[x][i].second; int p = LCA(x, node); hashInt b = dis[node] - dis[p]; b = b * b; } for (int i = head[x]; i; i = e[i].next) { int node = e[i].node; if (node == f) continue; seq[++cnt] = x; pre[cnt].sum = pre[cnt - 1].sum + e[i].w * (cnt - 1); pre[cnt].sqr = delta(pre[cnt - 1], cnt - 1, e[i].w); dfs(node, x); --cnt; } } int main(int argc, char *argv[]) { scanf("%d", &n); for (int i = 1; i < n; ++i) { int x, y, w; scanf("%d%d%d", &x, &y, &w); addedge(x, y, w), addedge(y, x, w); } preUp(1, 0); preDown(1, 0); dep[1] = 1, preDA(1, 0); logn = (int)(log((double)n) / log(2.0)); for (int i = 1; i <= logn; ++i) for (int j = 1; j <= n; ++j) p[i][j] = p[i - 1][p[i - 1][j]]; scanf("%d", &q); while (q--) { int x, y; scanf("%d%d", &x, &y); int p = LCA(x, y); hashInt d = dis[x] + dis[y] - dis[p] * 2; hashInt ans = 0; if (p == y) { ans = delta(down[y], n - size[y], d); ans = up[x].sqr + down[x].sqr - ans * 2; } else { ans = delta(up[y], size[y], d); ans = ans * 2 - up[x].sqr - down[x].sqr; } printf("%d\n", ans.x); } fclose(stdin); fclose(stdout); return 0; }
#include <bits/stdc++.h> using namespace std; const int modulo = 1000000007; int N, E[200010], lvl[200010], first[100010], M[200010][18], max2[200010], S1[100010], S2[100010], nr[100010], droot[100010], indd[100010], T[100010], finalsol1[100010], finalsol2[100010]; vector<int> V[100010], C[100010], pd1[100010], pd2[100010]; int add(int x, int y) { x += y; return x >= modulo ? x - modulo : x; } int mult(int x, int y) { int ret = ((long long)x * y) % modulo; return ret < 0 ? ret + modulo : ret; } int sub(int x, int y) { x -= y; return x < 0 ? x + modulo : x; } void euler(int x, int& poz, int l = 0, int t = -1) { T[x] = t; for (auto i : V[x]) if (t != i) { E[poz] = x; lvl[poz++] = l; euler(i, poz, l + 1, x); } E[poz] = x; lvl[poz++] = l; } void precompute_lca() { int poz = 0; euler(0, poz); memset(first, -1, sizeof(first)); for (int i = 0; i < 2 * N - 1; i++) if (first[E[i]] == -1) first[E[i]] = i; for (int i = 0; i < 2 * N - 1; i++) M[i][0] = i; for (int k = 1; (1 << k) <= 2 * N - 1; k++) for (int i = 0; i + (1 << k) <= 2 * N - 1; i++) { int l = M[i][k - 1], r = M[i + (1 << (k - 1))][k - 1]; M[i][k] = lvl[l] < lvl[r] ? l : r; } for (int k = 1; (1 << k) <= 2 * N - 1; k++) max2[1 << k] = 1; for (int i = 1; i <= 2 * N - 1; i++) max2[i] += max2[i - 1]; } int lca(int x, int y) { int a = first[x], b = first[y]; if (a > b) swap(a, b); int len = b - a + 1, k = max2[len]; int l = M[a][k], r = M[b - (1 << k) + 1][k]; if (lvl[l] < lvl[r]) return E[l]; else return E[r]; } void calc_S(int x, int d = 0) { nr[x] = 1; droot[x] = d; for (int i = 0; i < V[x].size(); i++) { int y = V[x][i]; if (y == T[x]) continue; calc_S(y, add(d, C[x][i])); S1[x] = add(S1[x], add(S1[y], mult(C[x][i], nr[y]))); S2[x] = add(S2[x], add(S2[y], add(mult(nr[y], mult(C[x][i], C[x][i])), mult(2, mult(C[x][i], S1[y]))))); nr[x] += nr[y]; } } void calc_pd(int x, int ind = 0) { int up = 0; indd[x] = ind; if (T[x] != -1) { up = add(pd1[T[x]][ind], mult(C[T[x]][ind], N - nr[x])); } up = add(up, S1[x]); for (int i = 0; i < V[x].size(); i++) if (V[x][i] != T[x]) { pd1[x].push_back(sub(sub(up, S1[V[x][i]]), mult(C[x][i], nr[V[x][i]]))); } else { pd1[x].push_back(-1); } up = 0; if (T[x] != -1) { up = add( add(pd2[T[x]][ind], mult(mult(N - nr[x], C[T[x]][ind]), C[T[x]][ind])), mult(mult(2, C[T[x]][ind]), pd1[T[x]][ind])); } up = add(up, S2[x]); for (int i = 0; i < V[x].size(); i++) if (V[x][i] != T[x]) { int y = V[x][i]; pd2[x].push_back( sub(sub(sub(up, S2[y]), mult(mult(C[x][i], C[x][i]), nr[y])), mult(mult(2, C[x][i]), S1[y]))); } else { pd2[x].push_back(-1); } for (int i = 0; i < V[x].size(); i++) if (V[x][i] != T[x]) calc_pd(V[x][i], i); } int calc_d(int x, int y) { int z = lca(x, y); return sub(add(droot[x], droot[y]), mult(2, droot[z])); } int main() { scanf("%d", &N); for (int i = 0; i < N - 1; i++) { int a, b, c; scanf("%d %d %d", &a, &b, &c); a--, b--; V[a].push_back(b); V[b].push_back(a); C[a].push_back(c); C[b].push_back(c); } precompute_lca(); calc_S(0); calc_pd(0); int Q; scanf("%d", &Q); for (int i = 0; i < N; i++) if (T[i] != -1) { int t = T[i], ind = indd[i]; finalsol1[i] = add(pd1[T[i]][indd[i]], mult(C[T[i]][indd[i]], N - nr[i])); finalsol2[i] = add(add(pd2[t][ind], mult(mult(C[t][ind], C[t][ind]), N - nr[i])), mult(mult(2, C[t][ind]), pd1[t][ind])); } else { finalsol1[i] = finalsol2[i] = 0; } for (int i = 0; i < Q; i++) { int u, v; scanf("%d %d", &u, &v); u--, v--; int ret = 0; int duv = calc_d(u, v); if (lca(u, v) == v) { ret = add(ret, mult(N - nr[v], mult(duv, duv))); ret = add(ret, finalsol2[v]); ret = add(ret, mult(mult(2, duv), finalsol1[v])); ret = mult(ret, -2); ret = add(ret, add(S2[u], finalsol2[u])); } else { ret = add(ret, mult(nr[v], mult(duv, duv))); ret = add(ret, S2[v]); ret = add(ret, mult(mult(2, duv), S1[v])); ret = mult(ret, 2); ret = sub(ret, add(S2[u], finalsol2[u])); } printf("%d\n", ret); } return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 1e5 + 100, LOG = 20, MOD = 1000 * 1000 * 1000 + 7; int sum(int a, int b) { a += b; if (a >= MOD) a -= MOD; else if (a < 0) a += MOD; return a; } void _sum(int &a, int b) { a += b; if (a >= MOD) a -= MOD; else if (a < 0) a += MOD; } int mul(int a, int b) { return 1LL * a * b % MOD; } int n, u, v, w, q, h[N], sz[N], sum_down[N], sq_down[N], sq_up[N][LOG]; pair<int, int> upper[N][LOG], sum_up[N][LOG]; vector<pair<int, int> > nei[N]; int lca(int u, int v) { if (h[u] < h[v]) swap(u, v); for (int i = LOG - 1; i >= 0; i--) if (h[u] - (1 << i) >= h[v]) u = upper[u][i].first; if (u == v) return u; for (int i = LOG - 1; i >= 0; i--) if (upper[u][i].first != upper[v][i].first) { u = upper[u][i].first; v = upper[v][i].first; } return upper[u][0].first; } bool under(int u, int v) { return lca(u, v) == v; } int dis(int u, int v) { int res = 0; for (int i = LOG - 1; i >= 0; i--) if (h[u] - (1 << i) >= h[v]) { _sum(res, upper[u][i].second); u = upper[u][i].first; } return res; } int get_sq(int u, int v) { int res = 0, len = 0; for (int i = LOG - 1; i >= 0; i--) if (h[u] - (1 << i) >= h[v]) { _sum(res, sq_up[u][i]); _sum(res, mul(len, sum(mul(len, sum_up[u][i].second), mul(2, sum_up[u][i].first)))); _sum(len, upper[u][i].second); u = upper[u][i].first; } return res; } void dfs_down(int v, int par = 0) { for (int i = 1; i < LOG; i++) { pair<int, int> p1 = upper[v][i - 1], p2 = upper[p1.first][i - 1]; upper[v][i] = pair<int, int>(p2.first, sum(p1.second, p2.second)); } int SUM = 0, SQ = 0, SZ = 0; for (pair<int, int> p : nei[v]) if (p.first != par) { int u = p.first, d = p.second; upper[u][0] = pair<int, int>(v, d); h[u] = h[v] + 1; dfs_down(u, v); SZ += sz[u]; _sum(SUM, sum(sum_down[u], mul(sz[u], d))); _sum(SQ, sum(sq_down[u], mul(d, sum(mul(d, sz[u]), mul(2, sum_down[u]))))); } sz[v] = sum(SZ, 1); sum_down[v] = SUM; sq_down[v] = SQ; } void dfs_up(int v, int par = 0) { for (int i = 1; i < LOG; i++) { int u = upper[v][i - 1].first, d = upper[v][i - 1].second, SZ = sum_up[u][i - 1].second; sum_up[v][i].first = sum(sum_up[v][i - 1].first, sum(sum_up[u][i - 1].first, mul(SZ, d))); sum_up[v][i].second = sum(sum_up[v][i - 1].second, SZ); sq_up[v][i] = sum(sq_up[v][i - 1], sum(sq_up[u][i - 1], mul(d, sum(mul(SZ, d), mul(2, sum_up[u][i - 1].first))))); } for (pair<int, int> p : nei[v]) if (p.first != par) { int u = p.first, d = p.second; sum_up[u][0].first = sum(sum_down[v], sum(-mul(d, sz[u]), sum(-sum_down[u], mul(sz[v] - sz[u], d)))); sum_up[u][0].second = sz[v] - sz[u]; sq_up[u][0] = sum( sq_down[v], -sum(sq_down[u], mul(d, sum(mul(d, sz[u]), mul(2, sum_down[u]))))); _sum(sq_up[u][0], mul(d, sum(mul(d, sum_up[u][0].second), mul(2, sum(sum_up[u][0].first, -mul(d, sum_up[u][0].second)))))); dfs_up(u, v); } } int main() { ios::sync_with_stdio(false), cin.tie(0); cin >> n; for (int i = 0; i < n - 1; i++) { cin >> u >> v >> w; nei[--u].push_back(pair<int, int>(--v, w)); nei[v].push_back(pair<int, int>(u, w)); } dfs_down(0); dfs_up(0); cin >> q; while (q--) { cin >> u >> v; u--, v--; int ans = sum(sq_down[u], get_sq(u, 0)), LCA = lca(u, v), d = sum(dis(v, LCA), dis(u, LCA)); if (under(u, v)) _sum(ans, -mul(2, sum(get_sq(u, v), sq_down[u]))); else _sum(ans, -mul(2, sum(sq_down[v], mul(d, sum(mul(d, sz[v]), mul(2, sum_down[v])))))); ans = (-ans + MOD) % MOD; cout << ans << '\n'; } return 0; }
#include <bits/stdc++.h> using namespace std; const int INF = 1e9; const long long int INFLL = 1e18; const double EPS = 1e-8; const long long int MOD = 1000000007; template <class T> T &chmin(T &a, const T &b) { return a = min(a, b); } template <class T> T &chmax(T &a, const T &b) { return a = max(a, b); } struct Mod { unsigned n; Mod() {} Mod(long long int x) { if (x < 0) n = x % MOD + MOD; else n = x % MOD; } }; Mod operator+(Mod a, Mod b) { return Mod((a.n + b.n) % MOD); } Mod operator+=(Mod &a, Mod b) { return a = a + b; } Mod operator-(Mod a, Mod b) { return Mod((a.n + MOD - b.n) % MOD); } Mod operator-=(Mod &a, Mod b) { return a = a - b; } Mod operator*(Mod a, Mod b) { return Mod(((long long int)a.n * b.n) % MOD); } Mod operator*=(Mod &a, Mod b) { return a = a * b; } Mod modpow(Mod x, long long int k) { Mod res = 1; while (k) { if (k & 1) res *= x; k /= 2; x *= x; } return res; } Mod inv(Mod a) { return modpow(a, MOD - 2); } Mod operator/(Mod a, Mod b) { return Mod(((long long int)a.n * inv(b).n) % MOD); } Mod operator/=(Mod &a, Mod b) { return a = a / b; } struct Bit { vector<long long int> bit; int size; void init(int n) { n++; size = 1; while (size < n) size *= 2; bit = vector<long long int>(size, 0); } void add(int k, long long int x) { k++; while (k <= size) { bit[k] += x; k += k & -k; } } long long int sum(int k) { k++; long long int res = 0; while (k > 0) { res += bit[k]; k -= k & -k; } return res; } long long int get(int k) { return sum(k) - sum(k - 1); } long long int update(int k, long long int x) { add(k, x - get(k)); } }; struct Tree { vector<vector<pair<long long int, long long int> > > G; int n, logn, r; vector<int> nst, sst; vector<int> dep; vector<long long int> w; vector<int> par; vector<bool> used; vector<vector<int> > ps; vector<int> in, out; int etcnt; bool dfs_f, lca_f, et_f; Bit etbit; void init(int num, int root = 0) { n = num; r = root; G = vector<vector<pair<long long int, long long int> > >(n); par = vector<int>(n, -1); w = vector<long long int>(n, 1); dfs_f = lca_f = et_f = false; } Tree(int num, int root = 0) { init(num, root); } Tree() {} void set_weight(const vector<long long int> &weight) { w = weight; } void set_graph_dfs( const vector<vector<pair<long long int, long long int> > > &g, int x) { used[x] = true; for (auto &w : g[x]) { if (!used[w.first]) { G[x].push_back(w); set_graph_dfs(g, w.first); } } } void set_graph(const vector<vector<pair<long long int, long long int> > > &g, int root = 0) { init(g.size(), root); used = vector<bool>(n, 0); G = vector<vector<pair<long long int, long long int> > >(n); set_graph_dfs(g, root); } void set_graph(int root = 0) { vector<vector<pair<long long int, long long int> > > tempg = G; set_graph(tempg, root); } void add_edge(int x, int p, long long int co = 1) { G[p].push_back(pair<long long int, long long int>(x, co)); } void add_biedge(int a, int b, long long int co = 1) { G[a].push_back(pair<long long int, long long int>(b, co)); G[b].push_back(pair<long long int, long long int>(a, co)); } void dfs(int x, int p, int d) { used[x] = true; dep[x] = d; nst[x] = 1; sst[x] = w[x]; par[x] = p; for (auto &w : G[x]) { if (p != x && !used[w.first]) { dfs(w.first, x, d + 1); nst[x] += nst[w.first]; sst[x] += sst[w.first]; } } } void dfs() { used = vector<bool>(n, false); nst = sst = vector<int>(n); dep = vector<int>(n); dfs(r, -1, 0); dfs_f = true; } void init_lca() { if (!dfs_f) dfs(); logn = (int)log2(n) + 1; ps = vector<vector<int> >(logn, vector<int>(n, -1)); ps[0] = par; for (int i = (1); i < (int)(logn); i++) { for (int j = (0); j < (int)(n); j++) { if (ps[i - 1][j] == -1) ps[i][j] = -1; else ps[i][j] = ps[i - 1][ps[i - 1][j]]; } } lca_f = true; } int lca(int a, int b) { if (!lca_f) init_lca(); if (dep[a] > dep[b]) swap(a, b); for (int i = logn; i >= 0; i--) if ((dep[b] - dep[a]) & (1 << i)) b = ps[i][b]; if (a == b) return a; for (int i = logn - 1; i >= 0; i--) { if (ps[i][a] != ps[i][b]) { a = ps[i][a]; b = ps[i][b]; } } return ps[0][a]; } void etdfs(int x) { in[x] = etcnt++; for (auto &w : G[x]) { etdfs(w.first); etbit.add(in[w.first], w.second); etbit.add(out[w.first], -w.second); } out[x] = etcnt++; } void etdfs() { if (!dfs_f) dfs(); if (!lca_f) init_lca(); etcnt = 0; in = vector<int>(n); out = vector<int>(n); etbit.init(2 * n); etdfs(r); et_f = true; } void etupdate(int x, long long int d) { if (!et_f) etdfs(); etbit.update(in[x], d); etbit.update(out[x], -d); } long long int dist(int a, int b) { if (!et_f) etdfs(); return etbit.sum(in[a]) + etbit.sum(in[b]) - etbit.sum(in[lca(a, b)]) * 2; } vector<Mod> ds, dss; void dsdfs(int x) { for (auto &w : G[x]) { dsdfs(w.first); Mod c = w.second; ds[x] += ds[w.first] + Mod(nst[w.first]) * c; dss[x] += dss[w.first] + Mod(2) * c * ds[w.first] + c * c * Mod(nst[w.first]); } } void dsdfs() { ds = dss = vector<Mod>(n, 0); dsdfs(r); } vector<Mod> ss, sss; void qdfs(int x, Mod sum, Mod sums) { ss[x] = sum; sss[x] = sums; for (auto &w : G[x]) { int t = w.first; Mod c = w.second; qdfs(t, sum + Mod(n - 2 * nst[t]) * c, sums + c * c * Mod(n) - Mod(4) * (ds[t] + c * Mod(nst[t])) * c + Mod(2) * sum * c); } } void qdfs() { dsdfs(); ss = sss = vector<Mod>(n); qdfs(r, ds[r], dss[r]); } Mod mdist(int u, int v) { return Mod(dist(u, v)); } Mod querya(int u, int v) { if (lca(u, v) == v) { return sss[u] - (sss[v] - dss[v] + mdist(u, v) * mdist(u, v) * Mod(n - nst[v]) + Mod(2) * mdist(u, v) * (ss[v] - ds[v])); } else { return dss[v] + mdist(u, v) * mdist(u, v) * Mod(nst[v]) + Mod(2) * mdist(u, v) * ds[v]; } } Mod query(int u, int v) { return Mod(2) * querya(u, v) - sss[u]; } }; Tree T; int n, q; int main() { cin >> n; T.init(n); for (int i = (0); i < (int)(n - 1); i++) { int a, b, c; cin >> a >> b >> c; a--; b--; T.add_biedge(a, b, c); } T.set_graph(0); T.dfs(); T.init_lca(); T.etdfs(); T.qdfs(); cin >> q; for (int i = (0); i < (int)(q); i++) { int u, v; cin >> u >> v; u--; v--; cout << T.query(u, v).n << endl; } return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 1e5 + 7; const int LG = 20; const int MOD = 1e9 + 7; int dp[N][2], up[N][2], cnt[N]; vector<pair<int, int> > adj[N]; int d[N], par[N][LG], path[N][LG]; int n; void add(int &a, long long val) { a += val % MOD; a %= MOD; a += MOD; a %= MOD; } void dfs_down(int v, int p) { cnt[v]++; for (auto e : adj[v]) { int u = e.first; int w = e.second; if (u == p) continue; d[u] = d[v] + 1; par[u][0] = v; path[u][0] = w; for (int i = 1; i < LG; i++) { par[u][i] = par[par[u][i - 1]][i - 1]; path[u][i] = (path[u][i - 1] + path[par[u][i - 1]][i - 1]) % MOD; } dfs_down(u, v); cnt[v] += cnt[u]; add(dp[v][0], 1LL * dp[u][0] + 1LL * cnt[u] * w % MOD); add(dp[v][1], 1LL * dp[u][1] + 2LL * dp[u][0] * w % MOD + 1LL * cnt[u] * w % MOD * w % MOD); } } void dfs_up(int v, int p) { for (auto e : adj[v]) { int u = e.first; int w = e.second; if (u == p) continue; int sum = dp[v][0]; add(sum, -1LL * dp[u][0] + -1LL * cnt[u] * w % MOD); int sum2 = dp[v][1]; add(sum2, -1LL * dp[u][1] + -2LL * dp[u][0] * w % MOD + -1LL * cnt[u] * w % MOD * w % MOD); add(up[u][0], 1LL * (sum + up[v][0]) % MOD + 1LL * (n - cnt[u]) * w % MOD); add(up[u][1], 1LL * (sum2 + up[v][1]) % MOD + 2LL * (sum + up[v][0]) % MOD * w % MOD + 1LL * (n - cnt[u]) * w % MOD * w % MOD); dfs_up(u, v); } } pair<int, int> get_parent(int v, int a) { int ans = 0; for (int i = 0; i < LG; i++) if ((a >> i) & 1) { ans += path[v][i], ans %= MOD; v = par[v][i]; } return {v, ans}; } int lca(int v, int u) { if (d[u] > d[v]) swap(u, v); v = get_parent(v, d[v] - d[u]).first; if (v == u) return v; for (int i = LG - 1; i >= 0; i--) if (par[v][i] != par[u][i]) v = par[v][i], u = par[u][i]; return par[u][0]; } int main() { ios::sync_with_stdio(false); cin >> n; for (int i = 1; i < n; i++) { int u, v, w; cin >> u >> v >> w; u--, v--; adj[v].push_back({u, w}); adj[u].push_back({v, w}); } dfs_down(0, -1); dfs_up(0, -1); int q; cin >> q; while (q--) { int u, v; cin >> u >> v; u--, v--; int w = lca(u, v); int dis = (get_parent(v, d[v] - d[w]).second + get_parent(u, d[u] - d[w]).second) % MOD; int ans = 0; if (w == v) add(ans, 1LL * dp[u][1] + 1LL * up[u][1] + -2LL * (1LL * up[v][1] + 2LL * up[v][0] * dis % MOD + 1LL * (n - cnt[v]) * dis % MOD * dis % MOD) % MOD); else add(ans, -1LL * dp[u][1] + -1LL * up[u][1] + 2LL * (1LL * dp[v][1] + 2LL * dp[v][0] * dis % MOD + 1LL * cnt[v] * dis % MOD * dis % MOD) % MOD); cout << ans << "\n"; } return 0; }
#include <bits/stdc++.h> const int mo = (int)1e9 + 7; const int N = (int)1e5 + 5, logN = 17; int n, q; struct node; struct edge { node *ed; edge *next; int w; } E[N << 1], *newE = E; struct data { long long sum2, sum, cnt; data operator*(long long t) { t %= mo; return (data){(sum2 + 2 * t * sum % mo + t * t % mo * cnt % mo) % mo, (sum + t * cnt % mo) % mo, cnt}; } void operator+=(const data &t) { (sum2 += t.sum2) %= mo; (sum += t.sum) %= mo; (cnt += t.cnt) %= mo; } void operator-=(const data &t) { (sum2 -= t.sum2) %= mo; (sum -= t.sum) %= mo; (cnt -= t.cnt) %= mo; } }; struct node { edge *son; node *pa[logN]; int dep; long long depth; data s, a; void dfs() { for (int j = 1; j < logN; j++) pa[j] = pa[j - 1]->pa[j - 1]; s.cnt = 1; for (edge *e = son; e; e = e->next) if (e->ed != pa[0]) { e->ed->pa[0] = this; e->ed->dep = dep + 1; e->ed->depth = depth + e->w; e->ed->dfs(); s += e->ed->s * e->w; } } void dfs2(data now) { now += s; a = now; for (edge *e = son; e; e = e->next) if (e->ed != pa[0]) { now -= e->ed->s * e->w; e->ed->dfs2(now * e->w); now += e->ed->s * e->w; } } } V[N]; node *lca(node *u, node *v) { for (int j = logN - 1; j >= 0; j--) if (u->pa[j]->dep >= v->dep) u = u->pa[j]; for (int j = logN - 1; j >= 0; j--) if (v->pa[j]->dep >= u->dep) v = v->pa[j]; for (int j = logN - 1; j >= 0; j--) if (u->pa[j] != v->pa[j]) u = u->pa[j], v = v->pa[j]; if (u == v) return u; return u->pa[0]; } int main() { scanf("%d", &n); for (int i = 1; i < n; i++) { int x, y, w; scanf("%d%d%d", &x, &y, &w); *newE = (edge){V + y, V[x].son, w}, V[x].son = newE++; *newE = (edge){V + x, V[y].son, w}, V[y].son = newE++; } for (int j = 0; j < logN; j++) V[1].pa[j] = V + 1; V[1].dfs(); V[1].dfs2((data){0, 0, 0}); scanf("%d", &q); while (q--) { int x, y; scanf("%d%d", &x, &y); node *w = lca(V + x, V + y); long long d = V[x].depth + V[y].depth - w->depth * 2; data a = V[y].s * d; if (w == V + y) { data c = V[y].a; c -= V[y].s; a = V[x].a; a -= c * d; } data b = V[x].a; b -= a; a -= b; printf("%I64d\n", (a.sum2 + mo) % mo); } }
#include <bits/stdc++.h> using namespace std; int read() { char x = getchar(); int ans = 0, flag = 1; while (!isdigit(x)) if (x == '-') flag = -1, x = getchar(); else x = getchar(); while (isdigit(x)) ans = ans * 10 + x - '0', x = getchar(); return ans * flag; } long long head[100005], nxt[200005], pnt[200005], len[200005], E, DEP[100005], dep[100005]; long long bz[100005][20], siz[100005], dp1[100005], dp2[100005], dp[100005], dis[100005]; long long dist[100005], n, dp3[100005]; const long long mod = 1e9 + 7; long long mo(long long x) { if (x >= mod) x -= mod; if (x < 0) x += mod; return x; } void add_edge(long long u, long long v, long long w) { pnt[E] = v; nxt[E] = head[u]; len[E] = w; head[u] = E++; } void dfs(long long u, long long pre) { DEP[u] = DEP[pre] + 1; bz[u][0] = pre; for (long long i = 1; i <= 16; i++) bz[u][i] = bz[bz[u][i - 1]][i - 1]; siz[u] = 1; for (long long i = head[u]; i != -1; i = nxt[i]) { long long v = pnt[i]; if (v == pre) continue; dep[v] = mo(dep[u] + len[i]); dfs(v, u); siz[u] += siz[v]; dis[u] = mo(dis[u] + dis[v]); dis[u] = mo(dis[u] + siz[v] * len[i] % mod); dp1[u] = mo(dp1[u] + dp1[v]); dp1[u] = mo(dp1[u] + 2 * dis[v] * len[i] % mod); dp1[u] = mo(dp1[u] + len[i] * len[i] % mod * siz[v] % mod); dp2[u] = mo(dp2[u] + len[i] * siz[v] % mod); dp2[u] = mo(dp2[u] + dp2[v]); } } void dfs1(long long u, long long pre) { for (long long i = head[u]; i != -1; i = nxt[i]) { long long v = pnt[i]; if (v == pre) continue; dp3[v] = mo(dp3[u] - siz[v] * len[i] % mod); dp3[v] = mo(dp3[v] + (siz[1] - siz[v]) * len[i] % mod); dp[v] = mo(dp[u] + len[i] * len[i] % mod * siz[1] % mod); dp[v] = mo(dp[v] - 2 * len[i] % mod * ((dis[v] + siz[v] * len[i]) % mod) % mod); long long tmp = mo(dis[u] - dis[v]); tmp = mo(tmp - siz[v] * len[i] % mod); dp[v] = mo(dp[v] + 2 * len[i] % mod * mo(tmp + dist[u]) % mod); dist[v] = mo(dist[u] + tmp); dist[v] = mo(dist[v] + (siz[1] - siz[v]) * len[i] % mod); dfs1(v, u); } } long long lca(long long x, long long y) { if (DEP[x] < DEP[y]) swap(x, y); for (long long i = 16; i >= 0; i--) if (DEP[bz[x][i]] >= DEP[y]) x = bz[x][i]; if (x == y) return x; for (long long i = 16; i >= 0; i--) if (bz[x][i] != bz[y][i]) x = bz[x][i], y = bz[y][i]; return bz[x][0]; } signed main() { memset(head, -1, sizeof(head)); scanf("%lld", &n); for (long long i = 1; i < n; i++) { long long u, v, w; scanf("%lld%lld%lld", &u, &v, &w); add_edge(u, v, w); add_edge(v, u, w); } dfs(1, 0); dp[1] = dp1[1], dp3[1] = dp2[1]; dfs1(1, 0); long long q; scanf("%lld", &q); while (q--) { long long u, v; scanf("%d%d", &u, &v); long long LCA = lca(u, v), ans = 0; if (LCA == v) { long long tmp = mo(dp[LCA] - dp1[LCA]); tmp = mo(tmp + mo(dep[u] - dep[LCA]) * 2 % mod * mo(dp3[LCA] - dp2[LCA]) % mod); tmp = mo(tmp + (dep[u] - dep[LCA]) * (dep[u] - dep[LCA]) % mod * (siz[1] - siz[v]) % mod); ans = mo(dp[u] - tmp); ans = mo(ans * 2 - dp[u]); } else { long long diss = dep[u] + dep[v] - 2 * dep[LCA]; diss %= mod; if (diss < 0) diss += mod; ans = mo(dp1[v] + 2 * diss % mod * dp2[v] % mod); ans = mo(ans + diss * diss % mod * siz[v] % mod); ans = mo(mo(ans * 2) - dp[u]); } cout << ans << '\n'; } return 0; }
#include <bits/stdc++.h> using namespace std; int n; long long par[111111][25], d[3][111111][25], child[111111], up[111111][3], down[111111][3]; int depth[111111], in[111111], out[111111]; int logarit[111111]; int cnt = 0; vector<vector<pair<int, int> > > adj; long long mod = 1000000007; void dfs_1(int u, int p) { in[u] = cnt++; depth[u] = depth[p] + 1; for (int i = 0, _n = adj[u].size(); i < _n; i++) { int v = adj[u][i].first; int w = adj[u][i].second; if (v == p) continue; par[v][0] = u; d[0][v][0] = w; d[1][v][0] = 1ll * w * w % mod; dfs_1(v, u); child[u] += child[v]; down[u][0] = (down[u][0] + down[v][0] + 1ll * child[v] * w % mod) % mod; down[u][1] = (down[u][1] + down[v][1] + d[1][v][0] * child[v] % mod + 1ll * down[v][0] * 2 * w % mod) % mod; } out[u] = cnt++; } void init_logarit() { logarit[1] = 0; for (int i = 2, _b = n; i <= _b; i++) { if ((1 << (logarit[i - 1] + 1)) == i) logarit[i] = logarit[i - 1] + 1; else logarit[i] = logarit[i - 1]; } } void init_lca() { for (int i = 1, _b = n; i <= _b; i++) child[i] = 1; init_logarit(); memset(par, -1, sizeof par); dfs_1(1, 0); for (int j = 1, _b = logarit[n]; j <= _b; j++) for (int i = 1, _b = n; i <= _b; i++) if (par[i][j - 1] != -1) { par[i][j] = par[par[i][j - 1]][j - 1]; d[0][i][j] = (d[0][i][j - 1] + d[0][par[i][j - 1]][j - 1]) % mod; } } void dfs_2(int u, int p, int w) { if (u != 1) { up[u][0] = (up[p][0] + down[p][0] - down[u][0] + 1ll * (n - 2 * child[u] + 2 * mod) * w + mod) % mod; up[u][1] = (up[p][1] + down[p][1] - down[u][1] + 1ll * (n - 4 * child[u] + 4 * mod) * (1ll * w * w % mod) % mod + 2ll * w * (up[p][0] + down[p][0] - 2 * down[u][0] + 2 * mod) % mod + mod) % mod; } for (int i = 0, _n = adj[u].size(); i < _n; i++) { int v = adj[u][i].first; if (v == p) continue; dfs_2(v, u, adj[u][i].second); } } void init() { init_lca(); dfs_2(1, 0, 0); } long long find_lca(int u, int v) { if (depth[u] < depth[v]) swap(u, v); long long res = 0; for (int i = logarit[depth[u]]; i >= 0; i--) if (depth[u] - (1 << i) >= depth[v] && par[u][i] != -1) { res = (res + d[0][u][i]) % mod; u = par[u][i]; } if (u == v) return res; for (int i = logarit[depth[u]]; i >= 0; i--) if (par[v][i] != -1 && par[u][i] != -1 && par[v][i] != par[u][i]) { res = (res + d[0][u][i] + d[0][v][i]) % mod; u = par[u][i], v = par[v][i]; } res = (res + d[0][u][0] + d[0][v][0]) % mod; return res; } void Query(int u, int v) { long long tmp = find_lca(u, v); if (in[v] <= in[u] && out[u] <= out[v]) { long long res = (down[u][1] + up[u][1]) % mod; long long x = 2ll * (up[v][1] + 2ll * up[v][0] * tmp % mod + (tmp * tmp % mod) * (1ll * n - child[v]) % mod) % mod; res = (res - x + mod) % mod; printf("%d\n", (int)res); return; } long long res = (down[v][1] + (tmp * tmp) % mod * child[v] % mod + 2ll * down[v][0] * tmp % mod) % mod; long long x = (down[u][1] + up[u][1]) % mod; res = (2 * res - x + mod) % mod; printf("%d\n", (int)res); } int main() { int u, v, w, Q; scanf("%d", &n); adj.assign(n + 1, vector<pair<int, int> >()); for (int i = 0, _n = n - 1; i < _n; i++) { scanf("%d%d%d", &u, &v, &w); adj[u].push_back(pair<int, int>(v, w)); adj[v].push_back(pair<int, int>(u, w)); } init(); scanf("%d", &Q); while (Q--) { scanf("%d%d", &u, &v); Query(u, v); } return 0; }
#include <bits/stdc++.h> using namespace std; template <class T> T inline sqr(T x) { return x * x; } const long double pi = 3.1415926535897932384626433832795; const long double eps = 1e-8; const int N = 100500; const int MOD = 1e9 + 7; const int logN = 18; int par[logN][N]; int timer = 0; int tin[N], tout[N]; vector<pair<int, int> > g[N]; long long sumLin[N], sumSqr[N]; long long sumLinDown[N], sumSqrDown[N]; int cntDown[N]; long long h[N]; int n; inline long long M(long long x) { x %= MOD; if (x < 0) x += MOD; return x; } long long f(long long w, int n, long long sumLin) { return M(M(w * w) * n + 2 * sumLin * w); } void dfs_init(int v) { tin[v] = ++timer; int p = -1; for (int i = 0; i < (int)(g[v].size()); ++i) { int to = g[v][i].first, w = g[v][i].second; if (tin[to]) { p = i; } else { h[to] = h[v] + w; dfs_init(to); } } cntDown[v] = 1; if (p != -1) { par[0][v] = g[v][p].first; g[v].erase(g[v].begin() + p); } else par[0][v] = v; for (pair<int, int> ed : g[v]) { int to = ed.first; long long w = ed.second; cntDown[v] += cntDown[to]; sumLinDown[v] += sumLinDown[to] + w * cntDown[to]; sumSqrDown[v] += sumSqrDown[to] + f(w, cntDown[to], sumLinDown[to]); } sumLinDown[v] %= MOD; sumSqrDown[v] %= MOD; tout[v] = ++timer; } void dfs2(int v) { for (pair<int, int> ed : g[v]) { int to = ed.first; long long w = ed.second; int q = cntDown[to]; sumLin[to] = M(sumLin[v] - q * w + (n - q) * w); long long sumToChild = M(sumLinDown[to] + w * q); sumSqr[to] = M(sumSqr[v] + f(-w, q, sumToChild)) + f(w, n - q, M(sumLin[v] - sumToChild)); dfs2(to); } } bool isIn(int u, int v) { return tin[u] <= tin[v] && tout[u] >= tout[v]; } int lca(int u, int v) { if (isIn(u, v)) return u; for (int j = (int)(logN)-1; j >= 0; --j) { int nu = par[j][u]; if (!isIn(nu, v)) u = nu; } return par[0][u]; } int main() { cin >> n; for (int i = 0; i < (int)(n - 1); ++i) { int a, b, c; cin >> a >> b >> c; --a, --b; g[a].push_back(make_pair(b, c)); g[b].push_back(make_pair(a, c)); } dfs_init(0); cerr << "init\n"; for (int i = 1; i <= (int)(logN - 1); ++i) for (int j = 0; j < (int)(N); ++j) par[i][j] = par[i - 1][par[i - 1][j]]; sumSqr[0] = sumSqrDown[0]; sumLin[0] = sumLinDown[0]; dfs2(0); cerr << "dfs2\n"; for (int i = 0; i < (int)(n); ++i) { } int q; cin >> q; for (int i = 0; i < (int)(q); ++i) { int u, v; cin >> u >> v; --u, --v; long long ans = 0; int l = lca(u, v); long long d = M(h[u] + h[v] - 2 * h[l]); if (isIn(v, u)) { ans = M(sumSqr[v] - sumSqrDown[v]); ans = M(ans + f(d, n - cntDown[v], sumLin[v] - sumLinDown[v])); ans = M(sumSqr[u] - 2 * ans); } else { ans = sumSqrDown[v] + f(d, cntDown[v], sumLinDown[v]); ans = M(2 * ans - sumSqr[u]); } cout << ans << "\n"; } return 0; }
#include <bits/stdc++.h> using std::vector; const int maxn = 1e5 + 1; template <class T> inline void read(T &x) { T f = 1; x = 0; char s = getchar(); while (s < '0' || s > '9') { if (s == '-') f = -1; s = getchar(); } while (s >= '0' && s <= '9') { x = (x * 10) + (s & 15); s = getchar(); } x *= f; } const long long p = 1e9 + 7; struct Edge { long long u, v, w; } e[maxn << 1]; long long head[maxn], ecnt; inline void addedge(long long u, long long v, long long w) { e[++ecnt].v = v; e[ecnt].w = w; e[ecnt].u = head[u]; head[u] = ecnt; } inline void add(long long u, long long v, long long w) { addedge(u, v, w); addedge(v, u, w); } long long f1[maxn], f[maxn], g[maxn], g1[maxn], siz[maxn], dfn[maxn], idx, top[maxn], fq[maxn], son[maxn], dis[maxn], n, q, a, b, c, ans, dep[maxn]; inline void dfs1(long long x, long long fa) { dfn[x] = (++idx); siz[x] = 1; f[x] = 0; fq[x] = fa; f1[x] = 0; dis[x] %= p; for (long long i = head[x], v; i && (v = e[i].v); i = e[i].u) { if (v == fa) continue; dis[v] = dis[x] + e[i].w; dep[v] = dep[x] + 1; dfs1(v, x); siz[x] += siz[v]; if (siz[v] > siz[son[x]]) son[x] = v; f1[x] += (f1[v] + e[i].w * siz[v] % p); f1[x] %= p; f[x] += (f[v] + f1[v] * 2 % p * e[i].w % p + siz[v] * e[i].w % p * e[i].w % p); f[x] %= p; } } inline void dfs2(long long x, long long topf) { top[x] = topf; if (!son[x]) return; dfs2(son[x], topf); for (long long i = head[x], v; i && (v = e[i].v); i = e[i].u) { if (v == son[x] || v == fq[x]) continue; dfs2(v, v); } } inline void dfs2(long long x) { for (long long i = head[x], v; i && (v = e[i].v); i = e[i].u) { if (v == fq[x]) continue; g1[v] = (g1[x] - e[i].w * siz[v] % p + e[i].w * (n - siz[v]) % p); g1[v] %= p; g[v] = ((f[v] + (g[x] - ((f[v] + 2 * e[i].w % p * f1[v] % p) % p + siz[v] * e[i].w % p * e[i].w % p) % p) % p) % p + ((g1[x] - f1[v] - siz[v] * e[i].w % p) % p * 2 * e[i].w % p + (n - siz[v]) * e[i].w % p * e[i].w % p) % p); g[v] %= p; dfs2(v); } } inline long long LCA(long long x, long long y) { while (top[x] != top[y]) (dep[top[x]] > dep[top[y]]) ? (x = fq[top[x]]) : (y = fq[top[y]]); return dep[x] < dep[y] ? x : y; } inline long long Dis(long long x, long long y) { return dis[x] + dis[y] - (dis[LCA(x, y)] << 1); } signed main() { read(n); for (long long i = 1; i <= n - 1; i++) { read(a); read(b); read(c); add(a, b, c); } dfs1(1, 0); dfs2(1, 1); g[1] = f[1]; g1[1] = f1[1]; dfs2(1); read(q); for (long long i = 1; i <= q; i++) { read(a); read(b); if ((dfn[a] >= dfn[b]) && (dfn[a] <= (dfn[b] + siz[b] - 1))) { long long add = (dis[a] - dis[b]), X = (g[b] - f[b]), Ans; Ans = (X + 2 * add % p * (g1[b] - f1[b]) % p + (n - siz[b]) * add % p * add) % p; Ans = (g[a] - (Ans * 2) % p); Ans %= p; printf("%lld\n", ((Ans + p) % p)); } else { long long add = (Dis(a, b)) % p, X = f[b], Ans; Ans = (X + 2 * add % p * f1[b] % p + siz[b] * add % p * add % p); (Ans += p) %= p; Ans = ((Ans << 1) - g[a]); Ans %= p; printf("%lld\n", ((Ans + p) % p)); } } }
#include <bits/stdc++.h> using namespace std; const int INF = 1e9; const long long int INFLL = 1e18; const double EPS = 1e-8; const long long int MOD = 1000000007; template <class T> T &chmin(T &a, const T &b) { return a = min(a, b); } template <class T> T &chmax(T &a, const T &b) { return a = max(a, b); } struct Mod { unsigned n; Mod() {} Mod(long long int x) { if (x < 0) n = x % MOD + MOD; else n = x % MOD; } }; Mod operator+(Mod a, Mod b) { return Mod(a.n + b.n); } Mod operator+=(Mod &a, Mod b) { return a = a + b; } Mod operator-(Mod a, Mod b) { return Mod(a.n + MOD - b.n); } Mod operator-=(Mod &a, Mod b) { return a = a - b; } Mod operator*(Mod a, Mod b) { return Mod((long long int)a.n * b.n); } Mod operator*=(Mod &a, Mod b) { return a = a * b; } Mod modpow(Mod x, long long int k) { Mod res = 1; while (k) { if (k & 1) res *= x; k /= 2; x *= x; } return res; } Mod inv(Mod a) { return modpow(a, MOD - 2); } Mod operator/(Mod a, Mod b) { return Mod(((long long int)a.n * inv(b).n) % MOD); } Mod operator/=(Mod &a, Mod b) { return a = a / b; } struct Bit { vector<long long int> bit; int size; void init(int n) { n++; size = 1; while (size < n) size *= 2; bit = vector<long long int>(size, 0); } void add(int k, long long int x) { k++; while (k <= size) { bit[k] += x; k += k & -k; } } long long int sum(int k) { k++; long long int res = 0; while (k > 0) { res += bit[k]; k -= k & -k; } return res; } long long int get(int k) { return sum(k) - sum(k - 1); } long long int update(int k, long long int x) { add(k, x - get(k)); } }; struct Tree { vector<vector<pair<long long int, long long int> > > G; int n, logn, r; vector<int> nst, sst; vector<int> dep; vector<long long int> w; vector<int> par; vector<bool> used; vector<vector<int> > ps; vector<int> in, out; int etcnt; bool dfs_f, lca_f, et_f; Bit etbit; void init(int num, int root = 0) { n = num; r = root; G = vector<vector<pair<long long int, long long int> > >(n); par = vector<int>(n, -1); w = vector<long long int>(n, 1); dfs_f = lca_f = et_f = false; } Tree(int num, int root = 0) { init(num, root); } Tree() {} void set_weight(const vector<long long int> &weight) { w = weight; } void set_graph_dfs( const vector<vector<pair<long long int, long long int> > > &g, int x) { used[x] = true; for (auto &w : g[x]) { if (!used[w.first]) { G[x].push_back(w); set_graph_dfs(g, w.first); } } } void set_graph(const vector<vector<pair<long long int, long long int> > > &g, int root = 0) { init(g.size(), root); used = vector<bool>(n, 0); G = vector<vector<pair<long long int, long long int> > >(n); set_graph_dfs(g, root); } void set_graph(int root = 0) { vector<vector<pair<long long int, long long int> > > tempg = G; set_graph(tempg, root); } void add_edge(int x, int p, long long int co = 1) { G[p].push_back(pair<long long int, long long int>(x, co)); } void add_biedge(int a, int b, long long int co = 1) { G[a].push_back(pair<long long int, long long int>(b, co)); G[b].push_back(pair<long long int, long long int>(a, co)); } void dfs(int x, int p, int d) { used[x] = true; dep[x] = d; nst[x] = 1; sst[x] = w[x]; par[x] = p; for (auto &w : G[x]) { if (p != x && !used[w.first]) { dfs(w.first, x, d + 1); nst[x] += nst[w.first]; sst[x] += sst[w.first]; } } } void dfs() { used = vector<bool>(n, false); nst = sst = vector<int>(n); dep = vector<int>(n); dfs(r, -1, 0); dfs_f = true; } void init_lca() { if (!dfs_f) dfs(); logn = (int)log2(n) + 1; ps = vector<vector<int> >(logn, vector<int>(n, -1)); ps[0] = par; for (int i = (1); i < (int)(logn); i++) { for (int j = (0); j < (int)(n); j++) { if (ps[i - 1][j] == -1) ps[i][j] = -1; else ps[i][j] = ps[i - 1][ps[i - 1][j]]; } } lca_f = true; } int lca(int a, int b) { if (!lca_f) init_lca(); if (dep[a] > dep[b]) swap(a, b); for (int i = logn; i >= 0; i--) if ((dep[b] - dep[a]) & (1 << i)) b = ps[i][b]; if (a == b) return a; for (int i = logn - 1; i >= 0; i--) { if (ps[i][a] != ps[i][b]) { a = ps[i][a]; b = ps[i][b]; } } return ps[0][a]; } void etdfs(int x) { in[x] = etcnt++; for (auto &w : G[x]) { etdfs(w.first); etbit.add(in[w.first], w.second); etbit.add(out[w.first], -w.second); } out[x] = etcnt++; } void etdfs() { if (!dfs_f) dfs(); if (!lca_f) init_lca(); etcnt = 0; in = vector<int>(n); out = vector<int>(n); etbit.init(2 * n); etdfs(r); et_f = true; } void etupdate(int x, long long int d) { if (!et_f) etdfs(); etbit.update(in[x], d); etbit.update(out[x], -d); } long long int dist(int a, int b) { if (!et_f) etdfs(); return etbit.sum(in[a]) + etbit.sum(in[b]) - etbit.sum(in[lca(a, b)]) * 2; } vector<Mod> ds, dss; void dsdfs(int x) { for (auto &w : G[x]) { dsdfs(w.first); Mod c = w.second; ds[x] += ds[w.first] + Mod(nst[w.first]) * c; dss[x] += dss[w.first] + Mod(2) * c * ds[w.first] + c * c * Mod(nst[w.first]); } } void dsdfs() { ds = dss = vector<Mod>(n, 0); dsdfs(r); } vector<Mod> ss, sss; void qdfs(int x, Mod sum, Mod sums) { ss[x] = sum; sss[x] = sums; for (auto &w : G[x]) { int t = w.first; Mod c = w.second; qdfs(t, sum + Mod(n - 2 * nst[t]) * c, sums + c * c * Mod(n) - Mod(4) * (ds[t] + c * Mod(nst[t])) * c + Mod(2) * sum * c); } } void qdfs() { dsdfs(); ss = sss = vector<Mod>(n); qdfs(r, ds[r], dss[r]); } Mod mdist(int u, int v) { return Mod(dist(u, v)); } Mod querya(int u, int v) { if (lca(u, v) == v) { return sss[u] - (sss[v] - dss[v] + mdist(u, v) * mdist(u, v) * Mod(n - nst[v]) + Mod(2) * mdist(u, v) * (ss[v] - ds[v])); } else { return dss[v] + mdist(u, v) * mdist(u, v) * Mod(nst[v]) + Mod(2) * mdist(u, v) * ds[v]; } } Mod query(int u, int v) { return Mod(2) * querya(u, v) - sss[u]; } }; Tree T; int n, q; int main() { cin >> n; T.init(n); for (int i = (0); i < (int)(n - 1); i++) { int a, b, c; cin >> a >> b >> c; a--; b--; T.add_biedge(a, b, c); } T.set_graph(0); T.dfs(); T.init_lca(); T.etdfs(); T.qdfs(); cin >> q; for (int i = (0); i < (int)(q); i++) { int u, v; cin >> u >> v; u--; v--; cout << T.query(u, v).n << endl; } return 0; }
#include <bits/stdc++.h> using namespace std; const int MAXN = 1e5 + 100; const int LOG = 20; const int MOD = 1e9 + 7; int s_time[MAXN], f_time[MAXN]; int from[MAXN], to[MAXN], we[MAXN]; int n, q; int v, u, w; long long num; long long sum_up[3][MAXN], sum_down[3][MAXN]; long long sum_total[MAXN]; int par[LOG + 5][MAXN]; int row[MAXN]; vector<int> adj[MAXN]; bool is_child(int u, int v) { return (s_time[v] <= s_time[u] && f_time[u] <= f_time[v]); } int get_par(int k, int v) { for (int i = 0; i < 20; i++) if (k & (1 << i)) v = par[i][v]; return v; } int lca(int u, int v) { if (row[u] > row[v]) swap(u, v); v = get_par(row[v] - row[u], v); if (u == v) return u; for (int i = LOG; i >= 0; i--) if (par[i][v] != par[i][u]) { u = par[i][u]; v = par[i][v]; } return par[0][v]; } void dfs_down(int p, int v) { s_time[v] = num++; sum_down[0][v]++; par[0][v] = p; for (int i = 1; i < LOG; i++) par[i][v] = par[i - 1][par[i - 1][v]]; for (int i = 0; i < ((int)adj[v].size()); i++) { int id = adj[v][i]; long long w = we[id]; int u = from[id] + to[id] - v; if (u == p) continue; row[u] = row[v] + 1; dfs_down(v, u); sum_down[0][v] += sum_down[0][u]; sum_down[1][v] += sum_down[1][u] + (w * sum_down[0][u]); sum_down[2][v] += (w * w % MOD * sum_down[0][u]) + sum_down[2][u] + (2 * w * sum_down[1][u]); sum_down[0][v] %= MOD; sum_down[1][v] %= MOD; sum_down[2][v] %= MOD; } f_time[v] = num; } void dfs_up(int p, int v) { for (int i = 0; i < ((int)adj[v].size()); i++) { int id = adj[v][i]; long long w = we[id]; int u = from[id] + to[id] - v; if (u == p) continue; sum_total[u] = (sum_total[v] + w) % MOD; sum_up[0][u] = n - sum_down[0][u]; sum_up[1][u] = sum_up[1][v] + sum_down[1][v] - sum_down[1][u] - (w * sum_down[0][u]) % MOD + (sum_up[0][u] * w) % MOD; sum_up[2][u] = (sum_up[0][u] * w % MOD * w) % MOD + sum_up[2][v] + sum_down[2][v] - sum_down[2][u] - 2 * w % MOD * sum_down[1][u] - w * w % MOD * sum_down[0][u] % MOD + (2 * w % MOD * ((sum_up[1][v] + sum_down[1][v] - sum_down[1][u] - sum_down[0][u] * w) % MOD)); sum_up[0][u] %= MOD; sum_up[1][u] %= MOD; sum_up[2][u] %= MOD; dfs_up(v, u); } } long long calc_1(int u, int v) { long long y = (sum_total[u] + sum_total[v] - 2 * sum_total[lca(u, v)]) % MOD; long long s = (sum_up[2][v] + 2 * y % MOD * sum_up[1][v] + y * y % MOD * sum_up[0][v]) % MOD; long long tot = (sum_down[2][u] + sum_up[2][u]) % MOD; return ((tot - 2 * s) % MOD + MOD) % MOD; } long long calc_2(int u, int v) { long long y = sum_total[u] + sum_total[v] - 2 * sum_total[lca(u, v)]; long long s = sum_down[2][v] + 2 * y % MOD * sum_down[1][v] % MOD + y * y % MOD * sum_down[0][v] % MOD; long long tot = sum_down[2][u] + sum_up[2][u]; return ((s - (tot - s)) % MOD + MOD) % MOD; } int main() { ios::sync_with_stdio(false), cin.tie(0), cout.tie(0); cin >> n; for (int i = 0; i < n - 1; i++) { cin >> u >> v >> w; u--, v--; adj[u].push_back(i); adj[v].push_back(i); from[i] = u; to[i] = v; we[i] = w; } dfs_down(0, 0); dfs_up(0, 0); cin >> q; while (q--) { cin >> u >> v; u--; v--; if (is_child(u, v)) cout << calc_1(u, v); else cout << calc_2(u, v); cout << "\n"; } return 0; }
#include <bits/stdc++.h> #pragma GCC optimize("O2") using namespace std; const long long MXN = 2e5 + 10; const long long LOG = 20; const long long Mod = 1e9 + 7; long long n, timer, q; long long Jad[LOG][MXN], dis[MXN], Stm[MXN], Ftm[MXN]; long long dp[2][MXN], sig[2][MXN], sub[MXN], Tdis[MXN]; vector<pair<long long, long long>> adj[MXN]; void prep(long long u, long long par) { timer++, Stm[u] = timer, Jad[0][u] = par; for (int i = 1; i < LOG; i++) { Jad[i][u] = Jad[i - 1][Jad[i - 1][u]]; } for (auto Pr : adj[u]) { long long v, w; tie(v, w) = Pr; if (v == par) continue; dis[v] = (dis[u] + w) % Mod; Tdis[v] = Tdis[u] + 1; prep(v, u); } Ftm[u] = timer; } long long K_Jad(long long u, long long k) { for (int i = 0; i < LOG; i++) { if ((k >> i) & 1LL) u = Jad[i][u]; } return u; } long long LCA(long long u, long long v) { if (Tdis[u] > Tdis[v]) swap(u, v); v = K_Jad(v, Tdis[v] - Tdis[u]); if (u == v) return u; for (int i = LOG - 1; ~i; i--) { if (Jad[i][u] != Jad[i][v]) { u = Jad[i][u], v = Jad[i][v]; } } return Jad[0][u]; } inline long long Fix(long long x) { x %= Mod; if (x < 0) x += Mod; return x; } inline long long DIS(long long u, long long v) { return Fix(dis[u] + dis[v] - (2ll * dis[LCA(u, v)] % Mod)); } inline long long Is_Jad(long long x, long long u) { return (Stm[x] <= Stm[u] && Ftm[u] <= Ftm[x]); } inline long long Func(long long a, long long b) { return (((a * a % Mod) * (b * b % Mod) % Mod) + (a * b % Mod) * 2 % Mod) % Mod; } void DFS_down(long long u, long long par) { sub[u] = 1; for (auto Pr : adj[u]) { long long v, w, nw; tie(v, w) = Pr; if (v == par) continue; DFS_down(v, u); sub[u] += sub[v]; sig[0][u] = (sig[0][u] + sig[0][v] + w * sub[v] % Mod) % Mod; nw = (dp[0][v] + sub[v] * (w * w % Mod) % Mod) % Mod; nw = (nw + 2 * w * sig[0][v] % Mod) % Mod; dp[0][u] = (dp[0][u] + nw) % Mod; } } void DFS_up(long long u, long long par, long long prw) { long long ex, now, nw; if (par) { sig[1][u] = (sig[1][u] + sig[1][par] + prw * (n - sub[par]) % Mod) % Mod; nw = Fix(sig[0][par] - (sig[0][u] + prw * sub[u] % Mod)); sig[1][u] = (sig[1][u] + nw) % Mod; sig[1][u] = (sig[1][u] + (sub[par] - sub[u]) * prw % Mod) % Mod; dp[1][u] = (dp[1][u] + dp[1][par] + (prw * prw % Mod) * (n - sub[par]) % Mod); dp[1][u] = (dp[1][u] + (2 * prw % Mod) * sig[1][par] % Mod) % Mod; ex = (dp[0][u] + sub[u] * (prw * prw % Mod) % Mod) % Mod; ex = (ex + 2 * prw * sig[0][u] % Mod) % Mod; now = (prw * prw % Mod) * (sub[par] - sub[u]) % Mod; now = (now + (nw * prw % Mod) * 2) % Mod; dp[1][u] = (dp[1][u] + Fix(dp[0][par] - ex) + now) % Mod; } for (auto Pr : adj[u]) { long long v, w, nw; tie(v, w) = Pr; if (v == par) continue; DFS_up(v, u, w); } } int main() { ios::sync_with_stdio(0); cin.tie(0); cout.tie(0); cin >> n; for (int i = 1; i < n; i++) { long long u, v, w; cin >> u >> v >> w; adj[u].push_back({v, w}); adj[v].push_back({u, w}); } prep(1, 0); DFS_down(1, 0); DFS_up(1, 0, 0); cin >> q; while (q--) { long long u, v, val1, val2, nw, ex, d, kol; cin >> u >> v; d = DIS(u, v); kol = (dp[0][u] + dp[1][u]) % Mod; if (Is_Jad(v, u)) { val2 = (((dp[1][v] + (d * d % Mod) * (n - sub[v]) % Mod) % Mod) + (sig[1][v] * d % Mod) * 2 % Mod) % Mod; val1 = Fix(kol - val2 + Mod); cout << Fix(val1 - val2) << '\n'; } else { val1 = (dp[0][v] + (d * d % Mod) * sub[v] + (d * sig[0][v]) * 2) % Mod; val2 = Fix(kol - val1); cout << Fix(val1 - val2) << '\n'; } } return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 200100; const int P = 1000000007; int H[N], to[N], len[N], nxt[N], e = 1; void addedge(int t, int v, int s) { e++, to[e] = v, len[e] = s, nxt[e] = H[t], H[t] = e; e++, to[e] = t, len[e] = s, nxt[e] = H[v], H[v] = e; } struct A { long long size, val, ans; }; A operator+(A x, A y) { return {x.size + y.size, (x.val + y.val) % P, (x.ans + y.ans) % P}; } A operator-(A x, A y) { return {x.size - y.size, (x.val - y.val) % P, (x.ans - y.ans) % P}; } A operator*(A x, long long mul) { return {x.size, (x.val + mul * x.size) % P, (x.ans + 2 * mul * x.val % P + mul * mul % P * x.size) % P}; } A dp[N], up[N], down[N]; void Build(int u, int f) { for (int i = H[u], v = to[i]; i; i = nxt[i], v = to[i]) if (v != f) { down[v] = (down[u] + dp[u] - up[v]) * len[i]; Build(v, u); } } void init_(int u, int f) { dp[u] = {1, 0, 0}; for (int i = H[u], v = to[i]; i; i = nxt[i], v = to[i]) if (v != f) { init_(v, u); up[v] = dp[v] * len[i]; dp[u] = dp[u] + up[v]; } } long long dis[N]; int dep[N], fa[N][21]; void dfs(int u, int f) { fa[u][0] = f; dep[u] = dep[f] + 1; for (int i = 1; i <= 20; i++) fa[u][i] = fa[fa[u][i - 1]][i - 1]; for (int i = H[u], v = to[i]; i; i = nxt[i], v = to[i]) if (v != f) { dis[v] = dis[u] + len[i]; dfs(v, u); } } int calc(int u, int v) { if (dep[u] < dep[v]) swap(u, v); for (int i = 20; i >= 0; i--) if (dep[fa[u][i]] >= dep[v]) u = fa[u][i]; if (u == v) return u; for (int i = 20; i >= 0; i--) if (fa[u][i] != fa[v][i]) u = fa[u][i], v = fa[v][i]; return fa[u][0]; } int main() { int n; cin >> n; for (int i = 2; i <= n; i++) { int t, v, s; scanf("%d%d%d", &t, &v, &s); addedge(t, v, s); } dfs(1, 0); init_(1, 0); Build(1, 0); int m; cin >> m; while (m--) { int u, v; scanf("%d%d", &u, &v); int s = calc(u, v); long long dist = (dis[u] + dis[v] - dis[s] * 2) % P; if (s == v) { A add = dp[u] + down[u]; A Dec = down[v] * dist; printf("%d\n", (int)((add.ans - 2 * Dec.ans) % P + P) % P); } else { A add = dp[v] * dist; A Dec = dp[u] + down[u]; printf("%d\n", (int)((2 * add.ans - Dec.ans) % P + P) % P); } } return 0; }
#include <bits/stdc++.h> using namespace std; int const N = 400400; int const mod = 1000000007; void add(int &a, int b) { if ((a += b) >= mod) a -= mod; } int prod(int a, int b) { return (long long)a * b % mod; } int sum[N], sq[N], down[N]; void apply(int v, int l, int r, int val) { add(sq[v], prod(2, prod(sum[v], val))); add(sq[v], prod(val, prod(val, r - l))); add(sum[v], prod(val, r - l)); add(down[v], val); } void push(int v, int l, int r) { int m = (l + r) / 2; apply(2 * v + 1, l, m, down[v]); apply(2 * v + 2, m, r, down[v]); down[v] = 0; } void add(int v, int l, int r, int from, int to, int val) { if (r <= from || to <= l) return; if (from <= l && r <= to) { apply(v, l, r, val); return; } push(v, l, r); int m = (l + r) / 2; add(2 * v + 1, l, m, from, to, val); add(2 * v + 2, m, r, from, to, val); sum[v] = sum[2 * v + 1] + sum[2 * v + 2]; add(sum[v], 0); sq[v] = sq[2 * v + 1] + sq[2 * v + 2]; add(sq[v], 0); } int get_sq(int v, int l, int r, int from, int to) { if (r <= from || to <= l) return 0; if (from <= l && r <= to) return sq[v]; push(v, l, r); int m = (l + r) / 2; int ans = get_sq(2 * v + 1, l, m, from, to) + get_sq(2 * v + 2, m, r, from, to); add(ans, 0); return ans; } int n; vector<pair<int, int>> g[N]; int tin[N], tout[N]; void dfs(int v, int par) { static int timer = 0; tin[v] = timer++; for (auto e : g[v]) { if (e.first != par) { dfs(e.first, v); add(0, 0, n, tin[e.first], tout[e.first], e.second); } } tout[v] = timer; } int ans[N]; vector<pair<int, int>> qs[N]; void calc(int v, int par) { for (auto q : qs[v]) { int cur = get_sq(0, 0, n, tin[q.first], tout[q.first]); int all = get_sq(0, 0, n, 0, n); ans[q.second] = prod(2, cur); add(ans[q.second], mod - all); } for (auto e : g[v]) { if (e.first != par) { add(0, 0, n, 0, n, e.second); add(0, 0, n, tin[e.first], tout[e.first], mod - prod(2, e.second)); calc(e.first, v); add(0, 0, n, 0, n, mod - e.second); add(0, 0, n, tin[e.first], tout[e.first], prod(2, e.second)); } } } int main() { scanf("%d", &n); for (int i = 0; i < n - 1; ++i) { int a, b, c; scanf("%d%d%d", &a, &b, &c); --a, --b; g[a].emplace_back(b, c); g[b].emplace_back(a, c); } dfs(0, -1); int q; scanf("%d", &q); for (int i = 0; i < q; ++i) { int u, v; scanf("%d%d", &u, &v); --u, --v; qs[u].emplace_back(v, i); } calc(0, -1); for (int i = 0; i < q; ++i) cout << ans[i] << '\n'; }
#include <bits/stdc++.h> using namespace std; int N, K, D, Q, st[200005], Dep[200005], Dis[200005], C[20][20], F[20][200005]; struct Lin { int v, c, next; } E[200005]; struct Nod { int A[20]; Nod() { memset(A, 0, sizeof(A)); } Nod operator*(int k) { Nod c; k = (k + 1000000007) % 1000000007; for (int i = 0; i <= K; i++) for (int j = i, x = 1; j + 1; j--) (c.A[i] += 1ll * x * A[j] % 1000000007 * C[i][j] % 1000000007) %= 1000000007, x = 1ll * x * k % 1000000007; return c; } Nod operator+(const Nod& b) { Nod c; for (int i = 0; i <= K; i++) c.A[i] = (A[i] + b.A[i]) % 1000000007; return c; } Nod operator-(const Nod& b) { Nod c; for (int i = 0; i <= K; i++) c.A[i] = (A[i] - b.A[i] + 1000000007) % 1000000007; return c; } } A[200005], T[200005]; int IN() { int x = 0, ch; for (; (ch = getchar()) < '0' || ch > '9';) ; for (; ch >= '0' && ch <= '9'; (ch = getchar())) (x *= 10) += ch - '0'; return x; } void Link(int c = IN(), int v = IN(), int u = IN()) { E[++D] = (Lin){v, c, st[u]}; st[u] = D; E[++D] = (Lin){u, c, st[v]}; st[v] = D; } void Pre(int u, int f) { T[u].A[0] = 1; F[0][u] = f; Dep[u] = Dep[f] + 1; for (int i = st[u], v; i; i = E[i].next) if ((v = E[i].v) ^ f) Pre(v, u), T[u] = T[u] + T[v] * E[i].c; A[u] = T[u]; } void DFS(int u, int f, Nod t) { T[u] = T[u] + t; for (int i = st[u], v; i; i = E[i].next) if ((v = E[i].v) ^ f) { Dis[v] = (Dis[u] + E[i].c) % 1000000007; DFS(v, u, (T[u] - T[v] * E[i].c) * E[i].c); } } int LCA(int u, int v) { if (Dep[u] > Dep[v]) swap(u, v); for (int i = 16, d = Dep[v] - Dep[u]; i + 1; i--) if ((1 << i) & d) v = F[i][v]; if (u == v) return u; for (int i = 16; i + 1; i--) if (F[i][u] != F[i][v]) u = F[i][u], v = F[i][v]; return F[0][u]; } int main() { N = IN(); K = 2; for (int i = 2; i <= N; i++) Link(); for (int i = 0; i <= K; i++) { C[i][0] = 1; for (int j = 1; j <= i; j++) C[i][j] = C[i - 1][j - 1] + C[i - 1][j]; } Pre(1, 0); DFS(1, 0, Nod()); for (int i = 1; i <= 16; i++) for (int j = 1; j <= N; j++) F[i][j] = F[i - 1][F[i - 1][j]]; for (Q = IN(); Q--;) { int u = IN(), v = IN(), x = 2, z = LCA(u, v); if (z == v) { Nod t = (T[v] - A[v]) * ((Dis[u] + Dis[v] - 2 * Dis[z]) % 1000000007); printf("%d\n", (T[u] - t - t).A[x]); } else { Nod t = A[v] * ((Dis[u] + Dis[v] - 2 * Dis[z]) % 1000000007); printf("%d\n", (t + t - T[u]).A[x]); } } }
#include <bits/stdc++.h> using namespace std; const int MOD = 1000 * 1000 * 1000 + 7; const int MAX_N = 100 * 1000 + 10; const int LOG = 20 + 5; vector<pair<int, int>> adj[MAX_N]; int dp1[MAX_N], dp2[MAX_N]; int dp3[MAX_N], dp4[MAX_N]; int par[MAX_N][LOG]; int cmp[MAX_N], n; int dis[MAX_N]; int h[MAX_N]; long long mul(long long a, long long b) { a %= MOD, b %= MOD; return a * b % MOD; } long long change(long long n) { return (n % MOD + MOD) % MOD; } void dfs1(int u = 0, int dad = 0) { par[u][0] = dad, cmp[u] = 1; for (int i = 1; i < LOG; i++) par[u][i] = par[par[u][i - 1]][i - 1]; for (auto x : adj[u]) if (x.first != dad) { int v = x.first, w = x.second; h[v] = h[u] + 1, dis[v] = change(dis[u] + w), dfs1(v, u); cmp[u] += cmp[v]; dp1[u] = change(dp1[u] + dp1[v] + mul(cmp[v], w)); dp2[u] = change(dp2[u] + dp2[v] + mul(cmp[v], mul(w, w)) + mul(2 * dp1[v], w)); } } void dfs2(int u = 0, int dad = 0, int w = 0) { dp3[u] = change(dp3[dad] + mul(n - 2 * cmp[u], w)); dp4[u] = change(dp4[dad] + mul(n, mul(w, w)) + mul(dp3[dad] - 2 * (dp1[u] + mul(cmp[u], w)), 2 * w)); for (auto x : adj[u]) if (x.first != dad) dfs2(x.first, u, x.second); } int get_par(int u, int k) { for (int i = 0; i < LOG; i++) if (k >> i & 1) u = par[u][i]; return u; } int lca(int u, int v) { if (h[u] > h[v]) swap(u, v); v = get_par(v, h[v] - h[u]); if (u == v) return u; for (int i = LOG - 1; ~i; i--) if (par[u][i] != par[v][i]) u = par[u][i], v = par[v][i]; return par[u][0]; } int F(int u, int v) { int x = lca(u, v); int d = change(dis[u] + dis[v] - 2 * dis[x]); if (x != v) return change(2 * (dp2[v] + mul(cmp[v], mul(d, d)) + mul(dp1[v], 2 * d)) - dp4[u]); return change(dp4[u] - 2 * (dp4[v] - dp2[v] + mul(n - cmp[v], mul(d, d)) + mul(dp3[v] - dp1[v], 2 * d))); } int main() { ios_base ::sync_with_stdio(false), cin.tie(NULL), cout.tie(NULL); cin >> n; for (int i = 1; i < n; i++) { int u, v, w; cin >> u >> v >> w; u--, v--; adj[u].push_back({v, w}); adj[v].push_back({u, w}); } dfs1(), dp3[0] = dp1[0], dp4[0] = dp2[0], dfs2(); int q; cin >> q; while (q--) { int u, v; cin >> u >> v; u--, v--; cout << F(u, v) << endl; } return 0; }
#include <bits/stdc++.h> using namespace std; const int maxn = 1e5, maxq = 5000, mod = 1e9 + 7; int n, dfn[maxn + 10], ed[maxn + 10], dcnt; int dep[maxn + 10], val[maxn + 10], q; vector<pair<int, int> > ask[maxn + 10]; int ans[maxn + 10]; struct edge { int to, w; }; vector<edge> g[maxn + 10]; void dfs(int p, int fa) { dfn[p] = ++dcnt; val[dcnt] = dep[p]; for (auto i : g[p]) { if (i.to != fa) { dep[i.to] = (dep[p] + i.w) % mod; dfs(i.to, p); } } ed[p] = dcnt; } namespace seg { int ls[maxn * 4 + 10], rs[maxn * 4 + 10]; int s1[maxn * 4 + 10], s2[maxn * 4 + 10], tag[maxn * 4 + 10]; void upd(int p) { s1[p] = (s1[p << 1] + s1[p << 1 | 1]) % mod; s2[p] = (s2[p << 1] + s2[p << 1 | 1]) % mod; } void build(int p, int l, int r) { ls[p] = l; rs[p] = r; if (l == r) { s1[p] = val[l]; s2[p] = 1ll * val[l] * val[l] % mod; } else { int mid = (l + r) >> 1; build(p << 1, l, mid); build(p << 1 | 1, mid + 1, r); upd(p); } } void apply(int p, int v) { int len = rs[p] - ls[p] + 1; (s2[p] += (1ll * v * v % mod * len + 2ll * v * s1[p]) % mod) %= mod; (s1[p] += 1ll * len * v % mod) %= mod; (tag[p] += v) %= mod; } void push(int p) { if (tag[p]) { apply(p << 1, tag[p]); apply(p << 1 | 1, tag[p]); tag[p] = 0; } } void modify(int p, int l, int r, int v) { if (ls[p] == l && rs[p] == r) apply(p, v); else { int mid = (ls[p] + rs[p]) >> 1; push(p); if (r <= mid) modify(p << 1, l, r, v); else if (l > mid) modify(p << 1 | 1, l, r, v); else { modify(p << 1, l, mid, v); modify(p << 1 | 1, mid + 1, r, v); } upd(p); } } int query(int p, int l, int r) { if (ls[p] == l && rs[p] == r) return s2[p]; else { int mid = (ls[p] + rs[p]) >> 1; push(p); if (r <= mid) return query(p << 1, l, r); else if (l > mid) return query(p << 1 | 1, l, r); else return (query(p << 1, l, mid) + query(p << 1 | 1, mid + 1, r)) % mod; } } } // namespace seg int adj(int x) { return (x % mod + mod) % mod; } void dfsans(int p, int fa) { for (auto i : ask[p]) { int w = i.first; int s1 = seg::query(1, dfn[w], ed[w]); int s2 = seg::query(1, 1, n); s2 = adj(s2 - s1); s2 = adj(s1 - s2); ans[i.second] = s2; } for (auto i : g[p]) { if (i.to != fa) { seg::modify(1, 1, n, i.w); seg::modify(1, dfn[i.to], ed[i.to], adj(-i.w * 2)); dfsans(i.to, p); seg::modify(1, 1, n, adj(-i.w)); seg::modify(1, dfn[i.to], ed[i.to], i.w * 2 % mod); } } } int main() { scanf("%d", &n); for (int i = 1; i < n; ++i) { int l, r, w; scanf("%d%d%d", &l, &r, &w); g[l].push_back((edge){r, w}); g[r].push_back((edge){l, w}); } dfs(1, 0); seg::build(1, 1, n); scanf("%d", &q); for (int i = 1; i <= q; ++i) { int x, y; scanf("%d%d", &x, &y); ask[x].push_back(make_pair(y, i)); } dfsans(1, 0); for (int i = 1; i <= q; ++i) printf("%d\n", ans[i]); }
#include <bits/stdc++.h> using namespace std; const int N = 1e5 + 10, mod = 1e9 + 7, lg = 16 + 2; int n, q, par[N][lg], sumup[N][lg], tvin[N][lg], sumin[N][lg], cntin[N][lg], sumst[N], tvst[N], cntst[N], updtv[N], updsum[N], updcnt[N], h[N]; vector<pair<int, int> > gr[N]; long long mrg(int ftv, int fsum, int fcnt, int add) { return 1ll * (1ll * ftv + 1ll * fsum * add % mod * 2 % mod + 1ll * add * add % mod * fcnt % mod) % mod; } void getSt(int v, int par = -1) { for (auto p : gr[v]) { int u = p.first, w = p.second; if (u != par) { getSt(u, v); updtv[u] = mrg(tvst[u], sumst[u], cntst[u], w), tvst[v] = (tvst[v] + updtv[u]) % mod; updsum[u] = (1ll * cntst[u] * w % mod + sumst[u]) % mod, sumst[v] = (sumst[v] + updsum[u]) % mod; updcnt[u] = cntst[u], cntst[v] = cntst[v] + updcnt[u]; } } cntst[v]++; } void getPr(int v, int parent = -1, int wb = -1) { if (parent != -1) { h[v] = h[parent] + 1; par[v][0] = parent, sumup[v][0] = wb; for (int i = 1; i < lg - 1; i++) par[v][i] = par[par[v][i - 1]][i - 1], sumup[v][i] = (sumup[v][i - 1] + sumup[par[v][i - 1]][i - 1]) % mod; cntin[v][0] = cntst[parent] - updcnt[v], sumin[v][0] = (sumst[parent] - updsum[v] + mod) % mod; tvin[v][0] = mrg((tvst[parent] - updtv[v] + mod) % mod, sumin[v][0], cntin[v][0], wb); sumin[v][0] = (sumin[v][0] + 1ll * cntin[v][0] * wb % mod) % mod; for (int i = 1; i < lg - 1; i++) { cntin[v][i] = (cntin[v][i - 1] + cntin[par[v][i - 1]][i - 1]) % mod; sumin[v][i] = ((sumin[v][i - 1] + 1ll * sumup[v][i - 1] * cntin[par[v][i - 1]][i - 1] % mod) % mod + sumin[par[v][i - 1]][i - 1] % mod) % mod; tvin[v][i] = (tvin[v][i - 1] + mrg(tvin[par[v][i - 1]][i - 1], sumin[par[v][i - 1]][i - 1], cntin[par[v][i - 1]][i - 1], sumup[v][i - 1])) % mod; } } for (auto p : gr[v]) { int u = p.first, w = p.second; if (u != parent) getPr(u, v, w); } } bool isAnc(int v, int u) { int diff = h[v] - h[u]; if (diff <= 0) return false; for (int i = 0; i < lg - 1; i++) if (((diff >> i) & 1)) v = par[v][i]; if (v == u) return true; return false; } int AnsAnc(int v, int u) { int pst = tvst[v], rtr = 0, sumrn = 0; int diff = h[v] - h[u]; for (int i = lg - 1; i >= 0; i--) { if (((diff >> i) & 1)) { rtr = (rtr + mrg(tvin[v][i], sumin[v][i], cntin[v][i], sumrn)) % mod; sumrn = (sumrn + sumup[v][i]) % mod; v = par[v][i]; } } return (rtr + pst) % mod; } int getSum(int v, int u) { if (h[u] > h[v]) swap(u, v); int diff = h[v] - h[u], rtr = 0; for (int i = 0; i < lg - 1; i++) { if (((diff >> i) & 1)) rtr = (rtr + sumup[v][i]) % mod, v = par[v][i]; } if (v == u) return rtr; for (int i = lg - 1; i >= 0; i--) { if (par[v][i] != par[u][i]) { rtr = ((rtr + sumup[v][i]) % mod + sumup[u][i]) % mod; v = par[v][i], u = par[u][i]; } } rtr = ((rtr + sumup[v][0]) % mod + sumup[u][0]) % mod; return rtr; } int AnsN(int v, int u) { int sum = getSum(v, u); return mrg(tvst[u], sumst[u], cntst[u], sum); } int32_t main() { ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0); cin >> n; for (int i = 0; i < n - 1; i++) { int x, y, w; cin >> x >> y >> w; x--, y--; gr[x].push_back({y, w}); gr[y].push_back({x, w}); } getSt(0); getPr(0); cin >> q; while (q--) { int x, y; cin >> x >> y; x--, y--; long long rtr; if (isAnc(x, y)) rtr = AnsAnc(x, y); else rtr = AnsN(x, y); int mn = AnsAnc(x, 0); rtr = ((rtr * 2 - mn) % mod + mod) % mod; cout << rtr << "\n"; } return 0; }
#include <bits/stdc++.h> #pragma comment(linker, "/STACK:128000000") using namespace std; void solve(); int main() { cin.tie(0); cout.sync_with_stdio(0); cout.precision(10); cout << fixed; cin.tie(0); int t = 1; while (t--) { solve(); } return 0; } int TIMER = 1; vector<pair<long long, long long> > g[101010]; int tin[101010]; int tout[101010]; long long depth[101010]; long long cntDown[101010]; long long sumDistDown[101010]; long long sumSqrDistDown[101010]; long long sumDist[101010]; long long sumSqrDist[101010]; long long sumDistUp[101010]; long long sumSqrDistUp[101010]; const int MOD = 1000000007; int n; int l = 17; vector<int> up[101010]; void dfs(int v, int p) { tin[v] = ++TIMER; cntDown[v] = 1; up[v][0] = p; for (int i = 1; i <= l; ++i) up[v][i] = up[up[v][i - 1]][i - 1]; for (pair<int, int> to : g[v]) { if (to.first == p) continue; depth[to.first] = depth[v] + to.second; depth[to.first] %= MOD; dfs(to.first, v); cntDown[v] += cntDown[to.first]; sumDistDown[v] += sumDistDown[to.first] + cntDown[to.first] * to.second; sumDistDown[v] %= MOD; sumSqrDistDown[v] += sumSqrDistDown[to.first] + to.second * 2 * sumDistDown[to.first] % MOD + cntDown[to.first] * to.second % MOD * to.second; sumSqrDistDown[v] %= MOD; } tout[v] = ++TIMER; } void dfs2(int v, int p) { for (pair<int, int> to : g[v]) { if (to.first == p) continue; sumDist[to.first] = sumDist[v] - to.second * cntDown[to.first] + to.second * (n - cntDown[to.first]); sumDist[to.first] %= MOD; sumDistUp[to.first] = (sumDist[to.first] - sumDistDown[to.first]) % MOD; sumSqrDist[to.first] = sumSqrDist[v] - 2 * to.second * (sumDistDown[to.first] + to.second * cntDown[to.first] % MOD) + cntDown[to.first] * to.second % MOD * to.second; sumSqrDist[to.first] += 2 * to.second * (sumDistUp[to.first] - to.second * (n - cntDown[to.first]) % MOD) + (n - cntDown[to.first]) * to.second % MOD * to.second; sumSqrDist[to.first] %= MOD; sumSqrDistUp[to.first] = (sumSqrDist[to.first] - sumSqrDistDown[to.first]) % MOD; dfs2(to.first, v); } tout[v] = ++TIMER; } bool upper(int v, int u) { return (tin[v] <= tin[u] && tout[v] >= tout[u]); } int lca(int a, int b) { if (upper(a, b)) return a; if (upper(b, a)) return b; for (int i = l; i >= 0; --i) if (!upper(up[a][i], b)) a = up[a][i]; return up[a][0]; } long long dist(long long u, long long v) { long long x = lca(u, v); return (depth[u] + depth[v] - 2 * depth[x]) % MOD; } void solve() { cin >> n; for (int i = 0; i < n - 1; ++i) { int a, b, c; cin >> a >> b >> c; --a, --b; g[a].push_back(make_pair(b, c)); g[b].push_back(make_pair(a, c)); } for (int i = 0; i < n; ++i) up[i].resize(l + 1); dfs(0, 0); sumDist[0] = sumDistDown[0]; sumSqrDist[0] = sumSqrDistDown[0]; dfs2(0, -1); int m; cin >> m; for (int i = 0; i < m; ++i) { int u, v; cin >> u >> v; --u, --v; long long ans = 0; long long d = dist(u, v); if (upper(v, u)) { ans = sumSqrDist[u] - (sumSqrDistUp[v] + 2 * d * sumDistUp[v] + d * d % MOD * (n - cntDown[v])); } else { ans = sumSqrDistDown[v] + 2 * d * sumDistDown[v] + cntDown[v] * d % MOD * d; } ans %= MOD; ans = 2 * ans - sumSqrDist[u]; ans %= MOD; ans += MOD; ans %= MOD; cout << ans << "\n"; } }
#include <bits/stdc++.h> using namespace std; const int N = 1e5 + 10; const int MOD = 1e9 + 7; struct segment { int l, r, to_add; pair<int, int> sum; int size() { return r - l; } int unity(int _l, int _r) { return max(0 * l, min(_r, r) - max(_l, l)); } segment(int _l = 0, int _r = 0) { l = _l; r = _r; sum = pair<int, int>(0, 0); to_add = 0; } } seg[N << 2]; int n, h[N], lp[N], rp[N], ans[N]; vector<pair<int, int> > que[N], g[N]; vector<int> st; int dfs(int, int = 0, int = 0, int = 0); void build(int, int, int = 1); void add(int, int, int = 1); pair<int, int> get(int, int, int = 0, int = 1); void update(int); pair<int, int> get(int); void answer(int, int = 0); pair<int, int> calc(pair<int, int>, int, int); pair<int, int> _pair_sum(pair<int, int>, pair<int, int>); int _sum(int, int); int _mul(int, int); int _neg(int); int32_t main() { ios::sync_with_stdio(false); cin.tie(0); cout.tie(0); cin >> n; for (int i = 1; i < n; i++) { int v, u, w; cin >> v >> u >> w; v--; u--; g[v].push_back({u, w}); g[u].push_back({v, w}); } dfs(0); build(0, n); int q; cin >> q; for (int i = 0; i < q; i++) { int v, u; cin >> v >> u; v--; u--; que[v].push_back({u, i}); } answer(0); for (int i = 0; i < q; i++) cout << ans[i] << endl; } int dfs(int v, int pv, int d, int cur_pos) { h[v] = d; lp[v] = cur_pos; rp[v] = cur_pos + 1; st.push_back(v); for (auto [u, w] : g[v]) if (u != pv) rp[v] = dfs(u, v, _sum(d, w), rp[v]); return rp[v]; } void answer(int v, int pv) { int sigma_t = _neg(get(0).second); for (auto [u, query] : que[v]) ans[query] = _sum(sigma_t, _mul(2, get(u).second)); for (auto [u, w] : g[v]) if (u != pv) { add(0, w); add(u, _mul(_neg(2), w)); answer(u, v); add(u, _mul(2, w)); add(0, _mul(_neg(1), w)); } } void build(int l, int r, int v) { seg[v] = segment(l, r); if (r - l == 1) { seg[v].sum = {h[st[l]], _mul(h[st[l]], h[st[l]])}; return; } int med = (l + r) / 2; build(l, med, v << 1); build(med, r, v << 1 | 1); update(v); } void add(int ver, int val, int v) { int l = lp[ver]; int r = rp[ver]; if (seg[v].unity(l, r) == 0) return; if (seg[v].unity(l, r) == seg[v].size()) { seg[v].to_add = _sum(seg[v].to_add, val); seg[v].sum = calc(seg[v].sum, seg[v].size(), val); return; } add(ver, val, v << 1); add(ver, val, v << 1 | 1); update(v); seg[v].sum = calc(seg[v].sum, seg[v].size(), seg[v].to_add); } pair<int, int> get(int ver) { return get(lp[ver], rp[ver]); } pair<int, int> get(int l, int r, int par_sum, int v) { if (seg[v].unity(l, r) == 0) return pair<int, int>(0, 0); if (seg[v].unity(l, r) == seg[v].size()) return calc(seg[v].sum, seg[v].size(), par_sum); pair<int, int> lc = get(l, r, _sum(par_sum, seg[v].to_add), v << 1); pair<int, int> rc = get(l, r, _sum(par_sum, seg[v].to_add), v << 1 | 1); return _pair_sum(lc, rc); } void update(int v) { seg[v].sum = _pair_sum(seg[v << 1].sum, seg[v << 1 | 1].sum); } pair<int, int> calc(pair<int, int> v, int cnt, int d) { auto [A, B] = v; int C = _mul(d, cnt); int sum_1 = _sum(A, C); int sum_2 = _sum(_sum(B, _mul(d, C)), _mul(_mul(2, d), A)); return pair<int, int>(sum_1, sum_2); } int _sum(int a, int b) { a += b; if (a >= MOD) a -= MOD; return a; } int _mul(int a, int b) { return 1LL * a * b % MOD; } int _neg(int x) { return MOD - x; x = -x; while (x < 0) x += MOD; return x; } pair<int, int> _pair_sum(pair<int, int> a, pair<int, int> b) { return pair<int, int>(_sum(a.first, b.first), _sum(a.second, b.second)); }
#include <bits/stdc++.h> using namespace std; int N; vector<pair<int, int> > G[100005]; int Level[100005], D[100005]; int Sum[100005], Total[100005], Sz[100005], Left[100005], Right[100005], cnt; int SumSq[100005], TotalSq[100005]; int Father[20][100005], Log[100005]; const int MOD = 1000000007; inline void Add(int& x, int y) { x += y; if (x >= MOD) x -= MOD; } inline void Sub(int& x, int y) { x -= y; if (x < 0) x += MOD; } void Read() { scanf("%d", &N); for (int i = 1; i < N; i++) { int x, y, c; scanf("%d%d%d", &x, &y, &c); G[x].push_back(make_pair(y, c)); G[y].push_back(make_pair(x, c)); } } void DFS(int node, int father, int cost) { Father[0][node] = father; Level[node] = Level[father] + 1; D[node] = D[father] + cost; if (D[node] >= MOD) D[node] -= MOD; Left[node] = ++cnt; Sz[node] = 1; for (int i = 0; i < G[node].size(); i++) { int neighb = G[node][i].first, c = G[node][i].second; if (neighb == father) continue; DFS(neighb, node, c); Sz[node] += Sz[neighb]; int val = Sum[neighb]; Add(val, (1LL * c * Sz[neighb]) % MOD); Add(Sum[node], val); val = SumSq[neighb]; int aux = (1LL * c * c) % MOD; Add(val, (1LL * aux * Sz[neighb]) % MOD); Add(val, (2LL * c * Sum[neighb]) % MOD); Add(SumSq[node], val); } Right[node] = cnt; } void DFS2(int node, int father, int cost) { if (node != 1) { Total[node] = Total[father]; Add(Total[node], (1LL * (N - Sz[node]) * cost) % MOD); Sub(Total[node], (1LL * Sz[node] * cost) % MOD); TotalSq[node] = TotalSq[father]; int val = (1LL * cost * cost) % MOD; val = (1LL * val * N) % MOD; int aux = Total[node]; Sub(aux, Sum[node]); Sub(aux, (1LL * (N - Sz[node]) * cost) % MOD); Add(val, (2LL * (aux)*cost) % MOD); int aux2 = Sum[node]; Add(aux2, (1LL * cost * Sz[node]) % MOD); Sub(val, (2LL * cost * aux2) % MOD); Add(TotalSq[node], val); } for (int i = 0; i < G[node].size(); i++) { int neighb = G[node][i].first, c = G[node][i].second; if (neighb == father) continue; DFS2(neighb, node, c); } } void precalcFather() { for (int i = 1; (1 << i) <= N; i++) { for (int j = 1; j <= N; j++) Father[i][j] = Father[i - 1][Father[i - 1][j]]; } } void precalcLog() { for (int i = 2; i <= N; i++) Log[i] = Log[i / 2] + 1; } int F(int node, int dist) { while (dist > 0) { int k = Log[dist]; node = Father[k][node]; dist -= (1 << k); } return node; } int LCA(int x, int y) { if (Level[x] > Level[y]) swap(x, y); y = F(y, Level[y] - Level[x]); if (x == y) return x; for (int k = Log[N]; k >= 0; k--) { if (Father[k][x] != Father[k][y]) { x = Father[k][x]; y = Father[k][y]; } } return Father[0][x]; } int Dist(int x, int y) { int lca = LCA(x, y); return (D[x] - D[lca] + D[y] - D[lca]) % MOD; } int Query(int u, int v) { int d = Dist(u, v); if (Left[u] >= Left[v] && Left[u] <= Right[v]) { int aux = d; d = (1LL * d * d) % MOD; int sumOut = (1LL * (N - Sz[v]) * d) % MOD; int val = Total[v]; Sub(val, Sum[v]); Add(sumOut, (2LL * aux * val) % MOD); Add(sumOut, TotalSq[v]); Sub(sumOut, SumSq[v]); int sum = TotalSq[u]; Sub(sum, (2LL * sumOut) % MOD); return sum; } else { int aux = d; d = (1LL * d * d) % MOD; int sumIn = (1LL * Sz[v] * d) % MOD; Add(sumIn, (2LL * aux * Sum[v]) % MOD); Add(sumIn, SumSq[v]); int sum = TotalSq[u]; Sub(sum, (2LL * sumIn) % MOD); sum = MOD - sum; if (sum >= MOD) sum -= MOD; return sum; } } int main() { Read(); precalcLog(); DFS(1, 0, 0); precalcFather(); for (int i = 1; i <= N; i++) { Add(Total[1], D[i]); Add(TotalSq[1], (1LL * D[i] * D[i]) % MOD); } DFS2(1, 0, 0); int Q; scanf("%d", &Q); for (int i = 1; i <= Q; i++) { int u, v; scanf("%d%d", &u, &v); int aux = Query(u, v); if (aux < 0) aux += MOD; if (aux >= MOD) aux -= MOD; printf("%d\n", aux); } return 0; }
#include <bits/stdc++.h> using namespace std; const long long N = 100005; template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << '(' << a.first << ", " << a.second << ')'; } template <class T> ostream &operator<<(ostream &os, const vector<T> &a) { os << '['; for (unsigned long long i = 0; i < a.size(); i++) os << a[i] << (i < a.size() - 1 ? ", " : ""); os << ']'; return os; } long long n; vector<vector<pair<long long, long long> > > a(N); const long long mod = 1e9 + 7; void norm(long long &x) { x %= mod; x += (x < 0 ? mod : 0); } struct LCAOn { pair<long long, long long> tour[2 * N], rmq[2 * N][22]; long long depth[N], par[N], dis[N], sta[N], en[N], lg2[2 * N], Time = 0; bool firstTime = true; void dfs(long long u, long long p) { tour[++Time] = {depth[u], u}; sta[u] = Time; par[u] = p; for (auto v : a[u]) if (v.first != p) depth[v.first] = depth[u] + 1, dis[v.first] = dis[u] + v.second, dfs(v.first, u); tour[++Time] = {depth[u], u}; en[u] = Time; } void build_rmq() { for (long long i = 1; i <= Time; ++i) rmq[i][0] = tour[i]; for (long long j = 1; (1 << j) <= Time; ++j) for (long long i = 1; i + (1 << j) - 1 <= Time; ++i) rmq[i][j] = min(rmq[i][j - 1], rmq[i + (1 << (j - 1))][j - 1]); } long long lca(long long u, long long v) { if (sta[v] < sta[u]) swap(u, v); if (en[u] >= en[v]) return u; long long dist = lg2[sta[v] - en[u] + 1]; auto ans = min(rmq[en[u]][dist], rmq[sta[v] - (1 << dist) + 1][dist]); return par[ans.second]; } long long distance(long long u, long long v) { long long p = lca(u, v); long long ret = dis[u] + dis[v] - 2 * dis[p]; norm(ret); return ret; } void init() { if (firstTime) for (long long i = 1; i < 2 * N; i++) lg2[i] = log2(i); firstTime = false; Time = 0; dfs(1, 1); build_rmq(); } } LCA; struct data { long long cnt, dis1, dis2; data(long long _cnt = 0, long long _dis1 = 0, long long _dis2 = 0) : cnt(_cnt), dis1(_dis1), dis2(_dis2){}; }; void norm(data &x) { norm(x.dis1); norm(x.dis2); } data up[N], down[N]; bool inSubtree(long long p, long long u) { if (LCA.lca(u, p) == p) return true; return false; } long long calAllTree(long long u) { return (up[u].dis2 + down[u].dis2) % mod; } long long calInSub(long long root, long long u) { if (root == 1) return calAllTree(u); long long w = LCA.distance(root, u); long long ret = up[root].dis2 + 2 * w * up[root].dis1 + up[root].cnt * w % mod * w % mod; norm(ret); ret = calAllTree(u) - ret; norm(ret); return ret; } long long calOutSub(long long root, long long u) { long long w = LCA.distance(root, u); long long ret = down[root].dis2 + 2 * w * down[root].dis1 + down[root].cnt * w % mod * w; norm(ret); return ret; } void dfsUp(long long u, long long p) { auto cur = down[u]; cur.cnt += up[u].cnt; cur.dis1 += up[u].dis1; cur.dis2 += up[u].dis2; norm(cur); for (auto it : a[u]) { long long v = it.first; long long w = it.second; if (v == p) continue; auto tmp = cur; tmp.cnt -= down[v].cnt; tmp.dis1 -= down[v].dis1 + w * down[v].cnt; tmp.dis2 -= down[v].dis2 + 2 * w * down[v].dis1 + down[v].cnt * w % mod * w; norm(tmp); up[v].cnt += tmp.cnt; up[v].dis1 += tmp.dis1 + w * tmp.cnt; up[v].dis2 += tmp.dis2 + 2 * w * tmp.dis1 + tmp.cnt * w % mod * w; norm(up[v]); dfsUp(v, u); } } void dfsDown(long long u, long long p) { for (auto it : a[u]) { long long v = it.first; long long w = it.second; if (v != p) { dfsDown(v, u); down[u].cnt += down[v].cnt; down[u].dis1 += down[v].dis1 + w * down[v].cnt; down[u].dis2 += down[v].dis2 + 2 * w * down[v].dis1 + down[v].cnt * w % mod * w; norm(down[u]); } } down[u].cnt++; } void prepDis() { dfsDown(1, 1); dfsUp(1, 1); } void preCheck() { for (long long u = (long long)1; u <= (long long)n; u++) { long long tup = 0; long long tdown = 0; for (long long v = (long long)1; v <= (long long)n; v++) { if (inSubtree(u, v)) tdown += LCA.distance(u, v) * LCA.distance(u, v) % mod; else tup += LCA.distance(u, v) * LCA.distance(u, v) % mod; } norm(tup); norm(tdown); assert(tup == up[u].dis2); } } signed main() { ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0); cin >> n; for (long long i = (long long)1; i <= (long long)n - 1; i++) { long long u, v, w; cin >> u >> v >> w; a[u].push_back(make_pair(v, w)); a[v].push_back(make_pair(u, w)); } LCA.init(); prepDis(); long long q; cin >> q; for (long long _ = (long long)1; _ <= (long long)q; _++) { long long u, v; cin >> u >> v; long long ret = 0; if (inSubtree(v, u)) ret = 2 * calInSub(v, u) - calAllTree(u); else ret = 2 * calOutSub(v, u) - calAllTree(u); norm(ret); cout << ret << '\n'; } }
#include <bits/stdc++.h> using namespace std; const int MAXN = 100005, MAXM = 17, Mod = 1000000007; int sz[MAXN], fa[MAXN][MAXM], dep[MAXN], q[MAXN], n, m, x, y, c, lca; long long s[MAXN], sons[MAXN], sonsq[MAXN], fs[MAXN], fsq[MAXN], dis, ans; struct Edge { int y, c; Edge *next; } pool[MAXN << 1], *mem = pool, *first[MAXN] = {0}; inline void addedge(int a, int b, int c) { mem->y = b; mem->c = c; mem->next = first[a]; first[a] = mem++; mem->y = a; mem->c = c; mem->next = first[b]; first[b] = mem++; } void dfs(int cur, int depth, int sum) { dep[cur] = depth; s[cur] = sum; for (int log = 1; (1 << log) <= depth; ++log) fa[cur][log] = fa[fa[cur][log - 1]][log - 1]; sz[cur] = 1; for (Edge *j = first[cur]; j; j = j->next) if (j->y != fa[cur][0]) { fa[j->y][0] = cur; dfs(j->y, depth + 1, (sum + j->c) % Mod); sz[cur] += sz[j->y]; sons[cur] = (sons[cur] + (sons[j->y] + (long long)sz[j->y] * j->c % Mod)) % Mod; sonsq[cur] += sonsq[j->y] + (j->c * sons[j->y] % Mod) * 2LL % Mod + ((long long)j->c * j->c % Mod) * sz[j->y] % Mod; sonsq[cur] %= Mod; } } void bfs() { int head = 0, tail = 0, cur; long long tmp, sum; q[tail++] = 1; fs[1] = 0; fsq[1] = 0; while (head != tail) { cur = q[head++]; for (Edge *j = first[cur]; j; j = j->next) if (j->y != fa[cur][0]) { tmp = sonsq[j->y] + (j->c * sons[j->y] % Mod) * 2LL % Mod + ((long long)j->c * j->c % Mod) * sz[j->y] % Mod; sum = (((long long)sz[j->y] * j->c % Mod) + sons[j->y]) % Mod; fs[j->y] = fs[cur] + sons[cur] - sum + (long long)j->c * (n - sz[j->y]) % Mod; fs[j->y] %= Mod; fsq[j->y] = fsq[cur] + sonsq[cur] - tmp + ((fs[cur] + sons[cur] - sum) * j->c % Mod) * 2LL % Mod + ((long long)j->c * j->c % Mod) * (n - sz[j->y]) % Mod; fsq[j->y] %= Mod; q[tail++] = j->y; } } } int getLCA(int a, int b) { int i, log; if (dep[a] < dep[b]) { a = a + b; b = a - b; a = a - b; } for (log = 0; (1 << (log + 1)) <= dep[a]; ++log) ; for (i = log; i >= 0; --i) if ((1 << i) <= dep[a] && dep[fa[a][i]] >= dep[b]) a = fa[a][i]; if (a == b) return a; for (i = log; i >= 0; --i) if (dep[a] >= (1 << i) && fa[a][i] != fa[b][i]) a = fa[a][i], b = fa[b][i]; return fa[a][0]; } int main() { scanf("%d", &n); for (int i = 1; i < n; ++i) { scanf("%d%d%d", &x, &y, &c); addedge(x, y, c); } dfs(1, 0, 0); bfs(); scanf("%d", &m); for (int i = 0; i < m; ++i) { scanf("%d%d", &x, &y); lca = getLCA(x, y); if (lca == y) { dis = s[x] - s[y]; ans = (sonsq[x] + fsq[x] - (2LL * (fsq[y] + (fs[y] * dis % Mod) * 2LL % Mod + (dis * dis % Mod) * (n - sz[y])) % Mod)) % Mod; } else { dis = (s[x] + s[y] - 2 * s[lca]) % Mod; ans = ((2LL * (sonsq[y] + (2LL * (sons[y] * dis % Mod) % Mod) + (dis * dis % Mod) * sz[y] % Mod) % Mod) - (sonsq[x] + fsq[x])) % Mod; } printf("%I64d\n", (ans + Mod) % Mod); } return 0; }
#include <bits/stdc++.h> using namespace std; int n, m, tot; int head[100010], to[300010], net[300010]; long long val[300010], mod = 1000000007; void add(int x, int y, int c) { net[++tot] = head[x], head[x] = tot, to[tot] = y, val[tot] = c; } int deep[100010], size[100010], son[100010], fa[100010], top[100010]; struct your { long long dis, sqr; } dp[100010], sum[100010], all[100010]; long long dis[100010]; void dfs(int x) { deep[x] = deep[fa[x]] + 1, size[x] = 1; for (int i = head[x]; i; i = net[i]) if (to[i] != fa[x]) { dis[to[i]] = (dis[x] + val[i]) % mod, fa[to[i]] = x, dfs(to[i]), size[x] += size[to[i]]; if (size[to[i]] > size[son[x]]) son[x] = to[i]; dp[x].dis = (dp[x].dis + dp[to[i]].dis % mod + (long long)size[to[i]] * val[i] % mod) % mod; long long tmp = (long long)size[to[i]] * val[i] % mod * val[i] % mod; long long nmp = (dp[to[i]].sqr + 2 * val[i] * dp[to[i]].dis % mod) % mod; dp[x].sqr = (dp[x].sqr + tmp + nmp) % mod; } } void dfs2(int x) { for (int i = head[x]; i; i = net[i]) { if (to[i] == fa[x]) continue; long long tmp = (sum[x].dis + (long long)(n - 2 * size[to[i]]) * val[i]) % mod; long long nmp = (dp[x].dis - dp[to[i]].dis + mod) % mod; sum[to[i]].dis = (tmp + nmp) % mod; tmp = (sum[x].sqr + 2 * sum[x].dis * val[i] % mod + (long long)(n - size[x]) * val[i] % mod * val[i] % mod) % mod; long long dx, dy, dc; dx = ((dp[x].sqr - dp[to[i]].sqr - 2 * val[i] * dp[to[i]].dis % mod - (long long)size[to[i]] * val[i] % mod * val[i] % mod) % mod + mod) % mod; dy = (long long)(size[x] - size[to[i]]) * val[i] % mod * val[i] % mod; dc = (2 * val[i] * (dp[x].dis - dp[to[i]].dis - (long long)val[i] * size[to[i]] % mod) % mod + mod) % mod; sum[to[i]].sqr = (tmp + dx + dy + dc) % mod; dfs2(to[i]); } } void dfs3(int x, int temp) { top[x] = temp; if (son[x]) dfs3(son[x], temp); for (int i = head[x]; i; i = net[i]) if (to[i] != fa[x] && to[i] != son[x]) dfs3(to[i], to[i]); } int lca(int x, int y) { while (top[x] != top[y]) { if (deep[top[x]] < deep[top[y]]) swap(x, y); x = fa[top[x]]; } return deep[x] < deep[y] ? x : y; } void check(int x, int y); int main() { scanf("%d", &n); for (int x, y, c, i = 1; i < n; i++) scanf("%d%d%d", &x, &y, &c), add(x, y, c), add(y, x, c); dfs(1), dfs2(1), dfs3(1, 1); for (int i = 1; i <= n; i++) { all[i].dis = (sum[i].dis + dp[i].dis) % mod; all[i].sqr = (sum[i].sqr + dp[i].sqr) % mod; } scanf("%d", &m); for (int x, y, i = 1; i <= m; i++) scanf("%d%d", &x, &y), check(x, y); return 0; } void check(int x, int y) { int l = lca(x, y); if (l != x && l != y) { long long c = ((dis[x] + dis[y] - 2 * dis[l]) % mod + mod) % mod; long long tmp = (dp[y].sqr + (long long)c * c % mod * size[y] % mod + 2 * c * dp[y].dis % mod) % mod; printf("%lld\n", (2 * tmp % mod - all[x].sqr + mod) % mod); } else if (l == x) { long long c = ((dis[x] + dis[y] - 2 * dis[l]) % mod + mod) % mod; long long tmp = (dp[y].sqr + (long long)c * c % mod * size[y] % mod + 2 * c * dp[y].dis % mod) % mod; printf("%lld\n", (2 * tmp % mod - all[x].sqr + mod) % mod); } else if (l == y) { long long c = ((dis[x] + dis[y] - 2 * dis[l]) % mod + mod) % mod; long long tmp = (sum[y].sqr + (long long)c * c % mod * (n - size[y]) % mod + 2 * c * sum[y].dis % mod) % mod; printf("%lld\n", ((all[x].sqr - 2 * tmp) % mod + mod) % mod); } }
#include <bits/stdc++.h> using namespace std; template <class T> inline T sqr(T x) { return x * x; } const double PI = acos(-1.0); using namespace std; int C[3][3]; class Tree { public: int head[200005], nxt[200005], e[200005], w[200005]; int dpson[200005][3], dpfa[200005][3]; int dp[200005][3]; int vis[200005]; int cnt; vector<pair<int, int> > stamp[200005]; void init(int n) { cnt = 0; for (int i = 0; i <= n; i++) head[i] = -1; this->n = n; } inline void addEdge(int u, int v, int w) { e[cnt] = v; this->w[cnt] = w; int tmp = head[u]; head[u] = cnt; nxt[cnt++] = tmp; } int dis[200005]; int p[200005][20]; int dis1[200005]; int L[200005]; int n; int tot; void dfs(int u, int fa, int d, int d1) { dis[u] = d; dis1[u] = d1; p[u][0] = fa; L[u] = tot++; for (int i = 1; (1 << i) <= n; i++) { if (~p[u][i - 1]) p[u][i] = p[p[u][i - 1]][i - 1]; else p[u][i] = -1; } for (int i = head[u]; ~i; i = nxt[i]) { int v = e[i]; if (v == fa) continue; dfs(v, u, d + 1, (d1 + w[i]) % 1000000007); stamp[u].push_back(make_pair(tot - 1, i)); } } int LCA(int u, int v) { if (dis[u] > dis[v]) swap(u, v); if (dis[u] < dis[v]) { int offset = dis[v] - dis[u]; for (int i = 0; (1 << i) <= n; i++) if (offset & (1 << i)) v = p[v][i]; } if (u != v) { for (int i = log2(n); i >= 0; i--) { if (p[u][i] != p[v][i]) u = p[u][i], v = p[v][i]; } u = p[u][0], v = p[v][0]; } return u; } void update(int a[], int b[], int w) { for (int j = 0; j <= 2; j++) { int now = 1; for (int l = 0; l <= j; l++) { Add(a[j], 1ll * C[j][l] * b[j - l] % 1000000007 * now % 1000000007); now = 1ll * now * w % 1000000007; } } } void dfs(int u, int fa) { for (int i = 0; i <= 2; i++) dpson[u][i] = 0; dpson[u][0] = 1; for (int i = head[u]; ~i; i = nxt[i]) { int v = e[i]; if (v == fa) continue; tofa[v] = w[i]; dfs(v, u); update(dpson[u], dpson[v], w[i]); } } int stack[200005]; int tmp[3]; int tofa[200005]; void dfs1(int u, int fa, int idx) { if (idx != -1) tofa[u] = w[idx]; else tofa[u] = 0; if (fa != -1) { update(dpfa[u], dpfa[fa], tofa[fa]); for (int i = 0; i <= 2; i++) { dp[idx][i] = dpson[u][i]; dp[idx ^ 1][i] = dpfa[u][i]; } } for (int i = 0; i <= 2; i++) tmp[i] = 0; int tot = 0; for (int i = head[u]; ~i; i = nxt[i]) { int v = e[i]; if (v == fa) continue; for (int j = 0; j <= 2; j++) Add(dpfa[v][j], tmp[j]); update(tmp, dpson[v], w[i]); stack[tot++] = i; } for (int i = 0; i <= 2; i++) tmp[i] = 0; for (int x = tot - 1; x >= 0; x--) { int i = stack[x]; int v = e[i]; if (v == fa) continue; for (int j = 0; j <= 2; j++) Add(dpfa[v][j], tmp[j]); update(tmp, dpson[v], w[i]); } for (int i = head[u]; ~i; i = nxt[i]) { int v = e[i]; if (v == fa) continue; dfs1(v, u, i); } } int sum[200005][3]; void Add(int &ans, int v) { ans += v; if (ans >= 1000000007) ans -= 1000000007; } void dpSum() { dfs(1, -1); for (int i = 1; i <= n; i++) { for (int j = 0; j <= 2; j++) dpfa[i][j] = 0; if (i > 1) dpfa[i][0] = 1; } dfs1(1, -1, -1); for (int i = 1; i <= n; i++) { for (int j = 0; j <= 2; j++) sum[i][j] = 0; for (int j = head[i]; ~j; j = nxt[j]) update(sum[i], dp[j], w[j]); } } } lca; int main(void) { C[0][0] = 1; for (int i = 1; i <= 2; i++) { C[i][0] = 1; for (int j = 1; j <= i; j++) C[i][j] = C[i - 1][j] + C[i - 1][j - 1]; } int n; scanf("%d", &n); lca.init(n); for (int i = 0; i < n - 1; i++) { int u, v, w; scanf("%d %d %d", &u, &v, &w); lca.addEdge(u, v, w); lca.addEdge(v, u, w); } lca.dfs(1, -1, 0, 0); lca.dpSum(); int q; scanf("%d", &q); while (q--) { int u, v; scanf("%d %d", &u, &v); int ans = -lca.sum[u][2]; int f = lca.LCA(u, v); int d = (0ll + lca.dis1[u] + lca.dis1[v] - 2 * lca.dis1[f]) % 1000000007; int ret = 0; if (v == 1) ret = lca.sum[u][2]; else if (f == v) { int fv = lca.p[v][0]; int pos = lower_bound(lca.stamp[fv].begin(), lca.stamp[fv].end(), make_pair(lca.L[v], -1)) - lca.stamp[fv].begin(); int idx = lca.stamp[fv][pos].second ^ 1; int now = 1; ret = lca.sum[u][2]; lca.Add(d, lca.w[idx]); for (int i = 0; i <= 2; i++) { lca.Add(ret, (1000000007 - 1ll * C[2][i] * lca.dp[idx][2 - i] % 1000000007 * now % 1000000007) % 1000000007); now = 1ll * now * d % 1000000007; } } else { int fv = lca.p[v][0]; int pos = lower_bound(lca.stamp[fv].begin(), lca.stamp[fv].end(), make_pair(lca.L[v], -1)) - lca.stamp[fv].begin(); int idx = lca.stamp[fv][pos].second; int now = 1; for (int i = 0; i <= 2; i++) { lca.Add(ret, 1ll * C[2][i] * lca.dp[idx][2 - i] % 1000000007 * now % 1000000007); now = 1ll * now * d % 1000000007; } } ans += 2 * ret % 1000000007; ans = (ans % 1000000007 + 1000000007) % 1000000007; printf("%d\n", ans); } return 0; }
#include <bits/stdc++.h> #pragma GCC optimize("Ofast") #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native") #pragma GCC optimize("-ffloat-store") using namespace std; clock_t time_p = clock(); void aryanc403() {} const long long int INF = 0xFFFFFFFFFFFFFFFL; long long int seed; mt19937 rng(seed = chrono::steady_clock::now().time_since_epoch().count()); inline long long int rnd(long long int l = 0, long long int r = INF) { return uniform_int_distribution<long long int>(l, r)(rng); } class CMP { public: bool operator()(pair<long long int, long long int> a, pair<long long int, long long int> b) { return !(a.first < b.first || (a.first == b.first && a.second <= b.second)); } }; void add(map<long long int, long long int>& m, long long int x, long long int cnt = 1) { auto jt = m.find(x); if (jt == m.end()) m.insert({x, cnt}); else jt->second += cnt; } void del(map<long long int, long long int>& m, long long int x, long long int cnt = 1) { auto jt = m.find(x); if (jt->second <= cnt) m.erase(jt); else jt->second -= cnt; } bool cmp(const pair<long long int, long long int>& a, const pair<long long int, long long int>& b) { return a.first < b.first || (a.first == b.first && a.second < b.second); } const long long int mod = 1000000007L; const long long int N = 100000L; template <class T> struct RMQ { vector<vector<T>> jmp; RMQ(const vector<T>& V) : jmp(1, V) { for (int pw = 1, k = 1; pw * 2 <= (long long int)(V).size(); pw *= 2, ++k) { jmp.emplace_back((long long int)(V).size() - pw * 2 + 1); for (int j = 0; j < ((long long int)(jmp[k]).size()); ++j) jmp[k][j] = min(jmp[k - 1][j], jmp[k - 1][j + pw]); } } T query(int a, int b) { assert(a < b); int dep = 31 - __builtin_clz(b - a); return min(jmp[dep][a], jmp[dep][b - (1 << dep)]); } }; struct LCA { int T = 0; vector<long long int> time, path, ret; vector<long long> dist; RMQ<long long int> rmq; LCA(vector<vector<pair<long long int, long long int>>>& C) : time((long long int)(C).size()), dist((long long int)(C).size()), rmq((dfs(C), ret)) {} void dfs(vector<vector<pair<long long int, long long int>>>& C, int v = 0, int p = -1, long long di = 0) { time[v] = T++, dist[v] = di; for (auto& e : C[v]) if (e.first != p) { path.push_back(v), ret.push_back(time[v]); dfs(C, e.first, v, di + e.second); } } int query(int a, int b) { if (a == b) return a; tie(a, b) = minmax(time[a], time[b]); return path[rmq.query(a, b)]; } long long distance(int a, int b) { int lca = query(a, b); return dist[a] + dist[b] - 2 * dist[lca]; } }; long long int T, n, i, j, k, in, cnt, l, r, u, v, x, y; long long int m; string s; vector<long long int> cst0, cst1, cst2; vector<long long int> scst0, scst1, scst2; vector<long long int> ucst1, ucst2; vector<vector<pair<long long int, long long int>>> e; vector<long long int> tin, tout, hei; void dfs(long long int u, long long int p, long long int h) { hei[u] = h; tin[u] = ++T; for (auto x : e[u]) { const long long int v = x.first, w = x.second; if (v == p) continue; dfs(v, u, (h + w) % mod); cst2[u] = (cst2[u] + cst2[v] + 2 * w * cst1[v] % mod + cst0[v] * (w * w % mod) % mod) % mod; cst1[u] = (cst1[u] + cst1[v] % mod + cst0[v] * w % mod) % mod; cst0[u] += cst0[v]; } cst0[u]++; tout[u] = ++T; } void dfs2(long long int u, long long int p, pair<long long int, long long int> up) { cst2[u] = (cst2[u] + up.second) % mod; cst1[u] = (cst1[u] + up.first) % mod; ucst2[u] = up.second % mod; ucst1[u] = up.first % mod; for (auto x : e[u]) { const long long int v = x.first, w = x.second; if (v == p) continue; long long int h2 = cst2[u], h1 = cst1[u], h0 = n - cst0[v]; h2 -= cst0[v] * (w * w % mod) % mod + (2 * w * cst1[v]) % mod + cst2[v]; h1 -= cst0[v] * w + cst1[v]; h1 %= mod; h2 %= mod; h2 += 2 * w * h1 % mod; h2 += (w * w % mod) * h0 % mod; h1 += w * h0 % mod; h1 %= mod; h2 %= mod; dfs2(v, u, {h1, h2}); } } long long int query(long long int u, long long int y) { y %= mod; long long int h0 = scst0[u]; long long int h1 = scst1[u]; long long int h2 = scst2[u]; h2 += 2 * y * h1 % mod; h2 += (y * y % mod) * h0 % mod; return h2; } long long int queryu(long long int u, long long int y) { y %= mod; long long int h0 = n - scst0[u]; long long int h1 = ucst1[u]; long long int h2 = ucst2[u]; h2 += 2 * y * h1 % mod; h2 += (y * y % mod) * h0 % mod; return h2; } int main(void) { ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL); { cin >> n; e.resize(n + 1); cst0.resize(n + 1); cst1.resize(n + 1); cst2.resize(n + 1); ucst1.resize(n + 1); ucst2.resize(n + 1); tin.resize(n + 1); tout.resize(n + 1); hei.resize(n + 1); for (i = 0; i < (n - 1); ++i) { long long int w; cin >> u >> v >> w; e[u].push_back({v, w}); e[v].push_back({u, w}); } dfs(1, -1, 0); scst0 = cst0; scst1 = cst1; scst2 = cst2; dfs2(1, -1, {0, 0}); e[0].push_back({1, 0}); e[1].push_back({0, 0}); LCA lca(e); long long int q; cin >> q; while (q--) { cin >> u >> v; long long int ans = 0; if (tin[v] <= tin[u] && tout[u] <= tout[v]) { ans += cst2[u]; ans -= queryu(v, lca.distance(u, v)); } else { ans += query(v, lca.distance(u, v)); } ans *= 2; ans -= cst2[u]; ans %= mod; ans += mod; ans %= mod; cout << ans << "\n"; } } aryanc403(); return 0; }
#include <bits/stdc++.h> using namespace std; template <typename T> inline T abs(T a) { return ((a < 0) ? -a : a); } template <typename T> inline T sqr(T a) { return a * a; } const int N = 100500; int n; vector<pair<int, int> > g[N]; const int MOD = 1e9 + 7; inline int add(int a, int b) { int res = a + b; if (res >= MOD) res -= MOD; return res; } inline int sub(int a, int b) { int res = a - b; if (res < 0) res += MOD; return res; } inline int mul(int a, int b) { long long res = a * 1LL * b; if (res >= MOD) res %= MOD; return int(res); } struct thing { int cnt, sum, sumSq; thing() {} thing(int cnt, int sum, int sumSq) : cnt(cnt), sum(sum), sumSq(sumSq) {} thing extend(int len) { thing res(cnt, add(sum, mul(len, cnt)), add(sumSq, add(mul(2, mul(sum, len)), mul(mul(len, len), cnt)))); return res; } }; thing operator+(const thing& a, const thing& b) { thing res(add(a.cnt, b.cnt), add(a.sum, b.sum), add(a.sumSq, b.sumSq)); return res; } thing operator-(const thing& a, const thing& b) { thing res(sub(a.cnt, b.cnt), sub(a.sum, b.sum), sub(a.sumSq, b.sumSq)); return res; } thing down[N]; void dfsDown(int v, int p = -1) { down[v] = thing(1, 0, 0); for (int i = int(0); i < int(int((g[v]).size())); ++i) { int to = g[v][i].first; if (to == p) continue; dfsDown(to, v); down[v] = down[v] + down[to].extend(g[v][i].second); } } const int LOG = 20; int pp[N][LOG]; thing sumAll[N]; thing ups[N]; int tin[N], tout[N], dep[N], curT; int depLen[N]; void dfs(int v, int p = -1, thing up = thing(0, 0, 0)) { ups[v] = up; sumAll[v] = up + down[v]; tin[v] = curT++; pp[v][0] = p == -1 ? v : p; for (int i = int(1); i < int(LOG); ++i) pp[v][i] = pp[pp[v][i - 1]][i - 1]; for (int i = int(0); i < int(int((g[v]).size())); ++i) { int to = g[v][i].first; if (to == p) continue; dep[to] = dep[v] + 1; depLen[to] = add(depLen[v], g[v][i].second); dfs(to, v, (sumAll[v] - down[to].extend(g[v][i].second)).extend(g[v][i].second)); } tout[v] = curT++; } bool isParent(int p, int v) { return tin[p] <= tin[v] && tout[v] <= tout[p]; } int lca(int a, int b) { if (dep[a] > dep[b]) swap(a, b); for (int i = LOG - 1; i >= 0; --i) { if (dep[pp[b][i]] > dep[a]) b = pp[b][i]; } if (dep[a] != dep[b]) b = pp[b][0]; assert(dep[a] == dep[b]); for (int i = LOG - 1; i >= 0; --i) { if (pp[a][i] != pp[b][i]) { a = pp[a][i]; b = pp[b][i]; } } if (a != b) { a = pp[a][0]; b = pp[b][0]; } assert(a == b); return a; } int d(int a, int b) { int p = lca(a, b); return sub(add(depLen[a], depLen[b]), mul(2, depLen[p])); } int f(int a, int b) { int res = sumAll[a].sumSq; if (isParent(b, a)) { res = sub(res, mul(2, ups[b].extend(d(a, b)).sumSq)); } else { res = sub(res, mul(2, down[b].extend(d(a, b)).sumSq)); res = sub(0, res); } return res; } bool solve() { if (scanf("%d", &n) != 1) return false; curT = 0; for (int i = int(0); i < int(n - 1); ++i) { int a, b, c; assert(scanf("%d%d%d", &a, &b, &c) == 3); --a; --b; g[a].push_back(pair<int, int>(b, c)); g[b].push_back(pair<int, int>(a, c)); } dep[0] = 0; depLen[0] = 0; dfsDown(0); dfs(0); int q; assert(scanf("%d", &q) == 1); for (int i = int(0); i < int(q); ++i) { int a, b; assert(scanf("%d%d", &a, &b) == 2); --a; --b; printf("%d\n", f(a, b)); } for (int i = int(0); i < int(n); ++i) { g[i].clear(); } return true; } int main() { cout << fixed << setprecision(10); cerr << fixed << setprecision(3); while (solve()) { } return 0; }
#include <bits/stdc++.h> using namespace std; template <class T> inline void R(T &xx) { xx = 0; char ch = getchar(); bool F = 0; while ((ch < '0' || ch > '9') && ch != '-') ch = getchar(); if (ch == '-') F = 1, ch = getchar(); while (ch >= '0' && ch <= '9') xx = xx + xx + (xx << 3) + ch - 48, ch = getchar(); if (F) xx = -xx; } template <class T> inline void add(int &x, T y) { for (x += y; x >= 1000000007; x -= 1000000007) ; } long long A[200011], B[200011], C[200011], sum[200011], sum2[200011], dis[200011]; int f[200011][23], dep[200011], sz[200011], n; vector<pair<int, int> > g[200011]; void dfs(int u, int fa) { f[u][0] = fa; sz[u] = 1; sum[u] = dis[u]; sum2[u] = (long long)dis[u] * dis[u] % 1000000007; dep[u] = dep[fa] + 1; for (int i = 0; i < (int)((int)g[u].size()); i++) if (g[u][i].first != fa) { int v = g[u][i].first; dis[v] = (dis[u] + g[u][i].second) % 1000000007; dfs(v, u); sz[u] += sz[v]; (sum[u] += sum[v]) %= 1000000007; (sum2[u] += sum2[v]) %= 1000000007; } } void dfs1(int u, int fa) { A[u] = 4ll * dis[fa] % 1000000007 * dis[fa] % 1000000007 * (sz[fa] - sz[u]) % 1000000007; B[u] = 4ll * dis[fa] % 1000000007 * (sz[fa] - sz[u]) % 1000000007; C[u] = 4ll * dis[fa] % 1000000007 * (sum[fa] - sum[u]) % 1000000007; (A[u] += A[fa]) %= 1000000007; (B[u] += B[fa]) %= 1000000007; (C[u] += C[fa]) %= 1000000007; for (int i = 0; i < (int)((int)g[u].size()); i++) if (g[u][i].first != fa) dfs1(g[u][i].first, u); } int LCA(int x, int y) { if (dep[x] < dep[y]) swap(x, y); for (int j = 21 - 1; ~j; j--) if (dep[f[x][j]] >= dep[y]) x = f[x][j]; if (x == y) return x; for (int j = 21 - 1; ~j; j--) if (f[x][j] != f[y][j]) x = f[x][j], y = f[y][j]; return f[x][0]; } long long cal(int x, int y) { long long ans = ((long long)dis[x] * dis[x] % 1000000007 * sz[y] % 1000000007 + sum2[y] + 2ll * dis[x] * sum[y] % 1000000007) % 1000000007; int lca = LCA(x, y); if (lca != y) { ans += 4ll * dis[lca] * dis[lca] % 1000000007 * sz[y] % 1000000007; ans -= 4ll * dis[lca] * dis[x] % 1000000007 * sz[y] % 1000000007; ans -= 4ll * dis[lca] * sum[y] % 1000000007; } else { ans += 4ll * dis[x] * dis[x] % 1000000007 * sz[x] % 1000000007; ans -= 4ll * dis[x] * dis[x] % 1000000007 * sz[x] % 1000000007; ans -= 4ll * dis[x] * sum[x] % 1000000007; ans += A[x] - A[y]; ans -= (B[x] - B[y]) * dis[x] % 1000000007; ans -= C[x] - C[y]; } return (ans % 1000000007 + 1000000007) % 1000000007; } int main() { int Q, x, y, z; R(n); for (int i = 1; i < n; i++) R(x), R(y), R(z), g[x].push_back(make_pair(y, z)), g[y].push_back(make_pair(x, z)); dfs(1, 0); dfs1(1, 0); for (int j = 1; j < 21; j++) for (int i = 1; i <= n; i++) f[i][j] = f[f[i][j - 1]][j - 1]; for (R(Q); Q--;) { R(x), R(y); printf("%I64d\n", (2ll * cal(x, y) - cal(x, 1) + 1000000007) % 1000000007); } return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 100005, LG = 18, Mod = 1e9 + 7; int n, q, ts, sz[N], st[N], en[N], H[N], P[N][LG]; long long D[N], dp[N], sum[N], dp2[N], sum2[N]; vector<pair<int, long long> > Adj[N]; inline int Fix(long long a) { a %= Mod; if (a < 0) a += Mod; return (a); } void DFS(int v, int p) { P[v][0] = p; sz[v] = 1; st[v] = ts++; for (int i = 1; i < LG; i++) P[v][i] = P[P[v][i - 1]][i - 1]; for (auto &u : Adj[v]) if (u.first != p) { H[u.first] = H[v] + 1; D[u.first] = (D[v] + u.second) % Mod; DFS(u.first, v); sz[v] += sz[u.first]; sum[v] = Fix(sum[v] + sum[u.first] + sz[u.first] * u.second); dp[v] += Fix(dp[u.first] + u.second * u.second % Mod * sz[u.first] % Mod); dp[v] = Fix(dp[v] + sum[u.first] * u.second * 2); } en[v] = ts; } void DFS2(int v, int p) { for (auto &u : Adj[v]) if (u.first != p) { sum2[u.first] = Fix(sum2[v] + sum[v] - sum[u.first] - u.second * (sz[u.first] * 2 - n)); dp2[u.first] = Fix(dp2[v] + dp[v] - dp[u.first] - u.second * u.second % Mod * sz[u.first]); dp2[u.first] += Fix(sum[u.first] * u.second * (-2) % Mod + u.second * u.second % Mod * (n - sz[u.first])); dp2[u.first] += Fix( u.second * Fix(sum2[v] + sum[v] - sum[u.first] - sz[u.first] * u.second) * 2); dp2[u.first] = Fix(dp2[u.first]); DFS2(u.first, v); } } inline int LCA(int v, int u) { if (H[v] < H[u]) return (LCA(u, v)); for (int i = LG - 1; ~i; i--) if ((H[v] - H[u]) & (1 << i)) v = P[v][i]; if (v == u) return (v); for (int i = LG - 1; ~i; i--) if (P[v][i] != P[u][i]) v = P[v][i], u = P[u][i]; return (P[v][0]); } inline int Dist(int v, int u) { return Fix(D[v] + D[u] - D[LCA(u, v)] * 2); } inline bool Sub(int v, int u) { return (st[u] <= st[v] && en[v] <= en[u]); } int main() { scanf("%d", &n); for (int i = 1, v, u, w; i < n; i++) scanf("%d%d%d", &v, &u, &w), Adj[v].push_back({u, w}), Adj[u].push_back({v, w}); DFS(1, 0); DFS2(1, 0); scanf("%d", &q); for (; q; q--) { int v, u; scanf("%d%d", &u, &v); long long tot = 0, d = Dist(u, v); if (Sub(u, v) && u != v) { tot = dp2[v] + d * d % Mod * (n - sz[v]); tot = Fix(tot + sum2[v] * d * 2); printf("%d\n", Fix(dp[u] + dp2[u] - tot * 2)); } else { tot = dp[v] + d * d % Mod * sz[v]; tot = Fix(tot + d * sum[v] * 2); printf("%d\n", Fix(tot * 2 - dp[u] - dp2[u])); } } return (0); }
#include <bits/stdc++.h> using namespace std; typedef struct { int f, t; long long int w; } edge; vector<edge> e[100514]; int n; int q[100514], qs, qe; int inq[100514]; edge* dad[100514]; long long int mod = 1000000007; long long int ds0[100514]; long long int ds1[100514]; long long int ds2[100514]; long long int us0[100514]; long long int us1[100514]; long long int us2[100514]; int up[20][100514]; int dpt[100514]; long long int dpl[100514]; int flca(int x, int y) { if (dpt[x] > dpt[y]) return flca(y, x); for (int j = 19; j >= 0; j--) { if (dpt[y] - (1 << j) >= dpt[x]) { y = up[j][y]; } } if (x == y) return x; for (int j = 19; j >= 0; j--) { if (up[j][x] != up[j][y]) { x = up[j][x]; y = up[j][y]; } } return up[0][x]; } void sol() { scanf("%d", &n); for (int i = 1; i < n; i++) { int a, b; long long int w; scanf("%d %d %I64d", &a, &b, &w); e[a].push_back((edge){a, b, w}); e[b].push_back((edge){b, a, w}); } qs = qe = 0; q[qe++] = 1; inq[1] = 1; dad[1] = 0; up[0][1] = 0; dpt[1] = 1; dpl[1] = 0; for (; qs != qe;) { int w = q[qs++]; for (int i = 0; i < (int)e[w].size(); i++) { int t = e[w][i].t; if (inq[t]) continue; q[qe++] = t; inq[t] = 1; dad[t] = &e[w][i]; up[0][t] = w; dpt[t] = dpt[w] + 1; dpl[t] = (dpl[w] + e[w][i].w) % mod; } } for (int i = 1; i <= n; i++) inq[i] = 0; for (int j = qe - 1; j >= 0; j--) { int w = q[j]; ds0[w] = 1; ds1[w] = 0; ds2[w] = 0; for (int i = 0; i < (int)e[w].size(); i++) { int t = e[w][i].t; long long int tw = e[w][i].w; ds0[w] = (ds0[w] + ds0[t]) % mod; ds1[w] = (ds1[w] + ds1[t] + ds0[t] * tw) % mod; ds2[w] = (ds2[w] + ds2[t] + ds1[t] * tw % mod * 2 + ds0[t] * tw % mod * tw) % mod; } } us0[1] = 0; us1[1] = 0; us2[1] = 0; for (int j = 1; j < qe; j++) { int w = q[j]; int d = dad[w]->f; long long int tw = dad[w]->w; us0[w] = n - ds0[w]; long long int up1 = ds1[d] + (mod - (ds1[w] + ds0[w] * tw) % mod) + us1[d]; up1 %= mod; us1[w] = (up1 + us0[w] * tw) % mod; us1[w] %= mod; long long int up2 = ds2[d] + (mod - (ds2[w] + ds1[w] * tw % mod * 2 + ds0[w] * tw % mod * tw) % mod) + us2[d]; up2 %= mod; us2[w] = (up2 + up1 * tw % mod * 2 + us0[w] * tw % mod * tw) % mod; } for (int j = 1; j < 20; j++) { for (int i = 1; i <= n; i++) { up[j][i] = up[j - 1][up[j - 1][i]]; } } int Q; scanf("%d", &Q); for (int s = 0; s < Q; s++) { int x, y; scanf("%d %d", &x, &y); int lca = flca(x, y); if (lca != y) { long long int dxy = (dpl[x] + dpl[y] + (mod - dpl[lca]) * 2) % mod; long long int pa = dxy * dxy % mod * ds0[y] % mod; pa += 2 * dxy % mod * ds1[y] % mod; pa += ds2[y] % mod; pa %= mod; long long int pb = (ds2[x] + us2[x] + (mod - pa)) % mod; printf("%I64d\n", (pa + mod - pb) % mod); } else { long long int dxy = (dpl[x] + dpl[y] + (mod - dpl[lca]) * 2) % mod; long long int pa = dxy * dxy % mod * us0[y] % mod; pa += 2 * dxy % mod * us1[y] % mod; pa += us2[y]; pa %= mod; long long int pb = (ds2[x] + us2[x] + (mod - pa)) % mod; printf("%I64d\n", (pb + mod - pa) % mod); } } } int main() { while (1) { sol(); break; } return 0; }
#include <bits/stdc++.h> using namespace std; typedef long long arr[100005]; arr cnt, d, sum, bot, top, T, L; int P[100005][21]; vector<pair<int, int> > a[100005]; int n; void DFS1(int u, int pre) { cnt[u] = 1; for (int i = 0; i < a[u].size(); i++) { int v = a[u][i].first; long long gt = a[u][i].second; if (v == pre) continue; d[v] = (d[u] + gt) % 1000000007; T[v] = T[u] + 1; DFS1(v, u); P[v][0] = u; cnt[u] += cnt[v]; sum[u] = (sum[u] + sum[v] + gt * cnt[v] % 1000000007) % 1000000007; bot[u] = (bot[u] + bot[v] + (gt * gt % 1000000007 * cnt[v] % 1000000007) + 2ll * sum[v] * gt % 1000000007) % 1000000007; } } void DFS2(int u, int pre) { for (int i = 0; i < a[u].size(); i++) { int v = a[u][i].first; long long gt = a[u][i].second; if (v == pre) continue; L[v] = (L[u] + (sum[u] - sum[v] - gt * cnt[v] % 1000000007) + gt * (n - cnt[v]) % 1000000007) % 1000000007; top[v] = (top[u] + 2ll * L[u] * gt % 1000000007 + gt * gt % 1000000007 * (n - cnt[u]) % 1000000007) % 1000000007; long long W = (bot[u] - bot[v] - (gt * gt % 1000000007 * cnt[v] % 1000000007) - 2ll * sum[v] * gt % 1000000007) % 1000000007; top[v] = (top[v] + W + gt * gt % 1000000007 * (cnt[u] - cnt[v]) % 1000000007 + 2ll * gt * (sum[u] - sum[v] - gt * cnt[v] % 1000000007) % 1000000007) % 1000000007; DFS2(v, u); } } void Build_LCA() { for (int j = 1; j < 20; j++) for (int i = 1; i <= n; i++) P[i][j] = P[P[i][j - 1]][j - 1]; } int LCA(int u, int v) { if (T[u] < T[v]) swap(u, v); int hi = T[u] - T[v]; for (int i = 0; i < 20; i++) if (((hi >> i) & 1)) u = P[u][i]; if (u == v) return u; for (int i = 19; i >= 0; i--) if (P[u][i] != P[v][i]) { u = P[u][i]; v = P[v][i]; } return P[u][0]; } int main() { cin >> n; int u, v, gt, q; for (int i = 1; i <= n - 1; i++) { cin >> u >> v >> gt; a[u].push_back(make_pair(v, gt)); a[v].push_back(make_pair(u, gt)); } DFS1(1, 0); DFS2(1, 0); Build_LCA(); cin >> q; while (q--) { cin >> u >> v; int Par = LCA(u, v); long long R1 = (bot[u] + top[u]) % 1000000007; long long kc = (d[u] + d[v] - 2ll * d[Par]) % 1000000007; if (Par == v) { long long R2 = (top[v] + 2ll * kc * L[v] % 1000000007 + kc * kc % 1000000007 * (n - cnt[v]) % 1000000007) % 1000000007; long long R3 = R1 - R2; cout << (2ll * R3 - R1 + 3ll * 1000000007) % 1000000007 << endl; } else { long long R2 = (bot[v] + 2ll * kc * sum[v] % 1000000007 + kc * kc % 1000000007 * (cnt[v]) % 1000000007) % 1000000007; cout << (2ll * R2 - R1 + 3ll * 1000000007) % 1000000007 << endl; } } }
#include <bits/stdc++.h> using namespace std; int n, x, y, z, num; const int MAXN = 100005; const int mod = 1e9 + 7; int b[MAXN]; int nxt[2 * MAXN], cost[2 * MAXN], a[2 * MAXN]; int fa[MAXN][25]; int be[MAXN], en[MAXN]; int sum, m, dep[MAXN]; long long len; int dist[MAXN], sumx[MAXN]; int ans, ans1, ans2; int sum1[MAXN], sum2[MAXN], siz1[MAXN], siz2[MAXN], sum21[MAXN], sum22[MAXN]; void add(int x, int y, int z) { ++num; a[num] = y; nxt[num] = b[x]; cost[num] = z; b[x] = num; } int lca(int x, int y) { if (dep[x] > dep[y]) swap(x, y); for (int i = 20; i >= 0; --i) { if ((1 << i) & (dep[y] - dep[x])) y = fa[y][i]; } if (x == y) return x; for (int i = 20; i >= 0; --i) { if (fa[x][i] != fa[y][i]) { x = fa[x][i]; y = fa[y][i]; } } return fa[x][0]; } void dfs(int x, int ga) { ++sum; be[x] = sum; fa[x][0] = ga; dep[x] = dep[ga] + 1; for (int i = 1; i <= 20; ++i) fa[x][i] = fa[fa[x][i - 1]][i - 1]; for (int i = b[x]; i != 0; i = nxt[i]) { int y = a[i]; if (y == ga) continue; dist[y] = dist[x] + cost[i]; dist[y] %= mod; dfs(y, x); } en[x] = sum; } void worksub(int x) { int dq; siz1[x] = 1; sum1[x] = 0; sum21[x] = 0; for (int i = b[x]; i != 0; i = nxt[i]) { int y = a[i]; if (y == fa[x][0]) continue; worksub(y); dq = sum21[y]; dq += 2LL * cost[i] * sum1[y] % mod; dq %= mod; dq += 1LL * cost[i] * cost[i] % mod * siz1[y] % mod; dq %= mod; sum21[x] += dq; sum21[x] %= mod; sum1[x] += sum1[y]; sum1[x] %= mod; sum1[x] += 1LL * cost[i] * siz1[y] % mod; sum1[x] %= mod; siz1[x] += siz1[y]; siz1[x] %= mod; } } void workout(int x) { int dq; for (int i = b[x]; i != 0; i = nxt[i]) { int y = a[i]; if (y == fa[x][0]) continue; siz2[y] = siz2[x] + siz1[x] - siz1[y]; sum2[y] = sum2[x] + (sum1[x] - sum1[y] + mod - 1LL * siz1[y] * cost[i] % mod + mod) % mod; sum2[y] %= mod; sum2[y] += 1LL * cost[i] * siz2[x] % mod; sum2[y] %= mod; sum2[y] += 1LL * cost[i] * (siz1[x] - siz1[y]) % mod; sum2[y] %= mod; sum22[y] = sum22[x]; sum22[y] += 1LL * cost[i] * cost[i] % mod * siz2[x] % mod; sum22[y] %= mod; sum22[y] += 2LL * cost[i] * sum2[x] % mod; sum22[y] %= mod; sum22[y] += sum21[x]; sum22[y] %= mod; sum22[y] = (sum22[y] - sum21[y] + mod) % mod; sum22[y] = (sum22[y] - 1LL * cost[i] * cost[i] % mod * siz1[y] % mod + mod) % mod; sum22[y] = (sum22[y] - 2LL * cost[i] * sum1[y] % mod + mod) % mod; sum22[y] = (sum22[y] + 1LL * cost[i] * cost[i] % mod * (siz1[x] - siz1[y]) % mod) % mod; sum22[y] = (sum22[y] + 2LL * cost[i] * (sum1[x] - sum1[y] + mod - 1LL * siz1[y] * cost[i] % mod + mod) % mod) % mod; workout(y); } } int main() { scanf("%d", &n); for (int i = 1; i < n; ++i) { scanf("%d%d%d", &x, &y, &z); add(x, y, z); add(y, x, z); } dfs(1, 0); worksub(1); workout(1); for (int i = 1; i <= n; ++i) sumx[i] = (sum21[i] + sum22[i]) % mod; scanf("%d", &m); while (m--) { scanf("%d%d", &x, &y); if (be[x] >= be[y] && be[x] <= en[y]) { ans = sum22[y]; len = dist[x] - dist[y] + mod; len %= mod; ans += 1LL * len * len % mod * siz2[y] % mod; ans %= mod; ans += 2LL * len * sum2[y] % mod; ans %= mod; ans1 = sumx[x] - ans + mod; ans1 %= mod; ans2 = ans; ans = ans1 - ans2 + mod; ans %= mod; } else { ans = sum21[y]; z = lca(x, y); len = dist[x] - dist[z]; len = (len + mod) % mod; len += dist[y] - dist[z]; len = (len + mod) % mod; ans += 1LL * len * len % mod * siz1[y] % mod; ans %= mod; ans += 2LL * len * sum1[y] % mod; ans %= mod; ans1 = ans; ans2 = sumx[x] - ans + mod; ans2 %= mod; ans = ans1 - ans2 + mod; ans %= mod; } printf("%d\n", ans); } return 0; }
#include <bits/stdc++.h> using namespace std; const int MOD = 1e9 + 7; int N, Q; set<pair<int, int> > g[100001]; int t0[100001], t1[100001], t2[100001]; int p[100001]; template <typename T> class range_minimum_query { public: std::vector<T> data; std::vector<std::vector<int> > block; std::vector<int> sblock; std::vector<int> lookup; int N; int lg; int min(int a, int b) { return data[b] < data[a] ? b : a; } range_minimum_query() {} range_minimum_query(std::vector<T> &t) { data = t; N = data.size(); lg = 32 - __builtin_clz(N); block.assign((N + lg - 1) / lg, std::vector<int>(lg, 0)); for (int i = 0; i < N; i++) { if (i % lg == 0) block[i / lg][0] = i; block[i / lg][0] = min(i, block[i / lg][0]); } for (int j = 1; j < lg; j++) for (int i = 0; i < block.size(); i++) block[i][j] = min( block[i][j - 1], block[i + (i + (1 << (j - 1)) < block.size() ? (1 << (j - 1)) : 0)] [j - 1]); sblock.assign(N, 0); std::vector<int> st; for (int i = 0; i < block.size(); i++) { st.clear(); for (int j = i * lg; j < N && j < i * lg + lg; j++) { while (!st.empty() && data[j] < data[st.back()]) st.pop_back(); sblock[j] = 1 << (i * lg + lg - j - 1); if (!st.empty()) sblock[j] |= sblock[st.back()]; st.push_back(j); } } lookup.assign(1 << lg, 0); for (int i = 1, ans = lg - 1; i < (1 << lg); i++) { if (1 << (lg - ans) <= i) ans--; lookup[i] = ans; } } int q(int l, int r) { if (r < l) swap(l, r); int l1 = l / lg + 1; int r1 = r / lg - 1; int ans = l; int t; if (l1 <= r1) { t = lg - lookup[r1 - l1 + 1] - 1; ans = min(ans, min(block[l1][t], block[r1 - (1 << t) + 1][t])); } t = l1 * lg - 1 < r ? l1 * lg - 1 : r; ans = min(ans, lookup[sblock[t] & (~(((1 << (l - (l1 * lg - lg))) - 1) << (l1 * lg - l)))] + l1 * lg - lg); t = r; l = l > r1 * lg + lg ? l : r1 * lg + lg; ans = min(ans, lookup[sblock[t] & (~(((1 << (l - (r1 * lg + lg))) - 1) << (r1 * lg + (lg << 1) - l)))] + r1 * lg + lg); return ans; } }; template <typename T> class segment_tree { public: vector<T> data; vector<T> tt; int N; int construct(int root, int cl, int cr) { if (cl == cr) return tt[root] = cl; int t1 = construct(root * 2, cl, (cl + cr) / 2); int t2 = construct(root * 2 + 1, (cl + cr) / 2 + 1, cr); return tt[root] = data[t2] < data[t1] ? t2 : t1; } int query(int root, int cl, int cr, int l, int r) { if (cl > r || cr < l) return N; if (l <= cl && cr <= r) return tt[root]; int t1 = query(root * 2, cl, (cl + cr) / 2, l, r); int t2 = query(root * 2 + 1, (cl + cr) / 2 + 1, cr, l, r); return data[t2] < data[t1] ? t2 : t1; } inline int q(int l, int r) { if (r < l) swap(l, r); return query(1, 0, N - 1, l, r); } segment_tree(){}; segment_tree(vector<T> a) { N = a.size(); data = a; data.push_back(INT_MAX); tt.resize(4 * N); construct(1, 0, N - 1); } }; class least_common_ancestor { public: int N; vector<vector<int> > g; vector<int> invf; vector<int> f; vector<int> ll; range_minimum_query<int> rmq; void inorder(int s = 0, int d = 0) { ll.push_back(d); invf[ll.size() - 1] = s; f[s] = ll.size() - 1; for (int i = 0; i < g[s].size(); i++) { inorder(g[s][i], d + 1); ll.push_back(d); invf[ll.size() - 1] = s; } } least_common_ancestor(){}; least_common_ancestor(vector<vector<int> > t) { g = t; N = g.size(); f.resize(N); invf.resize(2 * N - 1); inorder(); rmq = range_minimum_query<int>(ll); ll.clear(); g.clear(); } int q(int a, int b) { return invf[rmq.q(f[a], f[b])]; } }; void fix(int s) { for (pair<int, int> i : g[s]) { g[i.first].erase(g[i.first].lower_bound(make_pair(s, 0))); p[i.first] = s; fix(i.first); } } int add(int a, int b) { int ret = a + b; if (ret >= MOD) ret -= MOD; return ret; } int mul(int a, int b) { return (a * 1ll * b) % MOD; } int ddd[100001]; least_common_ancestor lca; int dist(int a, int b) { return add(add(ddd[a], ddd[b]), MOD - mul(2, ddd[1 + lca.q(a - 1, b - 1)])); } set<pair<int, int> > q[100001]; vector<int> ans; void dfs1(int s, int d = 0) { t0[s] = 1; ddd[s] = d; for (pair<int, int> i : g[s]) { dfs1(i.first, add(d, i.second)); t0[s] = add(t0[s], t0[i.first]); t1[s] = add(t1[s], mul(t0[i.first], i.second)); t1[s] = add(t1[s], t1[i.first]); t2[s] = add(t2[s], t2[i.first]); t2[s] = add(t2[s], mul(t1[i.first], mul(2, i.second))); t2[s] = add(t2[s], mul(t0[i.first], mul(i.second, i.second))); } } set<pair<int, pair<int, int> > > st[100001]; void dfs(int s) { for (pair<int, int> i : g[s]) { int pt0 = t0[i.first]; int pt1 = t1[i.first]; pt1 = add(pt1, mul(t0[i.first], i.second)); int pt2 = t2[i.first]; pt2 = add(pt2, mul(t1[i.first], mul(2, i.second))); pt2 = add(pt2, mul(t0[i.first], mul(i.second, i.second))); t0[s] = add(t0[s], MOD - pt0); t1[s] = add(t1[s], MOD - pt1); t2[s] = add(t2[s], MOD - pt2); int ppt0 = t0[s]; int ppt1 = t1[s]; ppt1 = add(ppt1, mul(t0[s], i.second)); int ppt2 = t2[s]; ppt2 = add(ppt2, mul(t1[s], mul(2, i.second))); ppt2 = add(ppt2, mul(t0[s], mul(i.second, i.second))); t0[i.first] = add(t0[i.first], ppt0); t1[i.first] = add(t1[i.first], ppt1); t2[i.first] = add(t2[i.first], ppt2); dfs(i.first); t0[i.first] = add(t0[i.first], MOD - ppt0); t1[i.first] = add(t1[i.first], MOD - ppt1); t2[i.first] = add(t2[i.first], MOD - ppt2); t0[s] = add(t0[s], pt0); t1[s] = add(t1[s], pt1); t2[s] = add(t2[s], pt2); } for (pair<int, int> i : g[s]) if (st[i.first].size() > st[s].size()) swap(st[i.first], st[s]); for (pair<int, int> i : g[s]) st[s].insert(st[i.first].begin(), st[i.first].end()); for (set<pair<int, pair<int, int> > >::iterator it = st[s].lower_bound(make_pair(s, make_pair(0, 0))); it != st[s].end() && it->first == s; it++) { if (s == 1) continue; int ooo = dist(p[s], it->second.first); ans[it->second.second] = add(ans[it->second.second], MOD - mul(2, add(t2[p[s]], add(mul(t1[p[s]], mul(2, ooo)), mul(t0[p[s]], mul(ooo, ooo)))))); } for (pair<int, int> i : q[s]) { if (i.first == s || lca.q(s - 1, i.first - 1) + 1 != i.first) { ans[i.second] = MOD - t2[s]; continue; } ans[i.second] = t2[s]; st[s].insert(make_pair(i.first, make_pair(s, i.second))); } } vector<vector<int> > g1; int main() { ios_base::sync_with_stdio(false); cin.tie(NULL); cin >> N; for (int i = 1, a, b, c; i < N; i++) { cin >> a >> b >> c; g[a].insert(make_pair(b, c)); g[b].insert(make_pair(a, c)); } g1.resize(N + 1); cin >> Q; ans.resize(Q); for (int i = 0, u, v; i < Q; i++) { cin >> u >> v; q[u].insert(make_pair(v, i)); } fix(1); for (int i = 1; i <= N; i++) for (pair<int, int> j : g[i]) g1[i - 1].push_back(j.first - 1); lca = least_common_ancestor(g1); dfs1(1); dfs(1); for (int s = 1; s <= N; s++) for (pair<int, int> i : q[s]) { if (s != i.first && lca.q(s - 1, i.first - 1) + 1 == i.first) continue; int ooo = dist(s, i.first); ans[i.second] = add(ans[i.second], mul(2, add(t2[i.first], add(mul(t1[i.first], mul(2, ooo)), mul(t0[i.first], mul(ooo, ooo)))))); } for (int i : ans) cout << i << '\n'; return 0; }
#include <bits/stdc++.h> using namespace std; int topstend[100000], topnode[100000], toppos, level[100000], dist[100000], parent[100000][20]; int n, topind[100000], q, a, b, c; int distsum[100000], distsqsum[100000], nchildren[100000]; int pdistsum[100000][20], pdistsqsum[100000][20], pnchildren[100000][20]; vector<pair<int, int> > conn[100000]; int m(long long val) { return (val % 1000000007 + 1000000007) % 1000000007; } int pathlen(int a, int b) { return m(dist[b] - dist[a]); } void topdfs(int pos, int lev, int curdist, int curparent) { int curtoppos = toppos; level[pos] = lev; dist[pos] = curdist; parent[pos][0] = curparent; topnode[curtoppos] = pos; topind[pos] = curtoppos; toppos++; for (int i = 0; i < conn[pos].size(); i++) if (conn[pos][i].first != parent[pos][0]) topdfs(conn[pos][i].first, lev + 1, m(curdist + conn[pos][i].second), pos); topstend[curtoppos] = toppos; } void calcdfs(int pos) { nchildren[pos] = 1; for (int i = 0; i < conn[pos].size(); i++) if (conn[pos][i].first != parent[pos][0]) { int child = conn[pos][i].first; calcdfs(child); nchildren[pos] += nchildren[child]; distsum[pos] = m(distsum[pos] + distsum[child] + 1LL * nchildren[child] * conn[pos][i].second); distsqsum[pos] = m(distsqsum[pos] + distsqsum[child] + 2LL * distsum[child] * conn[pos][i].second + 1LL * m(1LL * conn[pos][i].second * conn[pos][i].second) * nchildren[child]); pnchildren[child][0] = m(-nchildren[child]); pdistsum[child][0] = m(-distsum[child] - 1LL * nchildren[child] * conn[pos][i].second); pdistsqsum[child][0] = m(-distsqsum[child] - 2LL * distsum[child] * conn[pos][i].second - 1LL * m(1LL * conn[pos][i].second * conn[pos][i].second) * nchildren[child]); } for (int i = 0; i < conn[pos].size(); i++) if (conn[pos][i].first != parent[pos][0]) { int child = conn[pos][i].first; pnchildren[child][0] = m(pnchildren[child][0] + nchildren[pos]); pdistsum[child][0] = m(pdistsum[child][0] + distsum[pos]); pdistsqsum[child][0] = m(pdistsqsum[child][0] + distsqsum[pos]); pdistsqsum[child][0] = m(pdistsqsum[child][0] + 2LL * conn[pos][i].second * pdistsum[child][0] + 1LL * m(1LL * conn[pos][i].second * conn[pos][i].second) * pnchildren[child][0]); pdistsum[child][0] = m(pdistsum[child][0] + 1LL * pnchildren[child][0] * conn[pos][i].second); } } bool instree(int a, int b) { return topind[a] <= topind[b] && topind[b] < topstend[topind[a]]; } int getanc(int a, int b) { if (instree(a, b)) return a; for (int i = 19; i >= 0; i--) if (parent[a][i] != -1 && !instree(parent[a][i], b)) a = parent[a][i]; return parent[a][0]; } int getdistsum; int getsumto(int pos, int anc) { int ret = 0, rdistsum = 0, cdist = 0; for (int i = 19; i >= 0; i--) if (parent[pos][i] != -1 && (parent[pos][i] == anc || !instree(parent[pos][i], anc))) { rdistsum = m(rdistsum + pdistsum[pos][i] + 1LL * pnchildren[pos][i] * cdist); ret = m(ret + pdistsqsum[pos][i] + 2LL * pdistsum[pos][i] * cdist + 1LL * m(1LL * cdist * cdist) * pnchildren[pos][i]); cdist = m(cdist + pathlen(parent[pos][i], pos)); pos = parent[pos][i]; } getdistsum = rdistsum; return ret; } int main() { cin.sync_with_stdio(false); cin >> n; for (int i = 0; i < n - 1; i++) { cin >> a >> b >> c; a--, b--; conn[a].push_back(make_pair(b, c)); conn[b].push_back(make_pair(a, c)); } topdfs(0, 0, 0, -1); calcdfs(0); for (int j = 1; j < 20; j++) for (int i = 0; i < n; i++) { if (parent[i][j - 1] != -1) { int par = parent[i][j - 1]; parent[i][j] = parent[par][j - 1]; pnchildren[i][j] = pnchildren[i][j - 1] + pnchildren[par][j - 1]; pdistsum[i][j] = m(pdistsum[i][j - 1] + pdistsum[par][j - 1] + 1LL * pnchildren[par][j - 1] * pathlen(par, i)); pdistsqsum[i][j] = m(pdistsqsum[i][j - 1] + pdistsqsum[par][j - 1] + 2LL * pdistsum[par][j - 1] * pathlen(par, i) + 1LL * m(1LL * pathlen(par, i) * pathlen(par, i)) * pnchildren[par][j - 1]); } else parent[i][j] = -1; } cin >> q; for (int i = 0; i < q; i++) { cin >> a >> b, a--, b--; int res = 0; if (instree(b, a)) { res = distsqsum[a]; res = m(res + getsumto(a, b)); int bsqsum = getsumto(b, 0), cdist = pathlen(b, a); res = m(res - bsqsum - 2LL * getdistsum * cdist - 1LL * m(1LL * cdist * cdist) * m(nchildren[0] - nchildren[b])); } else { res = m(-distsqsum[a] - getsumto(a, 0)); int canc = getanc(a, b), cdist = m(pathlen(canc, a) + pathlen(canc, b)); res = m(res + 2LL * m(distsqsum[b] + 2LL * cdist * distsum[b] + 1LL * m(1LL * cdist * cdist) * nchildren[b])); } cout << res << '\n'; } return 0; }
#include <bits/stdc++.h> using namespace std; int readint() { int x = 0, f = 1; char ch = getchar(); while (ch < '0' || ch > '9') { if (ch == '-') f = -1; ch = getchar(); } while (ch >= '0' && ch <= '9') { x = x * 10 + ch - '0'; ch = getchar(); } return x * f; } struct node { long long s, ms, lazy; } t[300000]; const int cys = 1000000007; int n, m, tot, cnt; int v[200005], nxt[200005], c[200005], h[100005], rnk[100005], dfn[100005], siz[100005], ans[100005], dep[100005]; vector<pair<int, int> > q[100005]; int mod(int x) { return x >= cys ? x - cys : x; } void addedge(int x, int y, int z) { v[++tot] = y; c[tot] = z; nxt[tot] = h[x]; h[x] = tot; v[++tot] = x; c[tot] = z; nxt[tot] = h[y]; h[y] = tot; } void update(int id) { t[id].s = mod(t[id << 1].s + t[id << 1 | 1].s); t[id].ms = mod(t[id << 1].ms + t[id << 1 | 1].ms); } void build(int id, int l, int r) { if (l == r) { t[id].s = dep[rnk[l]], t[id].ms = 1ll * dep[rnk[l]] * dep[rnk[l]] % cys; return; } int mid = (l + r) / 2; build(id << 1, l, mid); build(id << 1 | 1, mid + 1, r); update(id); } void pushdown(int id, int l, int r) { if (t[id].lazy) { int mid = (l + r) / 2; t[id << 1].lazy = mod(t[id << 1].lazy + t[id].lazy), t[id << 1 | 1].lazy = mod(t[id << 1 | 1].lazy + t[id].lazy); t[id << 1].ms = mod(mod(t[id << 1].ms + 1ll * (mid - l + 1) * t[id].lazy % cys * t[id].lazy % cys) + 2ll * t[id].lazy * t[id << 1].s % cys); t[id << 1 | 1].ms = mod(mod(t[id << 1 | 1].ms + 1ll * (r - mid) * t[id].lazy % cys * t[id].lazy % cys) + 2ll * t[id].lazy * t[id << 1 | 1].s % cys); t[id << 1].s = mod(t[id << 1].s + 1ll * t[id].lazy * (mid - l + 1) % cys), t[id << 1 | 1].s = mod(t[id << 1 | 1].s + 1ll * t[id].lazy * (r - mid) % cys); t[id].lazy = 0; } } void change(int id, int l, int r, int ql, int qr, int c) { if (l == ql && r == qr) { t[id].lazy = mod(t[id].lazy + c); t[id].ms = mod(mod(t[id].ms + 1ll * (r - l + 1) * c % cys * c % cys) + 2ll * c * t[id].s % cys); t[id].s = mod(t[id].s + 1ll * c * (r - l + 1) % cys); return; } pushdown(id, l, r); int mid = (l + r) / 2; if (qr <= mid) change(id << 1, l, mid, ql, qr, c); else if (ql > mid) change(id << 1 | 1, mid + 1, r, ql, qr, c); else change(id << 1, l, mid, ql, mid, c), change(id << 1 | 1, mid + 1, r, mid + 1, qr, c); update(id); } int query(int id, int l, int r, int ql, int qr) { if (l == ql && r == qr) return t[id].ms; pushdown(id, l, r); int mid = (l + r) / 2; if (qr <= mid) return query(id << 1, l, mid, ql, qr); else if (ql > mid) return query(id << 1 | 1, mid + 1, r, ql, qr); else return mod(query(id << 1, l, mid, ql, mid) + query(id << 1 | 1, mid + 1, r, mid + 1, qr)); } void dfs1(int u, int fa) { dfn[u] = ++cnt, rnk[cnt] = u, siz[u] = 1; for (int p = h[u]; p; p = nxt[p]) { if (v[p] == fa) continue; dep[v[p]] = mod(dep[u] + c[p]); dfs1(v[p], u); siz[u] += siz[v[p]]; } } void dfs2(int u, int fa) { for (int i = 0; i < q[u].size(); i++) ans[q[u][i].second] = mod(mod(2 * query(1, 1, n, dfn[q[u][i].first], dfn[q[u][i].first] + siz[q[u][i].first] - 1)) + cys - t[1].ms); for (int p = h[u]; p; p = nxt[p]) { if (v[p] == fa) continue; change(1, 1, n, 1, n, c[p]); change(1, 1, n, dfn[v[p]], dfn[v[p]] + siz[v[p]] - 1, mod(2 * (cys - c[p]))); dfs2(v[p], u); change(1, 1, n, 1, n, cys - c[p]); change(1, 1, n, dfn[v[p]], dfn[v[p]] + siz[v[p]] - 1, mod(2 * c[p])); } } int main() { n = readint(); int x, y, z; for (int i = 1; i <= n - 1; i++) { x = readint(); y = readint(); z = readint(); addedge(x, y, z); } dfs1(1, -1); build(1, 1, n); m = readint(); for (int i = 1; i <= m; i++) { x = readint(); y = readint(); q[x].push_back(make_pair(y, i)); } dfs2(1, -1); for (int i = 1; i <= m; i++) printf("%d\n", ans[i]); return 0; }
#include <bits/stdc++.h> using namespace std; inline int getint() { int c, l = 0, x; for (; !isdigit(c = getchar()); l = c) if (c == EOF) return 1 << 31; for (x = c - '0'; isdigit(c = getchar()); x = x * 10 + c - '0') if (c == EOF) break; return l == '-' ? -x : x; } int buf[100]; inline int putint(int x) { int i = 0; x = x < 0 ? putchar('-'), -x : x; for (; buf[i++] = x % 10, x; x /= 10) ; for (i = i - 1 ? i - 1 : 1; i--; putchar(buf[i] + '0')) ; putchar(10); return 1; } const int N = 200100; const int mod = 1000000007; int K, n, m, q, tp[N], sz[N], hc[N], fa[N], clk, ne[N * 2], to[N * 2], da[N * 2], G[N], xb; long long dp[N], dg[N]; struct poly { int a[4]; poly() { memset(a, 0, sizeof a); } poly operator+(const poly& b) { poly c; for (int i = 0; i <= K; i++) c.a[i] = (a[i] + b.a[i]) % mod; return c; } poly operator-(const poly& b) { poly c; for (int i = 0; i <= K; i++) c.a[i] = (a[i] - b.a[i] + mod) % mod; return c; } poly operator<<(const long long& tt) { long long t = (tt % mod + mod) % mod; poly c; for (int i = K; i >= 0; i--) { for (int j = K; j; j--) c.a[j] = (t * c.a[j] + c.a[j - 1]) % mod; c.a[0] = (t * c.a[0] + a[i]) % mod; } return c; } int operator()(const long long& x) { long long ans = 0, s = x % mod; for (int i = K; i >= 0; i--) ans = (ans * s + a[i]) % mod; return ans; } } g[N], f[N]; void add(int x, int y, long long z) { ne[xb] = G[x]; to[xb] = y; da[xb] = z; G[x] = xb++; } int lca(int x, int y) { for (; tp[x] != tp[y]; x = fa[tp[x]]) if (dp[tp[x]] < dp[tp[y]]) swap(x, y); return dp[x] < dp[y] ? x : y; } int dfn[N], dft[N]; bool is(int x, int y) { return dfn[x] <= dfn[y] && dfn[y] <= dft[x]; } long long dst(int x, int y) { int z = lca(x, y); return dp[x] + dp[y] - 2 * dp[z]; } void dfs2(int x) { f[x].a[K] = 1; for (int i = G[x]; ~i; i = ne[i]) if (to[i] != fa[x]) { int u = to[i], v = da[i]; dp[u] = dp[x] + v; fa[u] = x; dfs2(u); f[x] = f[x] + (f[u] << v); sz[x] += sz[u]; if (sz[u] > sz[hc[x]]) hc[x] = u; } if (!sz[x]) sz[x] = 1; } void dfs3(int x, int y) { for (int i = G[x]; ~i; i = ne[i]) if (to[i] != fa[x]) { int u = to[i]; g[u] = (f[x] << -dp[x]) - (f[u] << dp[u] - 2 * dp[x]) + g[x]; } dfn[x] = ++clk; tp[x] = y; if (hc[x]) dfs3(hc[x], y); for (int i = G[x]; ~i; i = ne[i]) if (!dfn[to[i]]) dfs3(to[i], to[i]); dft[x] = clk; } int calc(int u, int v) { if (is(u, v)) { poly a = g[v] - g[u]; return (f[v](0) + a(dp[v])) % mod; } else { poly a = f[u]; return a(dst(v, u)); } } int main() { n = getint(); K = 2; m = n - 1; memset(G, -1, sizeof G); for (int i = 1; i <= m; i++) { int x = getint(), y = getint(), z = getint(); add(x, y, z); add(y, x, z); } dfs2(1); dfs3(1, 1); q = getint(); while (q--) { int u, v; v = getint(); u = getint(); putint(((2 * calc(u, v) - calc(1, v)) % mod + mod) % mod); } }
#include <bits/stdc++.h> #pragma warning(disable : 4996) using namespace std; int n, m; vector<pair<int, int> > edge[200000]; struct INFO { long long depth; long long dis; long long child; long long down1, down2, up1, up2; } d[200000]; int par[200000][20]; long long mod(long long x) { return (x % 1000000007 + 1000000007) % 1000000007; } void back(int now, int parent) { long long ccnt = 0, cnt1 = 0, cnt2 = 0; par[now][0] = parent == -1 ? now : parent; for (int i = 1; i < 20; i++) { par[now][i] = par[par[now][i - 1]][i - 1]; } for (auto e : edge[now]) { if (e.first == parent) continue; d[e.first].depth = d[now].depth + 1; d[e.first].dis = d[now].dis + e.second; d[e.first].dis %= 1000000007; back(e.first, now); ccnt += d[e.first].child; ccnt %= 1000000007; cnt1 += d[e.first].down1 + d[e.first].child * e.second; cnt1 %= 1000000007; cnt2 += d[e.first].down2 + 2 * d[e.first].down1 * e.second; cnt2 %= 1000000007; cnt2 += d[e.first].child * e.second % 1000000007 * e.second; cnt2 %= 1000000007; } d[now].child = ccnt + 1; d[now].down1 = cnt1; d[now].down2 = cnt2; } void upback(int now, int parent, int dis) { if (parent != -1) { long long u = d[parent].up1 + d[parent].down1 - (d[now].down1 + d[now].child * dis % 1000000007); d[now].up1 = u + dis * (n - d[now].child); d[now].up1 %= 1000000007; u = d[parent].up2 + d[parent].down2 - (d[now].down2 + 2 * d[now].down1 * dis % 1000000007 + d[now].child * dis % 1000000007 * dis % 1000000007); d[now].up2 = u + 2 * (d[now].up1 - dis * (n - d[now].child) % 1000000007) * dis % 1000000007 + (n - d[now].child) * dis % 1000000007 * dis % 1000000007; d[now].up2 %= 1000000007; } for (auto e : edge[now]) { if (e.first == parent) continue; upback(e.first, now, e.second); } } int getlca(int x, int y) { if (d[x].depth < d[y].depth) swap(x, y); int dis = d[x].depth - d[y].depth; int i, j; for (i = 0; i < 20; i++) { if (dis & (1 << i)) x = par[x][i]; } if (x == y) return x; for (i = 19; i >= 0; i--) { if (par[x][i] != par[y][i]) x = par[x][i], y = par[y][i]; } return par[x][0]; } int main() { int i, j, k; scanf("%d", &n); for (i = 0; i < n - 1; i++) { int x, y, z; scanf("%d%d%d", &x, &y, &z), x--, y--; edge[x].push_back(pair<int, int>(y, z)); edge[y].push_back(pair<int, int>(x, z)); } back(0, -1); upback(0, -1, 0); scanf("%d", &m); for (i = 0; i < m; i++) { int x, y; scanf("%d%d", &x, &y), x--, y--; int lca = getlca(x, y); if (lca == y) { long long dis = d[x].dis - d[y].dis; long long u = d[y].up2 + 2 * dis * d[y].up1 % 1000000007 + (n - d[y].child) * dis % 1000000007 * dis % 1000000007; long long dab = d[x].up2 + d[x].down2 - 2 * u; printf("%I64d\n", mod(dab)); } else { long long dis = d[x].dis + d[y].dis - 2 * d[lca].dis; long long u = d[y].down2 + 2 * dis * d[y].down1 % 1000000007 + d[y].child * dis % 1000000007 * dis % 1000000007; long long dab = 2 * u - d[x].down2 - d[x].up2; printf("%I64d\n", mod(dab)); } } return 0; }
#include <bits/stdc++.h> using namespace std; const long long MN = 101234, MOD = 1000 * 1000 * 1000 + 7; long long st[MN], fn[MN], h[MN], res[MN], n; vector<pair<long long, long long> > adj[MN], qwr[MN]; long long se1[MN * 4], se2[MN * 4], lz[MN * 4]; void boom(long long v, long long val, long long sz) { (se2[v] += val * val % MOD * sz % MOD + 2 * se1[v] * val % MOD) %= MOD; (se1[v] += val * sz % MOD) %= MOD; (lz[v] += val) %= MOD; } void add(long long l, long long r, long long val, long long s = 0, long long e = n, long long v = 1) { if (r <= s || e <= l) return; if (l <= s && e <= r) { boom(v, val, e - s); return; } long long mid = (s + e) / 2; boom(v * 2, lz[v], mid - s); boom(v * 2 + 1, lz[v], e - mid); lz[v] = 0; add(l, r, val, s, mid, v * 2); add(l, r, val, mid, e, v * 2 + 1); se1[v] = (se1[v * 2] + se1[v * 2 + 1]) % MOD; se2[v] = (se2[v * 2] + se2[v * 2 + 1]) % MOD; } long long get(long long l, long long r, long long s = 0, long long e = n, long long v = 1) { if (r <= s || e <= l) return 0; if (l <= s && e <= r) return se2[v]; long long mid = (s + e) / 2; boom(v * 2, lz[v], mid - s); boom(v * 2 + 1, lz[v], e - mid); lz[v] = 0; long long x = get(l, r, s, mid, v * 2); long long y = get(l, r, mid, e, v * 2 + 1); return (x + y) % MOD; } void dfs(long long v, long long p = 0) { static long long t = 0; st[v] = t++; for (auto [u, w] : adj[v]) { if (u == p) continue; h[u] = (h[v] + w) % MOD; dfs(u, v); } fn[v] = t; } void sar(long long v, long long p = 0) { for (auto [u, w] : adj[v]) { if (u == p) continue; add(0, n, w); add(st[u], fn[u], ((-2 * w) % MOD + MOD) % MOD); sar(u, v); add(0, n, (-w + MOD) % MOD); add(st[u], fn[u], 2 * w % MOD); } for (auto [u, i] : qwr[v]) res[i] = (get(st[u], fn[u]) * 2 % MOD - get(0, n) + MOD) % MOD; } int32_t main() { cin >> n; for (long long i = 1; i < n; i++) { long long u, v, w; cin >> u >> v >> w; adj[--u].push_back({--v, w}); adj[v].push_back({u, w}); } dfs(0); long long q; cin >> q; for (long long i = 0; i < q; i++) { long long u, v; cin >> u >> v; qwr[--u].push_back({--v, i}); } for (long long i = 0; i < n; i++) add(st[i], st[i] + 1, h[i]); sar(0); for (long long i = 0; i < q; i++) cout << res[i] << endl; }
#include <bits/stdc++.h> using namespace std; const long long N = 100100, MOD = 1000 * 1000 * 1000 + 7; long long n, q; vector<pair<long long, long long> > adl[N]; long long ks[N], ks2[N], as[N], as2[N], ted[N], anc[N][20], len[N], hei[N]; bool chk[N]; void dfs(long long v) { chk[v] = 1; ted[v] = 1; for (long long i = 0, u, w; i < adl[v].size(); ++i) { u = adl[v][i].first; w = adl[v][i].second; if (!chk[u]) { dfs(u); ted[v] += ted[u]; ks[v] += ks[u]; ks[v] %= MOD; ks[v] += w * ted[u]; ks[v] %= MOD; long long w2 = w * w; w2 %= MOD; long long res = (w * ks[u]) % MOD; ks2[v] += 2 * res; ks2[v] %= MOD; ks2[v] += ks2[u] + w2 * ted[u]; ks2[v] %= MOD; } } } void dfs(long long v, long long dad, long long wei) { chk[v] = 1; anc[v][0] = dad; len[v] = len[dad] + wei; len[v] %= MOD; hei[v] = hei[dad] + 1; if (!dad) { as[v] = ks[v]; as2[v] = ks2[v]; } else { long long other = n - ted[v]; long long dis = other - ted[v]; while (dis < 0) dis += MOD; as[v] = as[dad] + wei * (dis); as[v] %= MOD; long long sdis = as[dad] - 2 * ks[v] - ted[v] * wei; if (sdis < 0) sdis += wei * MOD; while (sdis < 0) sdis += MOD; sdis %= MOD; long long w2 = wei * wei; w2 %= MOD; as2[v] = as2[dad] + w2 * dis; as2[v] %= MOD; long long res = (wei * sdis) % MOD; as2[v] += res * 2; as2[v] %= MOD; } for (long long i = 0, u, w; i < adl[v].size(); ++i) { u = adl[v][i].first; w = adl[v][i].second; if (!chk[u]) dfs(u, v, w); } } int main() { ios_base::sync_with_stdio(false); cin >> n; for (long long i = 1, x, y, w; i < n; ++i) { cin >> x >> y >> w; adl[x].push_back(pair<long long, long long>(y, w)); adl[y].push_back(pair<long long, long long>(x, w)); } dfs(1); memset(chk, 0, sizeof chk); dfs(1, 0, 0); for (long long i = 1; i < 20; ++i) for (long long j = 1; j <= n; ++j) anc[j][i] = anc[anc[j][i - 1]][i - 1]; cin >> q; for (long long i = 1, x, y; i <= q; ++i) { cin >> x >> y; long long lca, ans = 0, cx = x, cy = y; if (hei[x] < hei[y]) swap(x, y); long long dis = hei[x] - hei[y]; for (long long j = 19; j >= 0; --j) if (dis & (1 << j)) x = anc[x][j]; if (x == y) { lca = x; if (hei[cx] >= hei[cy]) { long long fas = len[cx] + len[cy] - 2 * len[lca]; fas %= MOD; long long fas2 = fas * fas; fas2 %= MOD; long long res = ((fas * (as[cy] - ks[cy])) % MOD); ans = as2[cx] - 2 * (as2[cy] - ks2[cy] + fas2 * (n - ted[cy]) + 2 * res); if (ans < 0) ans += N * MOD; while (ans < 0) ans += MOD; ans %= MOD; cout << ans << "\n"; continue; } } else { for (long long j = 19; j >= 0; --j) if (anc[x][j] != anc[y][j]) { x = anc[x][j]; y = anc[y][j]; } lca = anc[x][0]; } long long fas = len[cx] + len[cy] - 2 * len[lca]; fas %= MOD; long long fas2 = fas * fas; fas2 %= MOD; ans = ks2[cy] + fas2 * ted[cy]; ans %= MOD; long long res = (fas * ks[cy]) % MOD; ans += res * 2; ans %= MOD; ans = ans - (as2[cx] - ans); if (ans < 0) ans += N * MOD; while (ans < 0) ans += MOD; ans %= MOD; cout << ans << "\n"; } return 0; }
#include <bits/stdc++.h> using namespace std; long long gcd(long long a, long long b) { while (a && b) { if (a >= b) a %= b; else b %= a; } return a + b; } long long power(long long a, long long n) { long long p = 1; while (n > 0) { if (n % 2) { p = p * a; } n >>= 1; a *= a; } return p; } long long power(long long a, long long n, long long mod) { long long p = 1; while (n > 0) { if (n % 2) { p = p * a; p %= mod; } n >>= 1; a *= a; a %= mod; } return p % mod; } int getint() { char c; int ret = c - '0', sgn = 0; while ((c = getchar()) && !(c >= '0' && c <= '9') && c != '-') ; if (c == '-') sgn = 1, ret = 0; while ((c = getchar()) && c >= '0' && c <= '9') ret = ret * 10 + c - '0'; if (sgn) ret = -ret; return ret; } const int maxn = 1e5 + 10; const int maxm = maxn * 2; const long long inf = 1e18; const long long mod = 1e9 + 7; int sz[maxn]; long long cost[maxn]; long long f[maxn], ft[maxn], f2[maxn], f1[maxn]; vector<pair<int, int> > g[maxn]; long long get(long long x, long long y) { x %= mod, y %= mod; x = ((x - y) % mod + mod) % mod; return x; } void add(long long& x, long long y) { x %= mod, y %= mod; x = (x + y) % mod; } void dfs1(int u, int pa) { int len = g[u].size(); sz[u] = 1; for (int i = 0; i < len; i++) { int v = g[u][i].first; long long w = g[u][i].second; if (v == pa) continue; cost[v] = w; dfs1(v, u); sz[u] += sz[v]; ft[u] += (ft[v] + w * sz[v] % mod) % mod; ft[u] %= mod; if (ft[u] < 0) ft[u] += mod; f[u] += ((f[v] + w * w % mod * sz[v] % mod) % mod + w * 2 % mod * ft[v] % mod) % mod; f[u] %= mod; } } int n; void dfs2(int u, int pa) { int len = g[u].size(); for (int i = 0; i < len; i++) { int v = g[u][i].first; long long w = g[u][i].second; if (v == pa) continue; long long temp = get(ft[u], sz[v] * w % mod) + (n - sz[v]) * w % mod; temp %= mod; long long temp2 = get(temp, ft[v]); temp2 = get(temp2, (n - sz[v]) * w % mod); f1[v] = temp2; long long temp3 = f[v]; f[v] = ((f[u] - 1LL * sz[v] * w % mod * w % mod) % mod - 1LL * 2 * w % mod * ft[v] % mod) % mod; f[v] = (f[v] + mod) % mod; f2[v] = get(f[v], temp3); f[v] = (f[v] + 1LL * (n - sz[v]) * w % mod * w % mod + 2LL * w % mod * temp2 % mod) % mod; ft[v] = temp; dfs2(v, u); } } int deep[maxn], fa[25][maxn]; long long ds[maxn], sumdis[maxn], sumq[maxn]; void dfs(int u, int pa, int d) { deep[u] = d; fa[0][u] = pa; int i; int len = g[u].size(); sumdis[u] = ds[u], sumq[u] = ds[u] * ds[u] % mod; for (int i = 0; i < len; i++) { int v = g[u][i].first, w = g[u][i].second; if (v == pa) continue; ds[v] = ds[u] + w; ds[v] %= mod; dfs(v, u, d + 1); add(sumdis[u], sumdis[v]); add(sumq[u], sumq[v]); } } void lca_init() { for (int k = 0; k < 20; k++) { for (int i = 1; i <= n; i++) { if (fa[k][i] == -1) fa[k + 1][i] = -1; else fa[k + 1][i] = fa[k][fa[k][i]]; } } } int lca(int u, int v) { if (deep[u] > deep[v]) swap(u, v); for (int k = 0; k < 22; k++) { if ((deep[v] - deep[u]) >> k & 1) { v = fa[k][v]; } } if (u == v) return u; for (int k = 21; k >= 0; k--) { if (fa[k][u] != fa[k][v]) { u = fa[k][u], v = fa[k][v]; } } return fa[0][v]; } int main() { cin >> n; for (int i = 1; i <= n; i++) g[i].clear(); for (int i = 1; i < n; i++) { int u, v, w; scanf("%d%d%d", &u, &v, &w); g[u].push_back(make_pair(v, w)); g[v].push_back(make_pair(u, w)); } memset(f, 0, sizeof(f)); f1[1] = f2[1] = 0; dfs1(1, -1); dfs2(1, -1); ds[1] = sumdis[1] = sumq[1] = 0; dfs(1, -1, 1); lca_init(); int q; cin >> q; while (q--) { int u, v; scanf("%d%d", &u, &v); int la = lca(u, v); long long ans = 0; if (la != v) { long long cnt = sz[v] - 1; long long x = get(ds[u] + ds[v], 2 * ds[la]), y = x; x = get(x, ds[v]); long long temp = (cnt * x % mod * x % mod + get(sumq[v], ds[v] * ds[v] % mod)) % mod + 2 * x % mod * get(sumdis[v], ds[v]) % mod; temp %= mod; add(temp, y * y % mod); ans = temp; } else { long long cnt = n - sz[v]; long long x = get(ds[u], ds[v]); long long ww = (x + cost[v]) % mod; long long temp = (f2[v] + cnt * ww % mod * ww % mod) % mod + ww * 2 % mod * f1[v] % mod; temp = temp % mod; ans = get(f[u], temp); } ans = get(ans, get(f[u], ans)); cout << ans << "\n"; } return 0; }
#include <bits/stdc++.h> using namespace std; const int MOD = 1e9 + 7; const int SIZE = 3e5 + 10; vector<int> e[SIZE], ev[SIZE]; int jump[20][SIZE], lv[SIZE], n; long long dis[SIZE]; void init(int x, int lt) { jump[0][x] = lt; for (int i = 0; i < (((int)(e[x]).size())); ++i) { int y = e[x][i]; if (y != lt) { dis[y] = dis[x] + ev[x][i]; lv[y] = lv[x] + 1; init(y, x); } } } int adv(int x, int v) { for (int i = 0; (1 << i) <= v; i++) { if ((v >> i) & 1) x = jump[i][x]; } return x; } int lca(int x, int y) { if (lv[x] > lv[y]) x = adv(x, lv[x] - lv[y]); else y = adv(y, lv[y] - lv[x]); if (x == y) return x; for (int i = 19; i >= 0; i--) if (jump[i][x] != jump[i][y]) { x = jump[i][x]; y = jump[i][y]; } return jump[0][x]; } void build() { init(1, 1); for (int i = (1); i < (20); ++i) { for (int x = (1); x < (n + 1); ++x) jump[i][x] = jump[i - 1][jump[i - 1][x]]; } } int num[SIZE], sum[SIZE], sum2[SIZE], all_sum[SIZE], all_sum2[SIZE]; void add(int &x, long long v) { x = (x + v) % MOD; } void dfs0(int x, int lt) { num[x] = 1; for (int i = 0; i < (((int)(e[x]).size())); ++i) { int y = e[x][i]; if (y == lt) continue; dfs0(y, x); num[x] += num[y]; sum[x] = (sum[x] + sum[y] + (long long)num[y] * ev[x][i]) % MOD; sum2[x] = (sum2[x] + sum2[y] + (long long)sum[y] * 2 * ev[x][i] + (long long)ev[x][i] * ev[x][i] % MOD * num[y]) % MOD; } } void dfs1(int x, int lt, long long v1, long long v2) { v1 %= MOD; v2 %= MOD; if (v1 < 0) v1 += MOD; if (v2 < 0) v2 += MOD; all_sum[x] = sum[x]; all_sum2[x] = sum2[x]; add(all_sum[x], v1); add(all_sum2[x], v2); for (int i = 0; i < (((int)(e[x]).size())); ++i) { int y = e[x][i]; if (y == lt) continue; dfs1(y, x, v1 + (long long)(n - num[y]) * ev[x][i] % MOD + sum[x] - sum[y] - (long long)num[y] * ev[x][i] % MOD, all_sum2[x] - sum2[y] - sum[y] * 2LL * ev[x][i] % MOD - (long long)ev[x][i] * ev[x][i] % MOD * num[y] + (long long)(n - num[y]) * ev[x][i] % MOD * ev[x][i] % MOD + 2LL * ev[x][i] * (v1 + sum[x] - sum[y] - (long long)num[y] * ev[x][i] % MOD) % MOD); } } int main() { scanf("%d", &(n)); for (int i = (1); i < (n); ++i) { int x, y, v; scanf("%d%d%d", &x, &y, &v); e[x].push_back(y); ev[x].push_back(v); e[y].push_back(x); ev[y].push_back(v); } build(); dfs0(1, 1); dfs1(1, 1, 0, 0); int(Q); scanf("%d", &Q); while (Q--) { int u, v; scanf("%d%d", &u, &v); int me = lca(u, v); int an = 0; long long dd = dis[u] + dis[v] - 2 * dis[me]; dd %= MOD; if (me != v) { an = -all_sum2[u] % MOD; add(an, (sum2[v] + dd * dd % MOD * num[v] % MOD + dd * 2LL * sum[v] % MOD) * 2); } else { an = all_sum2[u]; add(an, (all_sum2[v] - sum2[v] + dd * dd % MOD * (n - num[v]) % MOD + dd * 2LL * (all_sum[v] - sum[v]) % MOD) * -2); } if (an < 0) an += MOD; printf("%d\n", an); } return 0; }
#include <bits/stdc++.h> using namespace std; const long long INF = 0x3f3f3f3f; const int N = 1e5 + 10; const int M = 1e3 + 10; const long long mod = 1e9 + 7; const double PI = acos(-1); inline long long ab(long long x) { return x < 0 ? -x : x; } inline long long mm(long long x) { return x >= mod ? x - mod : x < 0 ? x + mod : x; } vector<pair<int, long long> > son[N]; struct Node { long long sum1 = 0, sum2 = 0, cnt = 0, deep = 0, len = 0; long long psum1 = 0, psum2 = 0, pcnt = 0; int fa[20]; } node[N]; void dfs(int o, int fa) { node[o].deep = node[fa].deep + 1, node[o].cnt = 1; node[o].fa[0] = fa; for (int i = 1; i < 20; ++i) node[o].fa[i] = node[node[o].fa[i - 1]].fa[i - 1]; for (auto it : son[o]) { if (it.first != fa) { node[it.first].len = node[o].len + it.second; dfs(it.first, o); node[o].sum1 = (node[it.first].sum1 + node[o].sum1 + node[it.first].cnt * it.second) % mod; node[o].cnt += node[it.first].cnt; node[o].sum2 = (node[o].sum2 + node[it.first].cnt * it.second % mod * it.second + node[it.first].sum2 + 2 * node[it.first].sum1 * it.second) % mod; } } } void bfs(int o, int fa) { long long sum1, cnt, sum2; for (auto it : son[o]) { if (it.first != fa) { sum1 = mm((node[o].sum1 - node[it.first].sum1 - node[it.first].cnt * it.second + node[o].psum1) % mod + mod); cnt = node[o].cnt - node[it.first].cnt + node[o].pcnt; sum2 = mm((node[o].psum2 + node[o].sum2 - node[it.first].cnt * it.second % mod * it.second - node[it.first].sum2 - 2 * node[it.first].sum1 * it.second) % mod + mod); node[it.first].psum1 = (sum1 + cnt * it.second) % mod; node[it.first].pcnt = cnt; node[it.first].psum2 = (cnt * it.second % mod * it.second % mod + sum2 + 2 * sum1 * it.second % mod) % mod; bfs(it.first, o); } } } int get_lca(int u, int v) { if (node[u].deep < node[v].deep) swap(u, v); int dd = node[u].deep - node[v].deep; for (int i = 19; i >= 0; --i) if ((dd >> i) & 1) u = node[u].fa[i]; if (u == v) return u; for (int i = 19; i >= 0; --i) if (node[u].fa[i] != node[v].fa[i]) u = node[u].fa[i], v = node[v].fa[i]; return node[u].fa[0]; } void solve(int u, int v) { int w = get_lca(u, v); if (w != v) { long long dd = (node[u].len + node[v].len - 2 * node[w].len) % mod; long long res = (node[v].cnt * dd % mod * dd % mod + node[v].sum2 + 2 * node[v].sum1 * dd % mod) % mod; long long all = mm(node[u].psum2 + node[u].sum2); printf("%I64d\n", mm((res * 2 - all) % mod + mod)); } else { long long dd = (node[u].len - node[v].len) % mod; long long res = mm((node[u].sum2 + node[u].psum2 - node[v].pcnt * 1ll * dd % mod * dd - node[v].psum2 - 2 * node[v].psum1 * dd) % mod + mod); long long all = mm(node[u].psum2 + node[u].sum2); printf("%I64d\n", mm((res * 2 - all) % mod + mod)); } } int main() { int n, u, v, w, q; scanf("%d", &n); for (int i = 1; i < n; ++i) { scanf("%d%d%I64d", &u, &v, &w); son[u].push_back({v, w}); son[v].push_back({u, w}); } dfs(1, 0); bfs(1, 0); scanf("%d", &q); for (int i = 1; i <= q; ++i) { scanf("%d%d", &u, &v); solve(u, v); } return 0; }
#include <bits/stdc++.h> using namespace std; template <class P, class Q> inline void smin(P &a, Q b) { if (b < a) a = b; } template <class P, class Q> inline void smax(P &a, Q b) { if (a < b) a = b; } const int mod = 1000000000 + 7; const int maxn = 100000 + 100; const int maxlg = 17 + 1; int n, q; vector<pair<int, int> > adj[maxn]; int par[maxlg][maxn]; int dep[maxn], dis[maxn]; int dw0[maxn], dw1[maxn], dw2[maxn]; int up0[maxn], up1[maxn], up2[maxn]; inline int fix(int x) { while (x < 0) x += mod; if (x >= mod) x -= mod; return x; } inline void addto(int &x, int y) { x += y; while (x < 0) x += mod; if (x >= mod) x -= mod; } void dfs(int u, int parent = 0, int depth = 0, int dist = 0) { dep[u] = depth; dis[u] = dist; par[0][u] = parent; for (int l = (int)(1), _n = (int)(maxlg); l < _n; l++) par[l][u] = par[l - 1][par[l - 1][u]]; dw0[u] = 1; for (int i = 0, _n = (int)((int((adj[u]).size()))); i < _n; i++) if (adj[u][i].first != parent) { int v = adj[u][i].first, w = adj[u][i].second; dfs(adj[u][i].first, u, depth + 1, fix(dist + w)); dw0[u] += dw0[v]; addto(dw1[u], (dw1[v] + w * (long long)dw0[v]) % mod); addto(dw2[u], (dw2[v] + 2 * (long long)w * dw1[v] + w * (long long)w % mod * dw0[v]) % mod); } } void dfs_up(int u, int parent = 0, int parw = 0) { if (u != 0) { up0[u] = n - dw0[u]; up1[u] = fix((up1[parent] + dw1[parent] + parw * (long long)n - dw1[u] - 2 * (long long)parw * dw0[u]) % mod); up2[u] = fix((up2[parent] + dw2[parent] + 2 * (long long)parw * (up1[parent] + dw1[parent]) + parw * (long long)parw % mod * n) % mod); addto(up2[u], -(dw2[u] + 2 * (long long)2 * parw * dw1[u] + 4 * (long long)parw * parw % mod * dw0[u]) % mod); } for (int i = 0, _n = (int)((int((adj[u]).size()))); i < _n; i++) if (adj[u][i].first != parent) { int v = adj[u][i].first, w = adj[u][i].second; dfs_up(v, u, w); } } int lca(int u, int v) { if (dep[u] > dep[v]) swap(u, v); for (int l = (int)(maxlg), _x = (int)(0); l-- > _x;) if (dep[par[l][v]] >= dep[u]) v = par[l][v]; if (u == v) return u; for (int l = (int)(maxlg), _x = (int)(0); l-- > _x;) if (par[l][u] != par[l][v]) u = par[l][u], v = par[l][v]; return par[0][u]; } int main() { ios_base::sync_with_stdio(false); cin.tie(0); cin >> n; for (int z = 0, _n = (int)(n - 1); z < _n; z++) { int u, v, c; cin >> u >> v >> c; u--, v--; adj[u].push_back(pair<int, int>(v, c)); adj[v].push_back(pair<int, int>(u, c)); } dfs(0); dfs_up(0); cin >> q; while (q--) { int u, v; cin >> u >> v; u--, v--; int t = lca(u, v); int d = fix(dis[u] - dis[t] + dis[v] - dis[t]); int ans = fix(dw2[u] + up2[u]); if (t == v) { addto(ans, -2 * (up2[v] + 2 * (long long)d * up1[v] + d * (long long)d % mod * up0[v]) % mod); } else { addto(ans, -2 * (dw2[v] + 2 * (long long)d * dw1[v] + d * (long long)d % mod * dw0[v]) % mod); ans = fix(-ans); } cout << ans << endl; } return 0; }
#include <bits/stdc++.h> using namespace std; vector<int> E[101000]; vector<long long> L[101000]; int n, Count[101000], Num[101000], cnt, par[101000], pp[18][101000]; long long Mod = 1000000007, D[101000], D2[101000], T[101000], T2[101000], pL[101000], DL[101000]; int Dep[101000]; void DFS(int a, int pp) { Num[a] = ++cnt; int i, x, y; x = Num[a]; Count[x]++; par[x] = Num[pp]; for (i = 0; i < E[a].size(); i++) { if (pp != E[a][i]) { DFS(E[a][i], a); y = Num[E[a][i]]; pL[y] = L[a][i]; Count[x] += Count[y]; D[x] = (D[x] + D[y] + L[a][i] * Count[y]) % Mod; D2[x] = (D2[x] + D2[y] + L[a][i] * L[a][i] % Mod * Count[y] + 2 * L[a][i] * D[y]) % Mod; } } } void Pro() { int i, p; long long X, Y; T[1] = D[1]; for (i = 2; i <= n; i++) { p = par[i]; DL[i] = DL[p] + pL[i]; Dep[i] = Dep[p] + 1; X = Count[i]; Y = n - Count[i]; T[i] = (T[p] + (Y - X + Mod) % Mod * pL[i]) % Mod; } } void Pro2() { int i; long long Gap1, Gap2, X, Y, p; T2[1] = D2[1]; for (i = 2; i <= n; i++) { p = par[i]; X = Count[i], Y = n - Count[i]; Gap1 = ((T[i] - D[i] - pL[i] * Y % Mod + Mod * 2) % Mod * 2 * pL[i] + pL[i] * pL[i] % Mod * Y) % Mod; Gap2 = (D[i] * 2 * pL[i] % Mod + pL[i] * pL[i] % Mod * X) % Mod; T2[i] = (T2[p] + Gap1 - Gap2 + Mod) % Mod; } } void PrePro() { int i, j; for (i = 1; i <= n; i++) pp[0][i] = par[i]; for (i = 0; i < 17; i++) { for (j = 1; j <= n; j++) { pp[i + 1][j] = pp[i][pp[i][j]]; } } } int LCA(int a, int b) { if (Dep[a] < Dep[b]) return LCA(b, a); int d = Dep[a] - Dep[b], i = 0; while (d) { if (d & 1) a = pp[i][a]; d >>= 1; i++; } for (i = 17; i >= 0; i--) { if (pp[i][a] != pp[i][b]) { a = pp[i][a], b = pp[i][b]; } } if (a != b) a = pp[0][a], b = pp[0][b]; return a; } long long dist(int a, int b) { int ppp = LCA(a, b); return (DL[a] + DL[b] - DL[ppp] * 2 + Mod * 2) % Mod; } long long Solve2(int a, int b) { long long d = dist(a, b); long long r = (D2[b] + 2 * d * D[b] % Mod + d * d % Mod * Count[b]) % Mod; return (r * 2 - T2[a] + Mod) % Mod; } long long Solve1(int a, int b) { long long d = dist(a, b); long long r = ((T2[b] - D2[b] + Mod) % Mod + (T[b] - D[b] + Mod) % Mod * 2 * d % Mod + d * d % Mod * (n - Count[b])) % Mod; return (T2[a] - r * 2 + Mod * 2) % Mod; } void Output() { int Q, a, b; scanf("%d", &Q); while (Q--) { scanf("%d%d", &a, &b); a = Num[a], b = Num[b]; if (LCA(a, b) == b) { printf("%lld\n", Solve1(a, b)); } else { printf("%lld\n", Solve2(a, b)); } } } int main() { int i, a, b, c; scanf("%d", &n); for (i = 1; i < n; i++) { scanf("%d%d%d", &a, &b, &c); E[a].push_back(b); E[b].push_back(a); L[a].push_back(c); L[b].push_back(c); } DFS(1, 0); Pro(); Pro2(); PrePro(); Output(); return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 100050; const int M = 6 * N; const int mod = 1e9 + 7; int add(int x, int y) { x += y; return x >= mod ? x - mod : x; } int sub(int x, int y) { x -= y; return x < 0 ? x + mod : x; } int mul(int x, int y) { return (long long)x * y % mod; } int pow(int x, int k) { int ans = 1; for (; k; k >>= 1, x = mul(x, x)) if (k & 1) ans = mul(ans, x); return ans; } int inv(int x) { return pow(x, mod - 2); } int sum_1[N], sum_2[N], lid[N], rid[N], tid, dfn[N], dep[N], n; vector<pair<int, int>> E[N]; void DFS(int u, int p) { lid[u] = ++tid; dfn[tid] = u; sum_1[tid] = add(sum_1[tid - 1], dep[u]); sum_2[tid] = add(sum_2[tid - 1], mul(dep[u], dep[u])); for (auto e : E[u]) if (e.first != p) dep[e.first] = add(dep[u], e.second), DFS(e.first, u); rid[u] = tid; } int root[3], tsz, ls[M], rs[M], sum[M], lzy_mul[M], lzy[M]; bool persistent; struct Node { int c, sum, lzy_mul, lzy; }; vector<Node> bck; void upd(int c, int ss, int se, int x) { if (persistent) bck.push_back({c, sum[c], lzy_mul[c], lzy[c]}); sum[c] = mul(x, se - ss + 1); lzy[c] = x; lzy_mul[c] = 1; } void upd_mul(int c, int x) { if (persistent) bck.push_back({c, sum[c], lzy_mul[c], lzy[c]}); sum[c] = mul(sum[c], x); if (lzy[c] != -1) lzy[c] = mul(lzy[c], x); else lzy_mul[c] = mul(lzy_mul[c], x); } void push(int c, int ss, int se) { if (!ls[c]) ls[c] = ++tsz, lzy[ls[c]] = -1, lzy_mul[ls[c]] = 1; if (!rs[c]) rs[c] = ++tsz, lzy[rs[c]] = -1, lzy_mul[rs[c]] = 1; if (lzy_mul[c] != 1) { if (persistent) bck.push_back({c, sum[c], lzy_mul[c], lzy[c]}); upd_mul(ls[c], lzy_mul[c]); upd_mul(rs[c], lzy_mul[c]); lzy_mul[c] = 1; } if (lzy[c] != -1) { if (persistent) bck.push_back({c, sum[c], lzy_mul[c], lzy[c]}); int mid = ss + se >> 1; upd(ls[c], ss, mid, lzy[c]); upd(rs[c], mid + 1, se, lzy[c]); lzy[c] = -1; } } void Set(int &c, int ss, int se, int qs, int qe, int val) { if (qs > qe || qs > se || ss > qe) return; if (!c) c = ++tsz, lzy_mul[c] = 1, lzy[c] = -1; if (qs <= ss && qe >= se) { upd(c, ss, se, val); return; } push(c, ss, se); int mid = ss + se >> 1; Set(ls[c], ss, mid, qs, qe, val); Set(rs[c], mid + 1, se, qs, qe, val); if (persistent) bck.push_back({c, sum[c], lzy_mul[c], lzy[c]}); sum[c] = add(sum[ls[c]], sum[rs[c]]); } void Mul(int &c, int ss, int se, int qs, int qe, int val) { if (qs > qe || qs > se || ss > qe) return; if (!c) c = ++tsz, lzy_mul[c] = 1, lzy[c] = -1; if (qs <= ss && qe >= se) { upd_mul(c, val); return; } push(c, ss, se); int mid = ss + se >> 1; Mul(ls[c], ss, mid, qs, qe, val); Mul(rs[c], mid + 1, se, qs, qe, val); if (persistent) bck.push_back({c, sum[c], lzy_mul[c], lzy[c]}); sum[c] = add(sum[ls[c]], sum[rs[c]]); } int Get(int &c, int ss, int se, int qs, int qe) { if (qs > qe || qs > se || ss > qe) return 0; if (!c) c = ++tsz, lzy_mul[c] = 1, lzy[c] = -1; if (qs <= ss && qe >= se) return sum[c]; push(c, ss, se); int mid = ss + se >> 1; return add(Get(ls[c], ss, mid, qs, qe), Get(rs[c], mid + 1, se, qs, qe)); } void Back(int sz) { while (bck.size() > sz) { sum[bck.back().c] = bck.back().sum; lzy_mul[bck.back().c] = bck.back().lzy_mul; lzy[bck.back().c] = bck.back().lzy; bck.pop_back(); } } vector<int> Qs[N]; int a[N], b[N], ans[N]; int Solve(int u, int l, int r) { if (l > r) return 0; int ans = mul(mul(dep[u], dep[u]), r - l + 1); ans = add(ans, sub(sum_2[r], sum_2[l - 1])); int lca_2 = Get(root[0], 1, n, l, r); ans = add(ans, mul(4, lca_2)); int dep_v = sub(sum_1[r], sum_1[l - 1]); ans = add(ans, mul(2, mul(dep_v, dep[u]))); int lca = Get(root[1], 1, n, l, r); ans = add(ans, mul(sub(0, 4), mul(lca, dep[u]))); ans = add(ans, mul(sub(0, 4), Get(root[2], 1, n, l, r))); return ans; } void Solve(int u, int p) { Set(root[0], 1, n, lid[u], rid[u], mul(dep[u], dep[u])); Set(root[1], 1, n, lid[u], rid[u], dep[u]); int sz = bck.size(); persistent = 1; Mul(root[2], 1, n, lid[u], rid[u], dep[u]); for (int i : Qs[u]) { ans[i] = sub(sub(Solve(u, lid[b[i]], rid[b[i]]), Solve(u, 1, lid[b[i]] - 1)), Solve(u, rid[b[i]] + 1, n)); } persistent = 0; for (auto e : E[u]) if (e.first != p) { int v = e.first; Back(sz); persistent = 1; Mul(root[2], 1, n, lid[u], lid[v] - 1, dep[u]); Mul(root[2], 1, n, rid[v] + 1, rid[u], dep[u]); persistent = 0; Solve(v, u); Set(root[0], 1, n, lid[v], rid[v], mul(dep[u], dep[u])); Set(root[1], 1, n, lid[v], rid[v], dep[u]); } Back(sz); } int main() { int u, v, w, q; scanf("%i", &n); for (int i = 1; i < n; i++) scanf("%i %i %i", &u, &v, &w), E[u].push_back(make_pair(v, w)), E[v].push_back(make_pair(u, w)); DFS(1, 0); for (int i = 1; i <= n; i++) Set(root[2], 1, n, lid[i], lid[i], dep[i]); scanf("%i", &q); for (int i = 1; i <= q; i++) scanf("%i %i", &a[i], &b[i]), Qs[a[i]].push_back(i); Solve(1, 0); for (int i = 1; i <= q; i++) printf("%i\n", ans[i]); return 0; }
#include <bits/stdc++.h> using namespace std; const int MOD = 1000000007; int N, Q; vector<pair<int, int> > V[100002]; vector<int> W[100002]; int Q1[100002], Q2[100002]; bool S[100002]; int in[100002], out[100002], nods[100002], tn; int D[100002]; int SUM[4 * 100002], ARB[4 * 100002], ADD[4 * 100002], A1, A2, As; int result[100002]; void setall(int nod, int i1, int i2) { if (i1 == i2) { SUM[nod] = D[nods[i1]]; ARB[nod] = ((long long)D[nods[i1]]) * D[nods[i1]] % MOD; return; } int mid = (i1 + i2) / 2; setall(nod * 2, i1, mid); setall(nod * 2 + 1, mid + 1, i2); ARB[nod] = (ARB[nod * 2] + ARB[nod * 2 + 1]) % MOD; SUM[nod] = (SUM[nod * 2] + SUM[nod * 2 + 1]) % MOD; } void renew(int nod, int i1, int i2) { ARB[nod] += ((long long)ADD[nod]) * ADD[nod] % MOD * (i2 - i1 + 1) % MOD; if (ARB[nod] >= MOD) ARB[nod] -= MOD; ARB[nod] += ((long long)ADD[nod]) * SUM[nod] * 2 % MOD; if (ARB[nod] >= MOD) ARB[nod] -= MOD; SUM[nod] += ((long long)ADD[nod]) * (i2 - i1 + 1) % MOD; if (SUM[nod] >= MOD) SUM[nod] -= MOD; if (i1 != i2) { ADD[nod * 2] += ADD[nod]; if (ADD[nod * 2] >= MOD) ADD[nod * 2] -= MOD; ADD[nod * 2 + 1] += ADD[nod]; if (ADD[nod * 2 + 1] >= MOD) ADD[nod * 2 + 1] -= MOD; } ADD[nod] = 0; } void update(int nod, int i1, int i2) { if (A1 <= i1 && i2 <= A2) { ADD[nod] += As; if (ADD[nod] >= MOD) ADD[nod] -= MOD; return; } if (ADD[nod] != 0) renew(nod, i1, i2); int mid = (i1 + i2) / 2; if (A1 <= mid) update(nod * 2, i1, mid); if (A2 > mid) update(nod * 2 + 1, mid + 1, i2); renew(nod * 2, i1, mid); renew(nod * 2 + 1, mid + 1, i2); ARB[nod] = (ARB[nod * 2] + ARB[nod * 2 + 1]) % MOD; SUM[nod] = (SUM[nod * 2] + SUM[nod * 2 + 1]) % MOD; } void query(int nod, int i1, int i2) { if (ADD[nod] != 0) renew(nod, i1, i2); if (A1 <= i1 && i2 <= A2) { As += ARB[nod]; if (As >= MOD) As -= MOD; return; } int mid = (i1 + i2) / 2; if (A1 <= mid) query(nod * 2, i1, mid); if (A2 > mid) query(nod * 2 + 1, mid + 1, i2); } void Dfs(int x) { S[x] = true; in[x] = ++tn; nods[tn] = x; for (auto nod : V[x]) if (!S[nod.first]) { D[nod.first] = (D[x] + nod.second) % MOD; Dfs(nod.first); } out[x] = tn; } void Prop(int x) { S[x] = true; for (auto qn : W[x]) { A1 = 1, A2 = N, As = 0; query(1, 1, N); result[qn] = (MOD - As) % MOD; A1 = in[Q2[qn]], A2 = out[Q2[qn]], As = 0; query(1, 1, N); As = 2 * As % MOD; result[qn] += As; if (result[qn] >= MOD) result[qn] -= MOD; } for (auto nod : V[x]) if (!S[nod.first]) { A1 = 1, A2 = N, As = nod.second; update(1, 1, N); A1 = in[nod.first], A2 = out[nod.first], As = (2 * MOD - 2 * nod.second) % MOD; update(1, 1, N); Prop(nod.first); A1 = 1, A2 = N, As = (MOD - nod.second) % MOD; update(1, 1, N); A1 = in[nod.first], A2 = out[nod.first], As = 2 * nod.second % MOD; update(1, 1, N); } } int main() { cin.sync_with_stdio(false); cin >> N; for (int i = 1, nod1, nod2, val; i <= N - 1; ++i) { cin >> nod1 >> nod2 >> val; V[nod1].push_back(make_pair(nod2, val)); V[nod2].push_back(make_pair(nod1, val)); } cin >> Q; for (int i = 1; i <= Q; ++i) { cin >> Q1[i] >> Q2[i]; W[Q1[i]].push_back(i); } Dfs(1); setall(1, 1, N); memset(S, 0, sizeof(S)); Prop(1); for (int i = 1; i <= Q; ++i) cout << result[i] << '\n'; }
#include <bits/stdc++.h> using namespace std; const int N = 1e5 + 5, LOG = 20; const long long mod = 1e9 + 7; int n, q, st[N], fn[N], up[N][LOG], h[N], timer, idx[N]; vector<pair<int, int> > adj[N]; long long dp[N][2], sz[N][2], sum[N][2], d[N]; int add(int a, int b) { a += b; if (a >= mod) a -= mod; if (a < 0) a += mod; return a; } int mult(int a, int b) { int ret = (1LL * a * b) % mod; return add(ret, 0); } void dfs_down(int v, int p = -1) { for (auto e : adj[v]) { int u = e.first, w = e.second; if (u == p) continue; dfs_down(u, v); dp[v][0] = add(dp[v][0], add(dp[u][0], add(mult(sz[u][0], mult(w, w)), mult(2, mult(w, sum[u][0]))))); sum[v][0] = add(sum[v][0], add(sum[u][0], mult(w, sz[u][0]))); sz[v][0] += sz[u][0]; } for (auto e : adj[v]) { int u = e.first, w = e.second; if (u == p) continue; int val = add(dp[u][0], add(mult(sz[u][0], mult(w, w)), mult(2, mult(w, sum[u][0])))); int tmp = add(sum[u][0], mult(w, sz[u][0])); dp[u][1] = add(add(dp[v][0], -val), add(mult(w, mult(w, (sz[v][0] - sz[u][0]))), mult(2, mult(w, add(sum[v][0], -tmp))))); sum[u][1] = add(mult(w, sz[v][0] - sz[u][0]), add(sum[v][0], -tmp)); } sz[v][0]++; } void dfs_up(int v, int p = -1) { sz[v][1] = n + 1 - sz[v][0]; for (auto e : adj[v]) { int u = e.first, w = e.second; if (u == p) continue; dp[u][1] = add(dp[u][1], add(dp[v][1], add(mult(sz[v][1], mult(w, w)), mult(2, mult(w, sum[v][1]))))); sum[u][1] = add(sum[u][1], add(sum[v][1], mult(w, sz[v][1]))); dfs_up(u, v); } } void setup(int v, int p = -1) { st[v] = timer++; idx[st[v]] = v; for (int i = 1; i < LOG; i++) up[v][i] = up[up[v][i - 1]][i - 1]; for (auto e : adj[v]) { int u = e.first, w = e.second; if (u ^ p) d[u] = add(d[v], w), up[u][0] = v, h[u] = h[v] + 1, setup(u, v); } fn[v] = timer; } bool is_ancestor(int v, int u) { return (st[v] <= st[u]) && (fn[u] <= fn[v]); } int lca(int v, int u) { if (h[v] < h[u]) swap(v, u); for (int i = LOG - 1; ~i; i--) if (h[up[v][i]] >= h[u]) v = up[v][i]; if (v == u) return v; for (int i = LOG - 1; ~i; i--) if (up[v][i] != up[u][i]) v = up[v][i], u = up[u][i]; return up[v][0]; } int dist(int v, int u) { return add(d[v], add(d[u], -mult(2, d[lca(v, u)]))); } int main() { ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0); cin >> n; for (int i = 0; i < n - 1; i++) { int v, u, w; cin >> v >> u >> w; v--, u--; adj[v].push_back({u, w}); adj[u].push_back({v, w}); } dfs_down(0); dfs_up(0); setup(0); cin >> q; while (q--) { int v, u; cin >> v >> u; v--, u--; long long res = 0, w = dist(v, u); if (!is_ancestor(u, v)) { res = mult(-1, add(dp[v][0], dp[v][1])); res = add(res, mult(2, add(mult(mult(w, w), sz[u][0]), add(dp[u][0], mult(2, mult(w, sum[u][0])))))); } else { res = add(res, add(dp[v][0], dp[v][1])); res = add(res, -mult(2, add(dp[u][1], add(mult(sz[u][1] - 1, mult(w, w)), mult(sum[u][1], mult(2, w)))))); } cout << res << "\n"; } }
#include <bits/stdc++.h> using namespace std; const int N = 1e5 + 5, mod = 1e9 + 7; int zrb(int a, int b) { return (1LL * a * b % mod); } int jm(int a, int b) { int tmp = (a + b) % mod; while (tmp < 0) tmp += mod; return (tmp); } int A[N], D[N << 2], SM[N << 2], SMLZ[N << 2], P[N], ST[N], FT[N], n, st, q, RT[N]; struct node { int x, id, c; }; vector<node> ND[N]; void build(int id = 1, int l = 0, int r = n) { if (r - l < 2) { D[id] = zrb(A[l], A[l]); SM[id] = A[l]; return; } int mid = ((l + r) >> 1); build((id << 1), l, mid); build((id << 1 | 1), mid, r); D[id] = jm(D[(id << 1)], D[(id << 1 | 1)]); SM[id] = jm(SM[(id << 1)], SM[(id << 1 | 1)]); } void shift(int id, int l, int r) { int ll = (id << 1), rr = (id << 1 | 1), mid = ((l + r) >> 1); D[ll] = jm(D[ll], zrb(2, zrb(SM[ll], SMLZ[id]))); D[rr] = jm(D[rr], zrb(2, zrb(SM[rr], SMLZ[id]))); D[ll] = jm(D[ll], zrb(mid - l, zrb(SMLZ[id], SMLZ[id]))); D[rr] = jm(D[rr], zrb(r - mid, zrb(SMLZ[id], SMLZ[id]))); SMLZ[ll] = jm(SMLZ[ll], SMLZ[id]); SMLZ[rr] = jm(SMLZ[rr], SMLZ[id]); SM[ll] = jm(SM[ll], zrb(mid - l, SMLZ[id])); SM[rr] = jm(SM[rr], zrb(r - mid, SMLZ[id])); SMLZ[id] = 0; } void add(int s, int e, int d, int id = 1, int l = 0, int r = n) { if (s >= e) return; if (l >= e || r <= s) return; if (l >= s && r <= e) { int ln = r - l; D[id] = jm(D[id], zrb(ln, zrb(d, d))); D[id] = jm(D[id], zrb(2, zrb(SM[id], d))); SM[id] = jm(SM[id], zrb(ln, d)); SMLZ[id] = jm(SMLZ[id], d); return; } int mid = ((l + r) >> 1); shift(id, l, r); add(s, e, d, (id << 1), l, mid); add(s, e, d, (id << 1 | 1), mid, r); D[id] = jm(D[(id << 1)], D[(id << 1 | 1)]); SM[id] = jm(SM[(id << 1)], SM[(id << 1 | 1)]); } int get(int s, int e, int id = 1, int l = 0, int r = n) { if (s >= e) return (0); if (l >= e || r <= s) return (0); if (l >= s && r <= e) return (D[id]); int mid = ((l + r) >> 1); shift(id, l, r); return (jm(get(s, e, (id << 1), l, mid), get(s, e, (id << 1 | 1), mid, r))); } vector<pair<int, int> > adj[N]; void prDFS(int u, int p, int d = 0) { ST[u] = st; A[st++] = d; for (pair<int, int> x : adj[u]) if (x.first ^ p) { P[x.first] = x.second; prDFS(x.first, u, jm(d, x.second)); } FT[u] = st; } void DFS(int u, int p) { for (node nd : ND[u]) { if (!nd.c) { RT[nd.id] = jm(RT[nd.id], get(ST[nd.x], FT[nd.x])); } else { RT[nd.id] = jm(RT[nd.id], -D[1]); RT[nd.id] = jm(RT[nd.id], get(ST[nd.x], FT[nd.x])); } } for (pair<int, int> x : adj[u]) if (x.first ^ p) { add(ST[x.first], FT[x.first], -x.second); add(0, ST[x.first], x.second); add(FT[x.first], n, x.second); DFS(x.first, u); add(ST[x.first], FT[x.first], x.second); add(0, ST[x.first], -x.second); add(FT[x.first], n, -x.second); } } int main() { scanf("%d", &n); for (int i = 1; i < n; i++) { int a, b, c; scanf("%d %d %d", &a, &b, &c); adj[a].push_back({b, c}); adj[b].push_back({a, c}); } prDFS(1, 0); build(); scanf("%d", &q); for (int Q = 0; Q < q; Q++) { int a, b; scanf("%d %d", &a, &b); node nd = {b, Q, 0}; ND[a].push_back(nd); nd = {b, Q, 1}; ND[a].push_back(nd); } DFS(1, 0); for (int i = 0; i < q; i++) printf("%d\n", RT[i]); }
#include <bits/stdc++.h> using namespace std; vector<pair<int, int> > E[100010]; int down[100010], vis[100010]; int n; const int MOD = 1e9 + 7; pair<int, int> S[100010]; pair<int, int> PP[100010]; void get_dfs(int x, int fa, int L, pair<int, int> &A) { down[x] = 1; A.first = (A.first + L) % MOD; A.second = (A.second + (long long)L * L) % MOD; for (auto e : E[x]) if (e.second != fa && vis[e.second] == 0) { get_dfs(e.second, x, (L + e.first) % MOD, A); down[x] += down[e.second]; } } void down_dfs(int x, int fa) { down[x] = 1; for (auto e : E[x]) if (e.second != fa && vis[e.second] == 0) { down_dfs(e.second, x); down[x] += down[e.second]; } } void put_dfs(int x, int fa, int L, pair<int, int> &A, int L0) { PP[x].second = (PP[x].second + A.second + A.first * 2LL * L + ((long long)L * L) % MOD * L0) % MOD; PP[x].first = (PP[x].first + A.first + (long long)L0 * L) % MOD; for (auto e : E[x]) if (e.second != fa && vis[e.second] == 0) { put_dfs(e.second, x, (L + e.first) % MOD, A, L0); } } void Do(int x) { down_dfs(x, -1); int c = x, h = down[x] / 2; while (1) { int f = 0; for (auto e : E[c]) if (vis[e.second] == 0 && down[e.second] < down[c] && down[e.second] > h) { c = e.second; f = 1; break; } if (f == 0) break; } vector<int> near; vector<pair<int, int> > G; vector<int> lu; pair<int, int> tot = pair<int, int>(0, 0); int L0 = 1; for (auto e : E[c]) if (!vis[e.second]) { near.push_back(e.second); pair<int, int> A = pair<int, int>(0, 0); get_dfs(e.second, c, e.first, A); G.push_back(A); lu.push_back(e.first); tot.first = (tot.first + A.first) % MOD; tot.second = (tot.second + A.second) % MOD; L0 += down[e.second]; } for (int i = 0; i < (int)near.size(); i++) { int u = near[i]; pair<int, int> A = pair<int, int>(tot.first - G[i].first, tot.second - G[i].second); if (A.first < 0) A.first += MOD; if (A.second < 0) A.second += MOD; put_dfs(u, c, lu[i], A, L0 - down[u]); } PP[c].second = (PP[c].second + tot.second) % MOD; PP[c].first = (PP[c].first + tot.first) % MOD; vis[c] = 1; for (int e : near) { Do(e); } } int dep[100010], ST[100010], EN[100010], ce; int up[100010][20]; int Ldep[100010]; tuple<int, int, int> DP[100010]; void DFS(int x, int fa) { get<0>(DP[x]) = 1; ST[x] = ++ce; for (auto e : E[x]) if (e.second != fa) { dep[e.second] = dep[x] + 1; Ldep[e.second] = (Ldep[x] + e.first) % MOD; up[e.second][0] = x; for (int i = 1; i < 20; i++) up[e.second][i] = up[up[e.second][i - 1]][i - 1]; DFS(e.second, x); int L = e.first; int a0 = get<0>(DP[e.second]); int a1 = get<1>(DP[e.second]); int a2 = get<2>(DP[e.second]); get<0>(DP[x]) += a0; get<1>(DP[x]) = (a1 + get<1>(DP[x]) + (long long)L * a0) % MOD; get<2>(DP[x]) = (get<2>(DP[x]) + ((long long)L * L) % MOD * a0 + (long long)2 * L * a1 + a2) % MOD; } EN[x] = ce; } int lca(int x, int y) { if (dep[x] < dep[y]) swap(x, y); for (int i = 0; i < 20; i++) if (1 << i & (dep[x] - dep[y])) x = up[x][i]; for (int i = 19; i >= 0; i--) if (up[x][i] != up[y][i]) x = up[x][i], y = up[y][i]; return x == y ? x : up[x][0]; } void solve() { scanf("%d", &n); for (int i = 0; i < n - 1; i++) { int x, y, z; scanf("%d%d%d", &x, &y, &z); E[x].push_back(pair<int, int>(z, y)); E[y].push_back(pair<int, int>(z, x)); } Do(1); DFS(1, -1); int q; scanf("%d", &q); while (q--) { int u, v; scanf("%d%d", &u, &v); if (ST[v] <= ST[u] && ST[u] <= EN[v]) { long long ans = PP[u].second; long long C = 0; long long a0 = n; long long a1 = PP[v].first; long long a2 = PP[v].second; a0 -= get<0>(DP[v]); a1 -= get<1>(DP[v]); a2 -= get<2>(DP[v]); long long L = Ldep[u] - Ldep[v]; if (L < 0) L += MOD; C += (L * L) % MOD * a0; C += 2LL * L * a1; C += a2; ans -= 2 * C; ans %= MOD; if (ans < 0) ans += MOD; printf("%lld\n", ans); } else { long long ans = -PP[u].second; int a0 = get<0>(DP[v]); int a1 = get<1>(DP[v]); int a2 = get<2>(DP[v]); int lc = lca(u, v); long long L = Ldep[u] + Ldep[v] - 2LL * Ldep[lc]; if (L < 0) L += MOD; ans += 2LL * (L * L) % MOD * a0; ans += 4LL * L * a1; ans += 2LL * a2; ans %= MOD; if (ans < 0) ans += MOD; printf("%lld\n", ans); } } } int main() { int Tc = 1; for (int tc = 1; tc <= Tc; tc++) { solve(); } return 0; }
#include <bits/stdc++.h> using namespace std; int n, q; vector<pair<int, int> > adj[100013]; int visited[100013]; int sizst[100013]; int sumst[100013]; int sqsst[100013]; int sumsq[100013]; int sumsm[100013]; int depth[100013]; int h[100013]; int ancestor[100013][20]; int up[100013]; int MOD = 1000000007; void dfsLCA(int x) { visited[x] = 1; for (int i = 0; i < adj[x].size(); i++) { int next = adj[x][i].first; int dist = adj[x][i].second; if (!visited[next]) { h[next] = h[x] + 1; depth[next] = (depth[x] + dist) % MOD; dfsLCA(next); ancestor[next][0] = x; up[next] = dist; } } ancestor[x][0] = -1; } int findkth(int x, int k) { int where = x; for (int i = 19; i >= 0; i--) if (k & (1 << i)) where = ancestor[where][i]; return where; } int lca(int a, int b) { if (h[a] > h[b]) swap(a, b); b = findkth(b, h[b] - h[a]); if (a == b) return a; for (int i = 19; i >= 0; i--) { if (h[a] < (1 << i)) continue; int na = ancestor[a][i]; int nb = ancestor[b][i]; if (na != nb) a = na, b = nb; } return ancestor[a][0]; } void dfs(int x) { visited[x] = 1; sizst[x] = 1; for (int i = 0; i < adj[x].size(); i++) { int next = adj[x][i].first; if (visited[next]) continue; dfs(next); int dist = adj[x][i].second; sizst[x] += sizst[next]; sumst[x] = (sumst[x] + sumst[next] + (long long)dist * sizst[next]) % MOD; int distsq = ((long long)dist * dist) % MOD; sqsst[x] = (sqsst[x] + (long long)distsq * sizst[next] + (long long)2 * dist * sumst[next] + sqsst[next]) % MOD; } } void dfs2(int x) { visited[x] = 1; if (x == 0) { sumsm[x] = sumst[x]; sumsq[x] = sqsst[x]; } else { int prev = ancestor[x][0]; int dist = up[x]; int distsq = ((long long)dist * dist) % MOD; int below = (sqsst[x] + (long long)2 * dist * sumst[x] + (long long)sizst[x] * distsq) % MOD; int abovesq = (sumsq[prev] - below + MOD) % MOD; int abovesm = ((sumsm[prev] - sumst[x] - (long long)dist * sizst[x] + MOD) % MOD + MOD) % MOD; int num = n - sizst[x]; sumsm[x] = (sumst[x] + abovesm + (long long)num * dist) % MOD; sumsq[x] = (sqsst[x] + (long long)distsq * num + ((long long)2 * dist * abovesm) % MOD + abovesq) % MOD; } for (int i = 0; i < adj[x].size(); i++) if (!visited[adj[x][i].first]) dfs2(adj[x][i].first); } int main() { scanf("%d", &n); for (int i = 1; i < n; i++) { int a, b, c; scanf("%d%d%d", &a, &b, &c); a -= 1; b -= 1; adj[a].push_back(make_pair(b, c)); adj[b].push_back(make_pair(a, c)); } dfsLCA(0); for (int i = 1; i < 20; i++) { for (int j = 0; j < n; j++) { if (h[j] < (1 << i)) ancestor[j][i] = -1; else ancestor[j][i] = ancestor[ancestor[j][i - 1]][i - 1]; } } for (int i = 0; i < n; i++) visited[i] = 0; dfs(0); for (int i = 0; i < n; i++) visited[i] = 0; dfs2(0); scanf("%d", &q); for (int i = 0; i < q; i++) { int u, v; scanf("%d%d", &u, &v); u -= 1; v -= 1; int l = lca(u, v); if (l == v) { int diff = (depth[u] - depth[v] + MOD) % MOD; int diffsq = ((long long)diff * diff) % MOD; int abovesq = (sumsq[v] - sqsst[v] + MOD) % MOD; int abovesm = (sumsm[v] - sumst[v] + MOD) % MOD; int tops = ((long long)diffsq * (n - sizst[v]) + ((long long)2 * diff * abovesm) % MOD + abovesq) % MOD; int part1 = (sumsq[u] - tops + MOD) % MOD; printf("%d\n", ((long long)2 * part1 - sumsq[u] + MOD) % MOD); } else { int diff = ((long long)depth[u] + depth[v] - 2 * depth[l] + 2 * MOD) % MOD; int diffsq = ((long long)diff * diff) % MOD; int part1 = ((long long)diffsq * sizst[v] + ((long long)2 * diff * sumst[v]) % MOD + sqsst[v]) % MOD; printf("%d\n", ((long long)2 * part1 - sumsq[u] + MOD) % MOD); } } return 0; }
#include <bits/stdc++.h> using namespace std; const int NMAX = 1e5; const int MOD = 1e9 + 7; struct node_t { int sum; int sum2; int lazy; node_t operator+(const node_t &other) const { node_t ans; ans.sum = (this->sum + other.sum) % MOD; ans.sum2 = (this->sum2 + other.sum2) % MOD; ans.lazy = 0; return ans; } void add_val(int val, int st, int dr) { this->lazy = (this->lazy + val) % MOD; this->sum2 = (this->sum2 + 1LL * (1LL * val * val % MOD) * (dr - st + 1) + 2LL * val * this->sum) % MOD; this->sum = (this->sum + 1LL * val * (dr - st + 1)) % MOD; } }; node_t aint[4 * NMAX + 5]; int init_d[NMAX + 5]; int lin[NMAX + 5], len; int fst[NMAX + 5]; int lst[NMAX + 5]; int n, q; int ans[NMAX + 5]; vector<pair<int, int> > graph[NMAX + 5]; vector<pair<int, int> > queries[NMAX + 5]; void build(int nod, int st, int dr) { if (st == dr) { aint[nod].lazy = 0; aint[nod].sum = init_d[lin[st]]; aint[nod].sum2 = 1LL * init_d[lin[st]] * init_d[lin[st]] % MOD; return; } int mid = (st + dr) / 2; build(nod * 2, st, mid); build(nod * 2 + 1, mid + 1, dr); aint[nod] = aint[2 * nod] + aint[2 * nod + 1]; } void propag(int nod, int st, int dr) { if (st == dr || aint[nod].lazy == 0) { aint[nod].lazy = 0; return; } int mid = (st + dr) / 2; aint[nod * 2].add_val(aint[nod].lazy, st, mid); aint[nod * 2 + 1].add_val(aint[nod].lazy, mid + 1, dr); aint[nod].lazy = 0; } void update(int nod, int st, int dr, int S, int D, int val) { propag(nod, st, dr); if (dr < S || st > D) { return; } if (S <= st && dr <= D) { aint[nod].add_val(val, st, dr); return; } int mid = (st + dr) / 2; update(nod * 2, st, mid, S, D, val); update(nod * 2 + 1, mid + 1, dr, S, D, val); aint[nod] = aint[2 * nod] + aint[2 * nod + 1]; } int query(int nod, int st, int dr, int S, int D) { propag(nod, st, dr); if (D < st || dr < S) { return 0; } if (S <= st && dr <= D) { return aint[nod].sum2; } int mid = (st + dr) / 2; return (query(nod * 2, st, mid, S, D) + query(nod * 2 + 1, mid + 1, dr, S, D)) % MOD; } void predfs(int nod, int tata, int dist) { init_d[nod] = dist; lin[++len] = nod; fst[nod] = len; for (auto it : graph[nod]) { if (it.first == tata) { continue; } predfs(it.first, nod, (dist + it.second) % MOD); } lst[nod] = len; } void dfs(int nod, int tata) { for (auto it : queries[nod]) { ans[it.second] = ((2 * query(1, 1, n, fst[it.first], lst[it.first]) - query(1, 1, n, 1, n)) % MOD + MOD) % MOD; } for (auto it : graph[nod]) { if (it.first == tata) { continue; } update(1, 1, n, 1, n, it.second); update(1, 1, n, fst[it.first], lst[it.first], (2 * MOD - 2 * it.second) % MOD); dfs(it.first, nod); update(1, 1, n, fst[it.first], lst[it.first], 2 * it.second % MOD); update(1, 1, n, 1, n, (MOD - it.second) % MOD); } } int main() { scanf("%d", &n); for (int i = 1; i < n; i++) { int x, y, z; scanf("%d %d %d", &x, &y, &z); graph[x].push_back({y, z}); graph[y].push_back({x, z}); } predfs(1, 0, 0); build(1, 1, n); scanf("%d", &q); for (int i = 1; i <= q; i++) { int u, v; scanf("%d %d", &u, &v); queries[u].push_back({v, i}); } dfs(1, 0); for (int i = 1; i <= q; i++) { printf("%d\n", ans[i]); } return 0; }
#include <bits/stdc++.h> using namespace std; const long long MAX_N = 1e5 + 10, MOD = 1e9 + 7, MAX_L = 23; long long n, q; vector<pair<long long, long long>> adj[MAX_N]; long long sz[MAX_N], dis[MAX_N], fazir[MAX_N], fazir2[MAX_N], fabal[MAX_N], fabal2[MAX_N], lca[MAX_N][MAX_L + 10], fasta1[MAX_N]; void down(long long v, long long par = 0, long long w = 0) { sz[v] = 1; dis[v] = dis[par] + 1; fasta1[v] = (fasta1[par] + w) % MOD; lca[v][0] = par; for (long long i = 1; i < MAX_L; i++) { lca[v][i] = lca[lca[v][i - 1]][i - 1]; } for (auto u : adj[v]) { if (u.first != par) { down(u.first, v, u.second); sz[v] += sz[u.first]; fazir[v] += (((u.second * sz[u.first]) % MOD) + fazir[u.first]) % MOD; fazir[v] %= MOD; fazir2[v] += ((((u.second * u.second % MOD * sz[u.first] % MOD) + fazir2[u.first]) % MOD) + (2 * u.second % MOD * fazir[u.first] % MOD)) % MOD; fazir2[v] %= MOD; } } } void up(long long v, long long par = 0, long long w = 0) { if (v != 1) { fabal[v] = ((fabal[par] + (w * (n - sz[v]) % MOD)) % MOD) + (((fazir[par] - (((w * sz[v] % MOD) + fazir[v]) % MOD)) + MOD) % MOD); fabal[v] %= MOD; fabal2[v] = w * w % MOD * (n - sz[v]) % MOD; fabal2[v] %= MOD; fabal2[v] += fabal2[par]; fabal2[v] %= MOD; fabal2[v] += 2 * w % MOD * fabal[par] % MOD; fabal2[v] %= MOD; fabal2[v] += (((fazir2[par] - (((w * w % MOD * sz[v] % MOD) + fazir2[v]) % MOD + (2 * w % MOD * fazir[v] % MOD)) % MOD) % MOD) + MOD) % MOD; fabal2[v] %= MOD; fabal2[v] += 2 * w % MOD * ((((fazir[par] - (((w * sz[v] % MOD) + fazir[v]) % MOD)) % MOD) + MOD) % MOD); fabal2[v] %= MOD; } for (auto u : adj[v]) { if (u.first != par) { up(u.first, v, u.second); } } } long long get_par(long long v, long long k) { for (long long i = 0; i < MAX_L; i++) { if (k >> i & 1) { v = lca[v][i]; } } return v; } long long get_lca(long long v, long long u) { if (dis[v] < dis[u]) { swap(v, u); } v = get_par(v, dis[v] - dis[u]); if (u == v) { return v; } for (long long i = MAX_L - 1; i >= 0; i--) { if (lca[v][i] != lca[u][i]) { v = lca[v][i]; u = lca[u][i]; } } return lca[v][0]; } int32_t main() { ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0); cin >> n; for (long long i = 0; i < n - 1; i++) { long long a, b, c; cin >> a >> b >> c; adj[a].push_back({b, c}); adj[b].push_back({a, c}); } dis[0] = -1; down(1); up(1); cin >> q; while (q--) { long long u, v, lc; long long ans = 0, fas; cin >> u >> v; lc = get_lca(u, v); fas = (((fasta1[v] + fasta1[u]) % MOD) - (2 * fasta1[lc] % MOD) + MOD) % MOD; if (lc == v) { ans = (((fazir2[u] + fabal2[u]) % MOD) - (((((fas * fas % MOD) * (n - sz[v])) % MOD) + fabal2[v] + ((2 * fas % MOD * fabal[v]) % MOD)) % MOD) + MOD) % MOD; } else { ans = ((fas * fas % MOD * sz[v]) % MOD) + fazir2[v] + ((2 * fas % MOD * fazir[v]) % MOD); } ans %= MOD; ans *= 2; ans %= MOD; ans -= ((fazir2[u] + fabal2[u]) % MOD); ans %= MOD; cout << (ans + MOD) % MOD << "\n"; } }
#include <bits/stdc++.h> using namespace std; const int Nmax = 100005, Mod = 1e9 + 7; vector<pair<int, int>> G[Nmax]; int SumDown[Nmax], SumDownS[Nmax], SumUp[Nmax], SumUpS[Nmax], Total[Nmax]; int Subtree[Nmax], H[Nmax]; int Father[17][Nmax], Lvl[Nmax]; int firstE[Nmax], lastE[Nmax]; int N, E; void dfs1(const int node, const int father) { firstE[node] = ++E; Subtree[node] = 1; for (auto& p : G[node]) { if (p.first == father) continue; Father[0][p.first] = node; Lvl[p.first] = Lvl[node] + 1; H[p.first] = (H[node] + p.second) % Mod; dfs1(p.first, node); int x = Subtree[p.first]; Subtree[node] += x; SumDown[node] = (SumDown[node] + SumDown[p.first] + 1LL * p.second * x % Mod) % Mod; SumDownS[node] = (SumDownS[node] + SumDownS[p.first] + 1LL * p.second * p.second % Mod * x % Mod + 2LL * p.second * SumDown[p.first] % Mod) % Mod; } lastE[node] = ++E; } void dfs2(const int node, const int father, const int lastCost) { if (father != 0) { int x = Subtree[node]; int sumf = (SumDown[father] + SumUp[father]) % Mod; sumf = (sumf + Mod - (SumDown[node] + 1LL * lastCost * x) % Mod) % Mod; int sumfs = (SumDownS[father] + SumUpS[father]) % Mod; sumfs = (sumfs + Mod - (SumDownS[node] + 1LL * lastCost * lastCost % Mod * x % Mod + 2LL * lastCost * SumDown[node] % Mod) % Mod) % Mod; SumUp[node] = (sumf + 1LL * lastCost * (N - x)) % Mod; SumUpS[node] = (sumfs + 1LL * lastCost * lastCost % Mod * (N - x) % Mod + 2LL * lastCost * sumf % Mod) % Mod; } for (auto& p : G[node]) if (p.first != father) dfs2(p.first, node, p.second); } void buildAscensors() { for (int k = 1; k < 17; ++k) for (int i = 1; i <= N; ++i) Father[k][i] = Father[k - 1][Father[k - 1][i]]; } inline bool isAscensor(int node, int asc) { return firstE[asc] <= firstE[node] && lastE[node] <= lastE[asc]; } int lca(int x, int y) { if (isAscensor(x, y)) return y; if (isAscensor(y, x)) return x; for (int k = 16; k >= 0; --k) if (!isAscensor(y, Father[k][x])) x = Father[k][x]; return Father[0][x]; } int main() { ios::sync_with_stdio(false); cin >> N; for (int i = 1; i < N; ++i) { int x, y, c; cin >> x >> y >> c; c %= Mod; G[x].push_back({y, c}); G[y].push_back({x, c}); } dfs1(1, 0); Father[0][1] = 1; dfs2(1, 0, 0); buildAscensors(); for (int i = 1; i <= N; ++i) Total[i] = (SumDownS[i] + SumUpS[i]) % Mod; int Q; cin >> Q; while (Q--) { int x, y; cin >> x >> y; int ans = 0; if (!isAscensor(x, y)) { ans = (Mod - Total[x]) % Mod; int l = lca(x, y); int dist = ((H[x] - H[l] + Mod) % Mod + (H[y] - H[l] + Mod) % Mod) % Mod; int add = (SumDownS[y] + 1LL * dist * dist % Mod * Subtree[y] % Mod + 2LL * dist * SumDown[y] % Mod) % Mod; ans = (ans + add) % Mod; ans = (ans + add) % Mod; } else { ans = Total[x]; int dist = (H[x] - H[y]) % Mod; int add = (SumUpS[y] + 1LL * dist * dist % Mod * (N - Subtree[y]) % Mod + 2LL * dist * SumUp[y] % Mod) % Mod; add = (Mod - add) % Mod; ans = (ans + add) % Mod; ans = (ans + add) % Mod; } cout << ans << '\n'; } }
#include <bits/stdc++.h> using namespace std; int m, tot; long long n; int head[100010], to[300010], net[300010]; long long val[300010], mod = 1000000007; void add(int x, int y, int c) { net[++tot] = head[x], head[x] = tot, to[tot] = y, val[tot] = c; } int deep[100010], son[100010], fa[100010], top[100010]; struct your { long long dis, sqr, tre; } dp[100010], sum[100010], all[100010]; long long dis[100010], size[100010]; void dfs(int x) { deep[x] = deep[fa[x]] + 1, size[x] = 1; for (int i = head[x]; i; i = net[i]) if (to[i] != fa[x]) { dis[to[i]] = (dis[x] + val[i]) % mod, fa[to[i]] = x, dfs(to[i]), size[x] += size[to[i]]; if (size[to[i]] > size[son[x]]) son[x] = to[i]; dp[x].dis = (dp[x].dis + dp[to[i]].dis % mod + size[to[i]] * val[i] % mod) % mod; long long tmp = size[to[i]] * val[i] % mod * val[i] % mod; long long nmp = (dp[to[i]].sqr + 2 * val[i] * dp[to[i]].dis % mod) % mod; dp[x].sqr = (dp[x].sqr + tmp + nmp) % mod; } } void dfs2(int x) { for (int i = head[x]; i; i = net[i]) { if (to[i] == fa[x]) continue; long long tmp = (sum[x].dis + (n - 2 * size[to[i]]) * val[i]) % mod; long long nmp = (dp[x].dis - dp[to[i]].dis + mod) % mod; sum[to[i]].dis = (tmp + nmp) % mod; tmp = (sum[x].sqr + 2 * sum[x].dis * val[i] % mod + (n - size[x]) * val[i] % mod * val[i] % mod) % mod; long long dx, dy, dc; dx = ((dp[x].sqr - dp[to[i]].sqr - 2 * val[i] * dp[to[i]].dis % mod - size[to[i]] * val[i] % mod * val[i] % mod) % mod + mod) % mod; dy = (size[x] - size[to[i]]) * val[i] % mod * val[i] % mod; dc = (2 * val[i] * (dp[x].dis - dp[to[i]].dis - val[i] * size[to[i]] % mod) % mod + mod) % mod; sum[to[i]].sqr = (tmp + dx + dy + dc) % mod; dfs2(to[i]); } } void dfs3(int x, int temp) { top[x] = temp; if (son[x]) dfs3(son[x], temp); for (int i = head[x]; i; i = net[i]) if (to[i] != fa[x] && to[i] != son[x]) dfs3(to[i], to[i]); } int lca(int x, int y) { while (top[x] != top[y]) { if (deep[top[x]] < deep[top[y]]) swap(x, y); x = fa[top[x]]; } return deep[x] < deep[y] ? x : y; } void check(int x, int y); int main() { scanf("%lld", &n); for (int x, y, c, i = 1; i < n; i++) scanf("%d%d%d", &x, &y, &c), add(x, y, c), add(y, x, c); dfs(1), dfs2(1), dfs3(1, 1); for (int i = 1; i <= n; i++) { all[i].dis = (sum[i].dis + dp[i].dis) % mod; all[i].sqr = (sum[i].sqr + dp[i].sqr) % mod; all[i].tre = (sum[i].tre + dp[i].tre) % mod; } scanf("%d", &m); for (int x, y, i = 1; i <= m; i++) scanf("%d%d", &x, &y), check(x, y); return 0; } void check(int x, int y) { int l = lca(x, y); if (l != x && l != y) { long long c = ((dis[x] + dis[y] - 2 * dis[l]) % mod + mod) % mod; long long tmp = (dp[y].sqr + (long long)c * c % mod * size[y] % mod + 2 * c * dp[y].dis % mod) % mod; printf("%lld\n", (2 * tmp % mod - all[x].sqr + mod) % mod); } else if (l == x) { long long c = ((dis[x] + dis[y] - 2 * dis[l]) % mod + mod) % mod; long long tmp = (dp[y].sqr + (long long)c * c % mod * size[y] % mod + 2 * c * dp[y].dis % mod) % mod; printf("%lld\n", (2 * tmp % mod - all[x].sqr + mod) % mod); } else if (l == y) { long long c = ((dis[x] + dis[y] - 2 * dis[l]) % mod + mod) % mod; long long tmp = (sum[y].sqr + (long long)c * c % mod * (n - size[y]) % mod + 2 * c * sum[y].dis % mod) % mod; printf("%lld\n", ((all[x].sqr - 2 * tmp) % mod + mod) % mod); } }
#include <bits/stdc++.h> using namespace std; const int maxn = 100000 + 10; struct P { int to; long long dis; }; vector<P> v[maxn]; map<int, int> mp[maxn]; vector<long long> psum[maxn], sqsum[maxn]; vector<int> sz[maxn]; long long sqval[maxn]; int anc[17][maxn], dep[maxn]; int tin[maxn], tout[maxn], tick; void dfs0(int x, int f, int d) { tin[x] = tick++; dep[x] = d; anc[0][x] = f; for (int i = 1; i < 17; i++) anc[i][x] = anc[i - 1][anc[i - 1][x]]; for (auto i : v[x]) if (f != i.to) dfs0(i.to, x, (i.dis + d) % 1000000007); tout[x] = tick++; } inline bool isfa(int x, int y) { return tin[x] <= tin[y] && tout[x] >= tout[y]; } int LCA(int x, int y) { if (isfa(x, y)) return x; if (isfa(y, x)) return y; for (int i = 16; i >= 0; i--) if (!isfa(anc[i][x], y)) x = anc[i][x]; return anc[0][x]; } int getlen(int x, int y) { int lca = LCA(x, y), ret = (dep[x] + dep[y] - 2 * dep[lca]) % 1000000007; if (ret < 0) ret += 1000000007; return ret; } inline long long cal_add_s(const P &i, int id) { return sqsum[i.to][id] + (i.dis * i.dis % 1000000007) * sz[i.to][id] + 2 * i.dis * psum[i.to][id]; } inline long long cal_add_p(const P &i, int id) { return psum[i.to][id] + sz[i.to][id] * i.dis; } int n, cnt[maxn]; void dfs(int x, int id) { if (psum[x][id] != -1) return; sz[x][id] = 1; long long &ans1 = psum[x][id]; long long &ans2 = sqsum[x][id]; ans1 = 0; if (v[x].size() == 1) return; for (auto i : v[x]) if (i.to != v[x][id].to) { int id2 = mp[i.to][x]; dfs(i.to, id2); ans1 = (ans1 + cal_add_p(i, id2)) % 1000000007; ans2 = (ans2 + cal_add_s(i, id2)) % 1000000007; sz[x][id] += sz[i.to][id2]; } if (++cnt[x] == 2) { int id2 = mp[v[x][id].to][x]; long long tot1 = ans1 + cal_add_p(v[x][id], id2); tot1 %= 1000000007; long long tot2 = ans2 + cal_add_s(v[x][id], id2); tot2 %= 1000000007; int totsz = sz[x][id] + sz[v[x][id].to][id2]; for (int i = 0; i < v[x].size(); i++) if (psum[x][i] == -1) { int id3 = mp[v[x][i].to][x]; assert(psum[v[x][i].to][id3] != -1); psum[x][i] = tot1 - cal_add_p(v[x][i], id3) % 1000000007; if (psum[x][i] < 0) psum[x][i] += 1000000007; sqsum[x][i] = tot2 - cal_add_s(v[x][i], id3) % 1000000007; if (sqsum[x][i] < 0) sqsum[x][i] += 1000000007; sz[x][i] = totsz - sz[v[x][i].to][id3]; } } } long long getval(int x) { long long ret = 0; for (auto i : v[x]) { int id = mp[i.to][x]; dfs(i.to, id); ret = (ret + cal_add_s(i, id)) % 1000000007; } return ret; } long long query(int u, int v) { long long ret = 0LL; if (!isfa(v, u)) { ret = -sqval[u] + 1000000007; int id = mp[v][anc[0][v]]; long long dis = getlen(u, v), add = (dis * dis % 1000000007) * sz[v][id]; add += sqsum[v][id]; add += 2 * dis * psum[v][id]; add %= 1000000007; return (ret + 2 * add) % 1000000007; } else if (v == 1) return sqval[u]; else { ret = sqval[u]; int v2 = anc[0][v], id = mp[v2][v]; long long dis = dep[u] - dep[v2]; if (dis < 0) dis += 1000000007; long long sub = (dis * dis % 1000000007) * sz[v2][id]; sub += sqsum[v2][id]; sub += 2 * dis * psum[v2][id]; sub %= 1000000007; return ((ret - 2 * sub) % 1000000007 + 1000000007) % 1000000007; } } int main() { scanf("%d", &n); for (int i = 1; i < n; i++) { int x, y; long long dis; scanf("%d%d%I64d", &x, &y, &dis); v[x].push_back((P){y, dis}); v[y].push_back((P){x, dis}); } for (int i = 1; i <= n; i++) { psum[i].resize(v[i].size()); sqsum[i].resize(v[i].size()); sz[i].resize(v[i].size()); for (int j = 0; j < v[i].size(); j++) mp[i][v[i][j].to] = j, psum[i][j] = -1; } dfs0(1, 1, 0); for (int i = 1; i <= n; i++) sqval[i] = getval(i); int Q; scanf("%d", &Q); while (Q--) { int x, y; scanf("%d%d", &x, &y); printf("%I64d\n", query(x, y)); } }
#include <bits/stdc++.h> using namespace std; int ri() { int x; scanf("%d", &x); return x; } const int N = 100000, MOD = (int)1e9 + 7; vector<pair<int, int> > e[N], q[N]; int dep[N], djs[N], ans[N]; struct D { int64_t cnt, sum, sum2; D operator~() { return operator+(*this); } D operator*(int64_t o) const { return {cnt, (sum + cnt * o) % MOD, (sum2 + sum * 2 * o + o * o % MOD * cnt) % MOD}; } D operator+(const D &o) const { return {cnt + o.cnt, (sum + o.sum) % MOD, (sum2 + o.sum2) % MOD}; } D operator-(const D &o) const { return {cnt - o.cnt, (sum - o.sum) % MOD, (sum2 - o.sum2) % MOD}; } } a[N], s[N]; int find(int v) { while (djs[v] != v) djs[v] = djs[djs[v]], v = djs[v]; return v; } void dfs(int v, int p, int d) { dep[v] = d; s[v] = {1, 0, 0}; for (auto ee : e[v]) if (ee.first != p) { dfs(ee.first, v, (d + ee.second) % MOD); s[v] = s[v] + s[ee.first] * ee.second; } } void tarjan(int v, D all) { a[v] = all; djs[v] = v; for (auto qq : q[v]) if (djs[qq.first] != -1) { int x = v, y = qq.first, id = qq.second; if (id < 0) id = ~id, swap(x, y); int w = find(qq.first), d = (int64_t(dep[x]) + dep[y] - 2 * dep[w]) % MOD; ans[id] = (w == y ? a[x] - ~((a[y] - s[y]) * d) : ~(s[y] * d) - a[x]).sum2; } for (auto ee : e[v]) if (djs[ee.first] == -1) { tarjan(ee.first, (all - s[ee.first] * ee.second) * ee.second + s[ee.first]); djs[ee.first] = v; } } int main() { int n = ri(); for (int i = (0); i < (n - 1); i++) { int v = ri() - 1, u = ri() - 1, w = ri(); e[v].push_back({u, w}); e[u].push_back({v, w}); } int m = ri(); for (int i = (0); i < (m); i++) { int v = ri() - 1, u = ri() - 1; q[v].push_back({u, i}); q[u].push_back({v, ~i}); } dfs(0, -1, 0); fill_n(djs, n, -1); tarjan(0, s[0]); for (int i = (0); i < (m); i++) printf("%d\n", (ans[i] + MOD) % MOD); }
#include <bits/stdc++.h> using namespace std; const long long N = 1e5 + 10, mod = 1e9 + 7, lg = 16 + 2; long long n, q, par[N][lg], sumup[N][lg], tvin[N][lg], sumin[N][lg], cntin[N][lg], sumst[N], tvst[N], cntst[N], updtv[N], updsum[N], updcnt[N], h[N]; vector<pair<long long, long long> > gr[N]; long long mrg(long long ftv, long long fsum, long long fcnt, long long add) { return 1ll * (1ll * ftv + 1ll * fsum * add % mod * 2 % mod + 1ll * add * add % mod * fcnt % mod) % mod; } void getSt(long long v, long long par = -1) { for (auto p : gr[v]) { long long u = p.first, w = p.second; if (u != par) { getSt(u, v); updtv[u] = mrg(tvst[u], sumst[u], cntst[u], w), tvst[v] = (tvst[v] + updtv[u]) % mod; updsum[u] = (1ll * cntst[u] * w % mod + sumst[u]) % mod, sumst[v] = (sumst[v] + updsum[u]) % mod; updcnt[u] = cntst[u], cntst[v] = cntst[v] + updcnt[u]; } } cntst[v]++; } void getPr(long long v, long long parent = -1, long long wb = -1) { if (parent != -1) { h[v] = h[parent] + 1; par[v][0] = parent, sumup[v][0] = wb; for (long long i = 1; i < lg - 1; i++) par[v][i] = par[par[v][i - 1]][i - 1], sumup[v][i] = (sumup[v][i - 1] + sumup[par[v][i - 1]][i - 1]) % mod; cntin[v][0] = cntst[parent] - updcnt[v], sumin[v][0] = (sumst[parent] - updsum[v] + mod) % mod; tvin[v][0] = mrg((tvst[parent] - updtv[v] + mod) % mod, sumin[v][0], cntin[v][0], wb); sumin[v][0] = (sumin[v][0] + 1ll * cntin[v][0] * wb % mod) % mod; for (long long i = 1; i < lg - 1; i++) { cntin[v][i] = (cntin[v][i - 1] + cntin[par[v][i - 1]][i - 1]) % mod; sumin[v][i] = ((sumin[v][i - 1] + 1ll * sumup[v][i - 1] * cntin[par[v][i - 1]][i - 1] % mod) % mod + sumin[par[v][i - 1]][i - 1] % mod) % mod; tvin[v][i] = (tvin[v][i - 1] + mrg(tvin[par[v][i - 1]][i - 1], sumin[par[v][i - 1]][i - 1], cntin[par[v][i - 1]][i - 1], sumup[v][i - 1])) % mod; } } for (auto p : gr[v]) { long long u = p.first, w = p.second; if (u != parent) getPr(u, v, w); } } bool isAnc(long long v, long long u) { long long diff = h[v] - h[u]; if (diff <= 0) return false; for (long long i = 0; i < lg - 1; i++) if (((diff >> i) & 1)) v = par[v][i]; if (v == u) return true; return false; } long long AnsAnc(long long v, long long u) { long long pst = tvst[v], rtr = 0, sumrn = 0; long long diff = h[v] - h[u]; for (long long i = lg - 1; i >= 0; i--) { if (((diff >> i) & 1)) { rtr = (rtr + mrg(tvin[v][i], sumin[v][i], cntin[v][i], sumrn)) % mod; sumrn = (sumrn + sumup[v][i]) % mod; v = par[v][i]; } } return (rtr + pst) % mod; } long long getSum(long long v, long long u) { if (h[u] > h[v]) swap(u, v); long long diff = h[v] - h[u], rtr = 0; for (long long i = 0; i < lg - 1; i++) { if (((diff >> i) & 1)) rtr = (rtr + sumup[v][i]) % mod, v = par[v][i]; } if (v == u) return rtr; for (long long i = lg - 1; i >= 0; i--) { if (par[v][i] != par[u][i]) { rtr = ((rtr + sumup[v][i]) % mod + sumup[u][i]) % mod; v = par[v][i], u = par[u][i]; } } rtr = ((rtr + sumup[v][0]) % mod + sumup[u][0]) % mod; return rtr; } long long AnsN(long long v, long long u) { long long sum = getSum(v, u); return mrg(tvst[u], sumst[u], cntst[u], sum); } int32_t main() { ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0); cin >> n; for (long long i = 0; i < n - 1; i++) { long long x, y, w; cin >> x >> y >> w; x--, y--; gr[x].push_back({y, w}); gr[y].push_back({x, w}); } getSt(0); getPr(0); cin >> q; while (q--) { long long x, y; cin >> x >> y; x--, y--; long long rtr; if (isAnc(x, y)) rtr = AnsAnc(x, y); else rtr = AnsN(x, y); long long mn = AnsAnc(x, 0); rtr = ((rtr * 2 - mn) % mod + mod) % mod; cout << rtr << "\n"; } return 0; }
#include <bits/stdc++.h> using namespace std; struct node { long long t, d, g, h, s, ds, dq, dis, sum; } A[100100]; int p[100100], nxt[2 * 100100], C[2 * 100100], V[2 * 100100], f[100100], g[100100][19], n, q, i, ed; int gi() { int s = 0; char c = getchar(); while (c < '0' || c > '9') c = getchar(); while (c >= '0' && c <= '9') s = s * 10 + c - '0', c = getchar(); return s; } void Add(int u, int v, int c) { V[++ed] = v, C[ed] = c, nxt[ed] = p[u], p[u] = ed; } long long sqr(long long x) { return (x * x) % 1000000007; }; long long Mul(long long x, long long y) { return ((x % 1000000007) * y) % 1000000007; } void Dfs(int x, int fa) { f[x] = fa, A[x].s = 1, A[x].t = A[f[x]].t + 1; for (int i = p[x]; i != -1; i = nxt[i]) { int v = V[i]; if (v == fa) continue; A[v].d = (A[x].d + C[i]) % 1000000007; A[v].g = (A[x].g + A[v].d) % 1000000007; A[v].h = (A[x].h + sqr(A[v].d)) % 1000000007; Dfs(v, x); A[x].s = (A[x].s + A[v].s) % 1000000007; A[x].ds = (A[x].ds + A[v].ds + A[v].s * C[i]) % 1000000007; A[x].dq = (A[x].dq + A[v].dq + Mul(A[v].s, sqr(C[i])) + 2LL * Mul(A[v].ds, C[i])) % 1000000007; } } void Calc(int x, long long c) { A[x].dis = (A[f[x]].dis - Mul(A[x].s, c) + Mul((n - A[x].s), c)) % 1000000007; A[x].sum = (A[f[x]].sum + Mul(n, sqr(c))) % 1000000007; A[x].sum = (A[x].sum - 2LL * Mul(A[x].ds + Mul(A[x].s, c), c)) % 1000000007; A[x].sum = (A[x].sum + 2LL * Mul(A[x].dis - A[x].ds - Mul(n - A[x].s, c), c)) % 1000000007; for (int i = p[x]; i != -1; i = nxt[i]) if (V[i] != f[x]) Calc(V[i], C[i]); } int Lca(int u, int v) { if (A[u].t < A[v].t) swap(u, v); for (int i = 18; i >= 0; i--) if (A[g[u][i]].t >= A[v].t) u = g[u][i]; if (u == v) return u; for (int i = 18; i >= 0; i--) if (g[u][i] != g[v][i]) u = g[u][i], v = g[v][i]; return f[u]; } int main() { memset(p, -1, sizeof(p)); scanf("%d", &n); for (i = 1; i < n; i++) { int u = gi(), v = gi(), c = gi(); Add(u, v, c), Add(v, u, c); } Dfs(1, 0); for (i = 1; i <= n; i++) g[i][0] = f[i]; for (i = 1; i <= 17; i++) for (int j = 1; j <= n; j++) g[j][i] = g[g[j][i - 1]][i - 1]; for (i = 1; i <= n; i++) A[1].sum += sqr(A[i].d), A[1].dis += A[i].d; A[1].sum %= 1000000007, A[1].dis %= 1000000007; for (i = p[1]; i != -1; i = nxt[i]) Calc(V[i], C[i]); scanf("%d", &q); for (i = 1; i <= q; i++) { int u = gi(), v = gi(); int z = Lca(u, v); long long ans, o, h, b; if (z == v && u != v) { o = (A[v].d - A[f[v]].d) % 1000000007; b = (A[u].d - A[f[v]].d) % 1000000007; h = (A[f[v]].dis - A[v].ds - Mul(o, A[v].s)) % 1000000007; ans = (A[f[v]].sum - A[v].dq - Mul(A[v].s, sqr(o)) - 2LL * Mul(A[v].ds, o)) % 1000000007; ans = (ans + Mul(n - A[v].s, sqr(b)) + 2LL * Mul(h, b)) % 1000000007; ans = (A[u].sum - 2 * ans) % 1000000007; if (v == 1) ans = A[u].sum; } else { long long det = (A[u].d + A[v].d - 2LL * A[z].d) % 1000000007; ans = (A[v].dq + Mul(A[v].s, sqr(det))) % 1000000007; o = (2LL * Mul(A[v].ds, det)) % 1000000007; ans = (2LL * (ans + o) - A[u].sum) % 1000000007; } printf("%I64d\n", (1000000007 + ans) % 1000000007); } }
#include <bits/stdc++.h> using namespace std; const int mod = 1e9 + 7; struct sol_t { int many; int sum2; int sum1; sol_t() { many = sum1 = sum2 = 0; } void include(const sol_t &other) { many = (many + other.many) % mod; sum2 = (sum2 + other.sum2) % mod; sum1 = (sum1 + other.sum1) % mod; } void uninclude(const sol_t &other) { many = (many - other.many + mod) % mod; sum2 = (sum2 - other.sum2 + mod) % mod; sum1 = (sum1 - other.sum1 + mod) % mod; } void increase_all(int by) { sum2 = (sum2 + (long long)many * by % mod * by % mod + 2LL * by * sum1) % mod; sum1 = (sum1 + (long long)many * by) % mod; } }; vector<pair<int, int> > adj[100000]; int height[100000]; long long depth[100000]; sol_t down[100000]; sol_t up[100000]; sol_t full[100000]; vector<int> path; vector<long long> pathsum; vector<pair<int, int> > queries[100000]; sol_t result[100000]; int logn; int parent[100000][16 + 1]; int goup(int a, int dist) { for (int l = 0; (1 << l) <= dist; l++) if (dist & (1 << l)) a = parent[a][l]; return a; } int lca(int a, int b) { if (height[a] < height[b]) swap(a, b); a = goup(a, height[a] - height[b]); if (a == b) return a; for (int l = logn; l >= 0; l--) if (parent[a][l] != parent[b][l]) { a = parent[a][l]; b = parent[b][l]; } return parent[a][0]; } long long dist(int a, int b) { return depth[a] + depth[b] - 2 * depth[lca(a, b)]; } void dfs3(int u, int p, long long sum = 0) { path.push_back(u); pathsum.push_back(sum); for (pair<int, int> query : queries[u]) { int v = query.first; int qid = query.second; if (height[v] < (int)path.size() && path[height[v]] == v) { result[qid].include(full[u]); sol_t temp = up[v]; temp.increase_all((sum - pathsum[height[v]]) % mod); result[qid].uninclude(temp); result[qid].uninclude(temp); } else { result[qid].uninclude(full[u]); sol_t temp = down[v]; temp.increase_all(dist(u, v) % mod); result[qid].include(temp); result[qid].include(temp); } } for (const pair<int, int> &pp : adj[u]) { int v2 = pp.first, dist = pp.second; if (v2 == p) continue; dfs3(v2, u, sum + dist); } path.pop_back(); pathsum.pop_back(); } void dfs2(int v, int p, sol_t got) { up[v] = got; full[v] = up[v]; full[v].include(down[v]); vector<pair<int, int> > child; for (const pair<int, int> &pp : adj[v]) { int v2 = pp.first, dist = pp.second; if (v2 == p) continue; child.push_back(make_pair(v2, dist)); } int nc = child.size(); sol_t sum = down[v]; for (int c = 0; c < nc; c++) { sol_t just = sum; { sol_t temp = down[child[c].first]; temp.increase_all(child[c].second); just.uninclude(temp); } just.include(got); just.increase_all(child[c].second); dfs2(child[c].first, v, just); } } void dfs(int v, int p, int h, long long d) { for (int l = 1; l <= logn; l++) parent[v][l] = parent[parent[v][l - 1]][l - 1]; height[v] = h; depth[v] = d; down[v] = sol_t(); down[v].many = 1; for (const pair<int, int> &pp : adj[v]) { int v2 = pp.first, dist = pp.second; if (v2 == p) continue; parent[v2][0] = v; dfs(v2, v, h + 1, d + dist); sol_t temp = down[v2]; temp.increase_all(dist); down[v].include(temp); } } int main() { int n; scanf("%d", &n); logn = 0; while ((1 << (logn + 1)) <= n) logn++; for (int i = 0; i < n - 1; i++) { int a, b, c; scanf("%d %d %d", &a, &b, &c); a--, b--; adj[a].push_back(make_pair(b, c)); adj[b].push_back(make_pair(a, c)); } parent[0][0] = 0; dfs(0, -1, 0, 0); sol_t temp; dfs2(0, -1, temp); int nq; scanf("%d", &nq); for (int q = 0; q < nq; q++) { int u, v; scanf("%d %d", &u, &v); u--, v--; queries[u].push_back(make_pair(v, q)); } dfs3(0, -1); for (int q = 0; q < nq; q++) printf("%d\n", result[q].sum2); return 0; }
#include <bits/stdc++.h> using namespace std; const int MAXL = 20, mod = 1e9 + 7; int timer = 0, n, k, l, w, q, used[100005], ans, tin[100005], tout[100005]; long long sz[100005], dist[100005], distsq[100005], updist[100005], updistsq[100005], two[100005][20], twodist[100005][20]; vector<long long> d[100005]; vector<int> c[100005]; void dfs(int v, int p = 0, int w = 0) { tin[v] = timer++; sz[v] = 1; used[v] = 1; two[v][0] = p; twodist[v][0] = w; for (int i = 1; i < MAXL; i++) { twodist[v][i] = (twodist[v][i - 1] + twodist[two[v][i - 1]][i - 1]) % mod; two[v][i] = two[two[v][i - 1]][i - 1]; } for (int i = 0; i < (int)c[v].size(); i++) if (used[c[v][i]] == 0) { dfs(c[v][i], v, d[v][i]); sz[v] += sz[c[v][i]]; dist[v] = (dist[v] + dist[c[v][i]] + sz[c[v][i]] * d[v][i]) % mod; distsq[v] = (distsq[v] + distsq[c[v][i]] + 2 * d[v][i] * dist[c[v][i]] + d[v][i] * ((d[v][i] * sz[c[v][i]]) % mod)) % mod; } tout[v] = timer++; } void dfs2(int v) { used[v] = 1; for (int i = 0; i < (int)c[v].size(); i++) if (used[c[v][i]] == 0) { updist[c[v][i]] = ((updist[v] + dist[v] - (dist[c[v][i]] + sz[c[v][i]] * d[v][i]) + (n - sz[c[v][i]]) * d[v][i]) % mod + mod) % mod; long long l = ((updistsq[v] + distsq[v] - (distsq[c[v][i]] + 2 * d[v][i] * dist[c[v][i]] + d[v][i] * ((d[v][i] * sz[c[v][i]]) % mod))) % mod + mod) % mod; updistsq[c[v][i]] = ((l - d[v][i] * ((d[v][i] * (n - sz[c[v][i]])) % mod) + 2 * d[v][i] * updist[c[v][i]]) % mod + mod) % mod; dfs2(c[v][i]); } } bool upper(int v, int u) { return (tin[v] <= tin[u] && tout[v] >= tout[u]); } int lca(int a, int b) { int res = 0; if (a == b) return 0; if (upper(a, b)) { for (int i = MAXL - 1; i >= 0; i--) if (!upper(two[b][i], a)) { res = (res + twodist[b][i]) % mod; b = two[b][i]; } return (res + twodist[b][0]) % mod; } if (upper(b, a)) { for (int i = MAXL - 1; i >= 0; i--) if (!upper(two[a][i], b)) { res = (res + twodist[a][i]) % mod; a = two[a][i]; } return (res + twodist[a][0]) % mod; } for (int i = MAXL - 1; i >= 0; i--) if (!upper(two[a][i], b)) { res = (res + twodist[a][i]) % mod; a = two[a][i]; } for (int i = MAXL - 1; i >= 0; i--) if (!upper(two[b][i], a)) { res = (res + twodist[b][i]) % mod; b = two[b][i]; } return ((res + twodist[a][0]) % mod + twodist[b][0]) % mod; } int main() { scanf("%d", &n); for (int i = 0; i < n - 1; i++) { scanf("%d%d%d", &k, &l, &w); k--; l--; c[k].push_back(l); c[l].push_back(k); d[k].push_back(w); d[l].push_back(w); } dfs(0); for (int i = 0; i < n; i++) used[i] = 0; dfs2(0); for (int i = 0; i < n; i++) used[i] = 0; scanf("%d", &q); for (int qq = 0; qq < q; qq++) { scanf("%d%d", &k, &l); k--; l--; long long x = lca(k, l); if (upper(l, k)) ans = ((((distsq[k] + updistsq[k] - 2 * (updistsq[l] + x * (x * (n - sz[l]) % mod) + 2 * x * updist[l])) % mod) + mod) % mod) % mod; else ans = ((2 * (x * ((x * sz[l]) % mod) + distsq[l] + 2 * x * dist[l]) - (distsq[k] + updistsq[k])) % mod + mod) % mod; printf("%d\n", ans); } return 0; }
#include <bits/stdc++.h> using namespace std; char ss[1 << 17], *A = ss, *B = ss; inline char gc() { if (A == B) { B = (A = ss) + fread(ss, 1, 1 << 17, stdin); if (A == B) return EOF; } return *A++; } template <class T> inline void read(T& x) { static char c; static int y; for (c = gc(), x = 0, y = 1; c < 48 || 57 < c; c = gc()) if (c == '-') y = -1; for (; 48 <= c && c <= 57; c = gc()) x = ((x + (x << 2)) << 1) + (c ^ '0'); x *= y; } const int mod = 1e9 + 7; struct node { int next, to, z; } w[200001]; int cnt, head[100001], f[100001][3], g[100001][3], ans, q; int top[100001], fa[100001], deep[100001], n, hs[100001]; int dis[100001]; inline int add(int x, int y) { return x + y >= mod ? x + y - mod : x + y; } inline int dec(int x, int y) { return x - y < 0 ? x - y + mod : x - y; } inline int mul(int x, int y) { return 1ll * x * y - 1ll * x * y / mod * mod; } inline void add_v(int x, int y, int z) { w[++cnt].next = head[x]; w[cnt].to = y; head[x] = cnt; w[cnt].z = z; } void dfs1(int x, int da) { f[x][0] = 1; fa[x] = da; for (int i = head[x]; i; i = w[i].next) { if (w[i].to == da) continue; deep[w[i].to] = add(deep[x], w[i].z); dis[w[i].to] = dis[x] + 1; dfs1(w[i].to, x); f[x][0] += f[w[i].to][0]; f[x][1] = add(add(f[x][1], f[w[i].to][1]), mul(f[w[i].to][0], w[i].z)); f[x][2] = add(add(f[x][2], f[w[i].to][2]), add(mul(w[i].z * 2 % mod, f[w[i].to][1]), mul(mul(w[i].z, w[i].z), f[w[i].to][0]))); if (f[w[i].to][0] > f[hs[x]][0]) hs[x] = w[i].to; } } void dfs2(int x, int tp) { top[x] = tp; if (hs[x]) dfs2(hs[x], tp); for (int i = head[x]; i; i = w[i].next) if (w[i].to != fa[x] && w[i].to != hs[x]) dfs2(w[i].to, w[i].to); } void dfs3(int x) { for (int i = head[x]; i; i = w[i].next) { int v = w[i].to; if (v == fa[x]) continue; g[v][0] = g[x][0] - f[v][0]; g[v][1] = dec(g[x][1], add(mul(f[v][0], w[i].z), f[v][1])); g[v][2] = dec(g[x][2], add(f[v][2], add(mul(f[v][0], mul(w[i].z, w[i].z)), mul(f[v][1], w[i].z * 2 % mod)))); g[v][2] = add(g[v][2], add(mul(mul(w[i].z, w[i].z), g[v][0]), mul(w[i].z * 2 % mod, g[v][1]))); g[v][1] = add(g[v][1], mul(w[i].z, g[v][0])); g[v][0] = add(g[v][0], f[v][0]); g[v][1] = add(g[v][1], f[v][1]); g[v][2] = add(g[v][2], f[v][2]); dfs3(v); } } inline int lca(int x, int y) { while (top[x] != top[y]) { if (dis[top[x]] < dis[top[y]]) swap(x, y); x = fa[top[x]]; } if (dis[x] < dis[y]) swap(x, y); return y; } int main() { int x, y, z; read(n); for (int i = 1; i < n; i++) { read(x), read(y), read(z); add_v(x, y, z); add_v(y, x, z); } dfs1(1, 0); dfs2(1, 1); g[1][0] = f[1][0], g[1][1] = f[1][1], g[1][2] = f[1][2]; dfs3(1); read(q); while (q--) { read(x), read(y); int l = lca(x, y); if (l == y) { z = dec(deep[x], deep[y]); ans = mul(mul(z, z), dec(g[y][0], f[y][0])); ans = add(ans, dec(g[y][2], f[y][2])); ans = add(ans, mul(z * 2 % mod, dec(g[y][1], f[y][1]))); ans = dec(g[x][2], ans * 2 % mod); printf("%d\n", ans); } else { z = dec(add(deep[x], deep[y]), deep[l] * 2 % mod); ans = add(mul(f[y][0], mul(z, z)), mul(f[y][1], z * 2 % mod)); ans = add(ans, f[y][2]); ans = dec(ans * 2 % mod, g[x][2]); printf("%d\n", ans); } } return 0; }
#include <bits/stdc++.h> struct fur { int a, b, i; long long ans; bool operator<(fur k) const { return a < k.a; } } ans[111111]; struct Trees { long long a, b, lazy; } tree[1111111]; int totree[1111111], tonum[1111111], fa[1111111], lfa[1111111], treetot, line[1111111], right[1111111], next[1111111], tail[1111111], val[1111111], num[1111111], n, tot, q, ansstart[1111111], done[1111111], nowat; long long inilength[1111111]; bool cmp(fur x, fur y) { return x.i < y.i; } void dfs(int k, long long length) { totree[k] = ++treetot; tonum[treetot] = k; line[++line[0]] = k; right[k] = k; inilength[k] = length; for (int i = next[k]; i; i = next[i]) if (fa[k] != num[i]) { fa[num[i]] = k; lfa[num[i]] = val[i]; dfs(num[i], length + val[i]); right[k] = right[num[i]]; } line[++line[0]] = k; } void ini(int now, int l, int r) { if (l == r) { tree[now].b = inilength[tonum[l]] % 1000000007; tree[now].a = (tree[now].b * tree[now].b % 1000000007); return; } int p = (l + r) / 2; ini(now * 2, l, p); ini(now * 2 + 1, p + 1, r); tree[now].a = (tree[now * 2].a + tree[now * 2 + 1].a) % 1000000007; tree[now].b = (tree[now * 2].b + tree[now * 2 + 1].b) % 1000000007; } void push_lazy(int now, int num) { if (!tree[now].lazy) return; tree[now].lazy %= 1000000007; tree[now * 2].lazy += tree[now].lazy; tree[now * 2 + 1].lazy += tree[now].lazy; tree[now].b += num * tree[now].lazy % 1000000007 + 1000000007; tree[now].a += (tree[now].lazy * tree[now].b * 2 - num * tree[now].lazy % 1000000007 * tree[now].lazy) % 1000000007 + 1000000007; tree[now].a %= 1000000007; tree[now].b %= 1000000007; tree[now].lazy = 0; } void change(int now, int l, int r, int x, int y, int num) { if (x == l && y == r) { tree[now].lazy += num; return; } int p = (l + r) / 2; push_lazy(now, r - l + 1); if (y <= p) change(now * 2, l, p, x, y, num); else if (x > p) change(now * 2 + 1, p + 1, r, x, y, num); else { change(now * 2, l, p, x, p, num); change(now * 2 + 1, p + 1, r, p + 1, y, num); } push_lazy(now * 2, p - l + 1); push_lazy(now * 2 + 1, r - p); tree[now].a = (tree[now * 2].a + tree[now * 2 + 1].a) % 1000000007; tree[now].b = (tree[now * 2].b + tree[now * 2 + 1].b) % 1000000007; } long long find(int now, int l, int r, int x, int y) { push_lazy(now, r - l + 1); if (l == x && r == y) return tree[now].a; int p = (l + r) / 2; if (y <= p) return find(now * 2, l, p, x, y); if (x > p) return find(now * 2 + 1, p + 1, r, x, y); return (find(now * 2, l, p, x, p) + find(now * 2 + 1, p + 1, r, p + 1, y)) % 1000000007; } void Output() { for (int i = 1; i <= n * 2; i++) printf("[%3d %2d %2d %2d] ", i, tree[i].a, tree[i].b, tree[i].lazy); printf("\n"); } int main() { scanf("%d", &n); for (tot = 1; tot <= n; tot++) tail[tot] = tot; for (int i = 1; i < n; i++) { int t1, t2, t3; scanf("%d%d%d", &t1, &t2, &t3); num[tail[t1] = next[tail[t1]] = ++tot] = t2; val[tot] = t3; ; num[tail[t2] = next[tail[t2]] = ++tot] = t1; val[tot] = t3; ; } dfs(1, 0); ini(1, 1, n); scanf("%d", &q); for (int i = 1; i <= q; i++) { scanf("%d%d", &ans[i].a, &ans[i].b); ans[i].i = i; } std::sort(ans + 1, ans + q + 1); for (int i = q; i >= 1; i--) ansstart[ans[i].a] = i; done[1] = 1; nowat = 1; for (int i = 2; i <= line[0]; i++) { if (done[line[i]]) { int delta = lfa[line[i]]; change(1, 1, n, 1, n, -delta); change(1, 1, n, totree[line[i]], totree[right[line[i]]], 2 * delta); nowat = fa[line[i]]; } else { int delta = lfa[line[i]]; change(1, 1, n, 1, n, delta); change(1, 1, n, totree[line[i]], totree[right[line[i]]], -2 * delta); nowat = line[i]; done[line[i]] = 1; } for (int j = ansstart[nowat]; j && ans[j].a == ans[ansstart[nowat]].a; j++) if (!ans[j].ans) { long long minus = find(1, 1, n, totree[ans[j].b], totree[right[ans[j].b]]); ans[j].ans = (minus * 2 - tree[1].a + 1000000007) % 1000000007; } } std::sort(ans + 1, ans + q + 1, cmp); for (int i = 1; i <= q; i++) printf("%I64d\n", ans[i].ans); }
#include <bits/stdc++.h> using namespace std; const int MAXN = 100100; const int LOGMAXN = 18; const int MOD = 1e+9 + 7; struct node { int xsum, xsqr, xcnt; node() : xsum(0), xsqr(0), xcnt(0) {} }; int N; vector<pair<int, int> > V[MAXN]; int dad[MAXN][LOGMAXN]; int dep[MAXN]; int sum[MAXN]; node data[MAXN]; node str[MAXN][LOGMAXN]; inline int sqr(int x) { return ((long long)x * x) % MOD; } inline int add(int a, int b) { int ret = a + b; if (ret >= MOD) ret -= MOD; return ret; } inline int sub(int a, int b) { int ret = a - b + MOD; if (ret >= MOD) ret -= MOD; return ret; } inline int mul(int a, int b) { return ((long long)a * b) % MOD; } inline int f(int curr, int k) { return add(mul(data[curr].xcnt, sqr(k)), add(mul(2, mul(k, data[curr].xsum)), data[curr].xsqr)); } namespace tr { int depth = 0; int curr_sum = 0; node build(int curr, int prev = 0) { dep[curr] = depth; sum[curr] = curr_sum; dad[curr][0] = prev; for (int i = 1; i < LOGMAXN - 1; ++i) dad[curr][i] = dad[dad[curr][i - 1]][i - 1]; node ret; ret.xcnt = 1; for (pair<int, int> nxt : V[curr]) { if (nxt.first == prev) continue; depth += 1; curr_sum = add(curr_sum, nxt.second); node get = build(nxt.first, curr); ret.xcnt = add(ret.xcnt, get.xcnt); ret.xsum = add(ret.xsum, mul(get.xcnt, nxt.second)); ret.xsum = add(ret.xsum, get.xsum); ret.xsqr = add(ret.xsqr, mul(get.xcnt, sqr(nxt.second))); ret.xsqr = add(ret.xsqr, get.xsqr); ret.xsqr = add(ret.xsqr, mul(2, mul(nxt.second, get.xsum))); curr_sum = sub(curr_sum, nxt.second); depth -= 1; } return data[curr] = ret; } void dfs(int curr, int prev = 0) { long long tmp = 0; str[curr][0].xsum = sub(data[dad[curr][0]].xsum, data[curr].xsum); str[curr][0].xsum = sub(str[curr][0].xsum, mul(data[curr].xcnt, sub(sum[curr], sum[dad[curr][0]]))); str[curr][0].xcnt = sub(data[dad[curr][0]].xcnt, data[curr].xcnt); str[curr][0].xsqr = sub(data[dad[curr][0]].xsqr, f(curr, sub(sum[curr], sum[dad[curr][0]]))); for (int i = 1; i < LOGMAXN - 1; ++i) { str[curr][i].xcnt = str[curr][i - 1].xcnt + str[dad[curr][i - 1]][i - 1].xcnt; int par1 = dad[curr][i - 1]; int par2 = dad[curr][i]; int edge_val = sub(sum[dad[curr][0]], sum[dad[par1][0]]); tmp = str[curr][i - 1].xsum + (long long)str[par1][i - 1].xsum + (long long)edge_val * str[par1][i - 1].xcnt; str[curr][i].xsum = (tmp % MOD + MOD) % MOD; int dist = sub(sum[dad[curr][0]], sum[dad[par1][0]]); str[curr][i].xsqr = add(str[curr][i - 1].xsqr, str[par1][i - 1].xsqr); str[curr][i].xsqr = add(str[curr][i].xsqr, mul(2, mul(str[par1][i - 1].xsum, dist))); str[curr][i].xsqr = add(str[curr][i].xsqr, mul(str[par1][i - 1].xcnt, sqr(dist))); } for (pair<int, int> nxt : V[curr]) { if (nxt.first == prev) continue; dfs(nxt.first, curr); } } } // namespace tr int lca(int u, int v) { if (dep[u] > dep[v]) swap(u, v); for (int i = 16; i >= 0; --i) { if (dep[v] - (1 << i) < dep[u]) continue; v = dad[v][i]; } for (int i = 16; i >= 0; --i) { int nu = dad[u][i]; int nv = dad[v][i]; if (nu == nv) continue; u = nu; v = nv; } if (u != v) u = dad[u][0]; return u; } int query(int u, int v) { int LCA = lca(u, v); int dist = sum[u] + sum[v] - 2 * sum[LCA]; if (LCA != v || u == v) return f(v, dist); int ret = data[u].xsqr; int curr = u; for (int i = 16; i >= 0; --i) { if (dep[curr] - (1 << i) < dep[v]) continue; const node get = str[curr][i]; int dist = sub(sum[u], sum[dad[curr][0]]); curr = dad[curr][i]; int tmp = add(get.xsqr, mul(sqr(dist), get.xcnt)); tmp = add(tmp, mul(2, mul(get.xsum, dist))); ret = add(ret, tmp); ret = (ret + MOD) % MOD; } return (ret % MOD + MOD) % MOD; } int main(void) { scanf("%d", &N); for (int i = 1; i < N; ++i) { int u, v, x; scanf("%d%d%d", &u, &v, &x); V[u].push_back({v, x}); V[v].push_back({u, x}); } tr::build(1); tr::dfs(1); int Q; scanf("%d", &Q); while (Q--) { int u, v; scanf("%d%d", &u, &v); int LCA = lca(u, v); int dist = sum[u] + sum[v] - 2 * sum[LCA]; printf("%d\n", (sub(mul(2, query(u, v)), query(u, 1)) % MOD + MOD) % MOD); } return 0; }
#include <bits/stdc++.h> using std::max; using std::min; using std::sort; using std::swap; const int maxn = 100007; const int maxm = 200007; const int mod = 1e9 + 7; struct E { int v, w; } e[maxm]; int first[maxn], nt[maxm], ES; inline void addE(int u, int v, int w) { e[++ES] = (E){v, w}; nt[ES] = first[u]; first[u] = ES; return; } int N, Q; int fa[maxn], dep[maxn], sz[maxn], dfn[maxn], ix, son[maxn]; long long dis[maxn], sumd[maxn], sumd2[maxn], F[maxn][2], f[maxn][2]; void dfs(int u) { sz[u] = 1; dfn[u] = ++ix; for (int v, i = first[u]; i; i = nt[i]) { v = e[i].v; if (v == fa[u]) continue; dep[v] = dep[u] + 1; dis[v] = dis[u] + e[i].w; if (dis[v] >= mod) dis[v] -= mod; fa[v] = u; dfs(v); F[u][1] = ((F[u][1] + F[v][1]) % mod + 1ll * sz[v] * e[i].w % mod * e[i].w % mod + 2ll * e[i].w * F[v][0] % mod) % mod; F[u][0] = (F[u][0] + F[v][0] + 1ll * sz[v] * e[i].w % mod) % mod; sz[u] += sz[v]; if (sz[v] > sz[son[u]]) son[u] = v; } return; } int top[maxn]; void dfs(int u, int tp) { top[u] = tp; if (son[u]) dfs(son[u], tp); for (int v, i = first[u]; i; i = nt[i]) { v = e[i].v; if (v == fa[u] || v == son[u]) continue; dfs(v, v); } return; } int LCA(int x, int y) { while (top[x] ^ top[y]) { if (dep[top[x]] < dep[top[y]]) swap(x, y); x = fa[top[x]]; } return dep[x] < dep[y] ? x : y; } void dfs2(int u) { long long d1, d2; for (int v, i = first[u]; i; i = nt[i]) { v = e[i].v; if (v == fa[u]) continue; f[v][0] = (f[u][0] + 1ll * (N - 2 * sz[v]) * e[i].w % mod) % mod; d1 = (F[v][0] + 1ll * sz[v] * e[i].w % mod) % mod; d2 = (F[v][1] + 1ll * sz[v] * e[i].w % mod * e[i].w % mod + 2ll * e[i].w * F[v][0] % mod) % mod; f[v][1] = ((f[u][1] - d2 + 1ll * (N - sz[v]) * e[i].w % mod * e[i].w % mod) % mod + (2ll * e[i].w * (f[u][0] - d1) % mod + F[v][1]) % mod) % mod; dfs2(v); } return; } int main() { scanf("%d", &N); int u, v, w; for (int i = 1; i < N; i++) scanf("%d%d%d", &u, &v, &w), addE(u, v, w), addE(v, u, w); dep[1] = 1; dfs(1); dfs(1, 1); f[1][1] = F[1][1]; f[1][0] = F[1][0]; dfs2(1); for (int i = 1; i <= N; i++) (sumd[dfn[i]] += dis[i]) %= mod, (sumd2[dfn[i]] += dis[i] * dis[i] % mod) %= mod; for (int i = 1; i <= N; i++) (sumd[i] += sumd[i - 1]) %= mod, (sumd2[i] += sumd2[i - 1]) %= mod; scanf("%d", &Q); int lca; long long re, sumv, sumv1, sumv2; while (Q--) { scanf("%d%d", &u, &v); re = 0; lca = LCA(u, v); if (u == v) { re = F[u][1]; re = 2 * re - f[u][1]; re %= mod; if (re < 0) re += mod; printf("%lld\n", re); continue; } else if (lca == v) { sumv = N - sz[v]; sumv1 = f[v][0] - F[v][0]; sumv2 = f[v][1] - F[v][1]; w = dis[u] - dis[v]; sumv2 = (sumv2 + 2ll * w * sumv1 % mod + sumv * w % mod * w % mod) % mod; re = f[u][1] - sumv2; re %= mod; if (re < 0) re += mod; re = 2 * re - f[u][1]; re %= mod; if (re < 0) re += mod; printf("%lld\n", re); continue; } sumv = sz[v]; sumv1 = sumd[dfn[v] + sz[v] - 1] - sumd[dfn[v] - 1]; if (sumv1 < 0) sumv1 += mod; sumv2 = sumd2[dfn[v] + sz[v] - 1] - sumd2[dfn[v] - 1]; if (sumv2 < 0) sumv2 += mod; re = (sumv * dis[u] % mod * dis[u] % mod + sumv2 + 2 * dis[u] * sumv1 % mod + 4 * sumv * dis[lca] % mod * dis[lca] % mod - 4 * (sumv * dis[u] % mod + sumv1) % mod * dis[lca] % mod) % mod; if (re < 0) re += mod; re = 2 * re - f[u][1]; re %= mod; if (re < 0) re += mod; printf("%lld\n", re); } return 0; }
#include <bits/stdc++.h> using namespace std; const int maxn = 1e5 + 10; const int mod = 1e9 + 7; int n; long long h[maxn], answer[maxn]; vector<pair<int, int> > t[maxn], query[maxn]; int Time = 0, st[maxn], ft[maxn]; struct node { long long d1; long long d2; long long lazy; node() { d1 = 0, d2 = 0, lazy = 0; } }; node seg[4 * maxn]; void propagate(int, int, int); int get(int id, int L, int R, int l, int r) { if (r <= L or R <= l) return 0; if (l <= L and R <= r) return seg[id].d2; propagate(id, L, R); int mid = (L + R) >> 1; return (get(2 * id + 0, L, mid, l, r) + get(2 * id + 1, mid, R, l, r)) % mod; } void add(int id, int L, int R, int l, int r, long long val) { if (r <= L or R <= l) return; if (l <= L and R <= r) { val %= mod; val = (val + mod) % mod; seg[id].d2 = (seg[id].d2 + 1ll * (R - L) * val % mod * val % mod + 2ll * val % mod * seg[id].d1 % mod) % mod; seg[id].d1 = (seg[id].d1 + 1ll * (R - L) * val % mod) % mod; seg[id].lazy = (seg[id].lazy + val) % mod; return; } propagate(id, L, R); int mid = (L + R) >> 1; add(2 * id + 0, L, mid, l, r, val); add(2 * id + 1, mid, R, l, r, val); seg[id].d1 = (seg[2 * id + 0].d1 + seg[2 * id + 1].d1) % mod; seg[id].d2 = (seg[2 * id + 0].d2 + seg[2 * id + 1].d2) % mod; } void propagate(int id, int L, int R) { if (seg[id].lazy == 0) return; int mid = (L + R) >> 1; add(2 * id + 0, L, mid, L, mid, seg[id].lazy); add(2 * id + 1, mid, R, mid, R, seg[id].lazy); seg[id].lazy = 0; } void dfs(int v, int par = -1) { for (auto Q : query[v]) { int idx = Q.first, u = Q.second; answer[idx] = 2ll * get(1, 0, n, st[u], ft[u]) % mod - get(1, 0, n, 0, n); answer[idx] = (answer[idx] + mod) % mod; } for (auto edge : t[v]) { int u = edge.first, w = edge.second; if (u != par) { add(1, 0, n, 0, n, +w); add(1, 0, n, st[u], ft[u], -2 * w); dfs(u, v); add(1, 0, n, st[u], ft[u], +2 * w); add(1, 0, n, 0, n, -w); } } } void dfs_init(int v, int par = -1) { st[v] = Time++; for (auto edge : t[v]) { int u = edge.first, w = edge.second; if (u != par) { h[u] = h[v] + w; dfs_init(u, v); } } ft[v] = Time; } int main() { ios_base::sync_with_stdio(false); cin >> n; for (int i = 0; i < n - 1; i++) { int v, u, w; cin >> v >> u >> w; v--, u--; t[v].push_back({u, w}); t[u].push_back({v, w}); } dfs_init(0); for (int i = 0; i < n; i++) add(1, 0, n, st[i], st[i] + 1, h[i]); int q; cin >> q; for (int i = 0; i < q; i++) { int v, u; cin >> v >> u; v--, u--; query[v].push_back({i, u}); } dfs(0); for (int i = 0; i < q; i++) cout << answer[i] << endl; }
#include <bits/stdc++.h> const int N = 100000 + 10, MOD = 1000000007; int n, fa[N], dep[N], size[N], son[N], top[N], map[N], dist[N]; int adj[N], to[2 * N], next[2 * N], tag[2 * N]; void link(int a, int b, int c) { static int cnt = 2; to[cnt] = b; next[cnt] = adj[a]; tag[cnt] = c; adj[a] = cnt++; } int f[N]; int down[N][3], up[N][3]; inline int sqr(int x) { return (long long)x * x % MOD; } void bfs() { static int q[N]; q[1] = dep[1] = 1; fa[1] = 0; for (int f = 1, r = 1; f <= r; ++f) { int a = q[f]; for (int i = adj[a]; i; i = next[i]) { int b = to[i], t = tag[i]; if (b != fa[a]) fa[b] = a, dep[b] = dep[a] + 1, dist[b] = (dist[a] + t) % MOD, q[++r] = b; } } for (int i = 1; i <= n; ++i) size[i] = 1; for (int i = n; i > 1; --i) size[fa[q[i]]] += size[q[i]]; for (int i = 2; i <= n; ++i) if (size[i] > size[son[fa[i]]]) son[fa[i]] = i; for (int i = 1, tot = 0; i <= n; ++i) { int a = q[i]; if (map[a]) continue; for (int b = a; b; b = son[b]) map[b] = ++tot, top[b] = a; } for (int i = n; i > 0; --i) { int a = q[i]; down[a][0] = 1; down[a][1] = down[a][2] = 0; for (int j = adj[a]; j; j = next[j]) { int b = to[j], t = tag[j]; if (b == fa[a]) continue; down[a][2] = (down[a][2] + (long long)sqr(t) * down[b][0] + 2LL * t * down[b][1] + down[b][2]) % MOD; down[a][1] = (down[a][1] + down[b][1] + (long long)down[b][0] * t) % MOD; down[a][0] += down[b][0]; } } for (int i = 1; i <= n; ++i) { int a = q[i]; f[a] = (up[a][2] + down[a][2]) % MOD; int sum[3]; memcpy(sum, up[a], sizeof sum); for (int j = adj[a]; j; j = next[j]) { int b = to[j], t = tag[j]; if (b == fa[a]) continue; sum[2] = (sum[2] + (long long)sqr(t) * down[b][0] + 2LL * t * down[b][1] + down[b][2]) % MOD; sum[1] = (sum[1] + down[b][1] + (long long)down[b][0] * t) % MOD; sum[0] += down[b][0]; } ++sum[0]; for (int j = adj[a]; j; j = next[j]) { int b = to[j], t = tag[j]; if (b == fa[a]) continue; int cur[3]; cur[2] = (sum[2] - ((long long)sqr(t) * down[b][0] + 2LL * t * down[b][1] + down[b][2])) % MOD; cur[1] = (sum[1] - (down[b][1] + (long long)down[b][0] * t)) % MOD; cur[0] = sum[0] - down[b][0]; up[b][2] = ((long long)sqr(t) * cur[0] + 2LL * t * cur[1] + cur[2]) % MOD; up[b][1] = (cur[1] + (long long)cur[0] * t) % MOD; up[b][0] = cur[0]; } } } int lca(int a, int b) { while (top[a] != top[b]) { if (dep[top[a]] < dep[top[b]]) std::swap(a, b); a = fa[top[a]]; } return dep[a] < dep[b] ? a : b; } int solve(int u, int v) { int t = lca(u, v); if (t == v) { int temp = (dist[u] - dist[t]) % MOD; int res = (((long long)sqr(temp) * up[v][0] + 2LL * temp * up[v][1] + up[v][2]) % MOD + MOD) % MOD; res = ((f[u] - res) % MOD + MOD) % MOD; return res; } else { int temp = (dist[u] + dist[v] - 2LL * dist[t]) % MOD; int res = ((long long)sqr(temp) * down[v][0] + 2LL * temp * down[v][1] + down[v][2]) % MOD; return (res + MOD) % MOD; } } int main() { scanf("%d", &n); for (int i = n - 1; i--;) { int a, b, c; scanf("%d%d%d", &a, &b, &c); link(a, b, c); link(b, a, c); } bfs(); int q; for (scanf("%d", &q); q--;) { int u, v; scanf("%d%d", &u, &v); int a = solve(u, v), b = ((f[u] - a) % MOD + MOD) % MOD; printf("%d\n", (a - b + MOD) % MOD); } return 0; }
#include <bits/stdc++.h> using namespace std; const int inf = 987654321; const long long int INF = 123456789987654321; const long long int mod = 1000000007; int N; vector<vector<pair<int, int> > > adj; vector<vector<int> > par; vector<int> dep, sz; vector<long long int> dist, dsum, ddsum; void dfs(int now, int bf) { if (bf != -1) dep[now] = dep[bf] + 1; if (bf != -1) par[0][now] = bf; for (int i = 1; i < 19; i++) { int t = par[i - 1][now]; if (t == -1) break; par[i][now] = par[i - 1][t]; } sz[now] = 1; dsum[now] = dist[now]; ddsum[now] = dist[now] * dist[now] % mod; for (int i = 0; i < adj[now].size(); i++) { int nxt = adj[now][i].first; int d = adj[now][i].second; if (nxt == bf) continue; dist[nxt] = dist[now] + (long long int)d; dist[nxt] %= mod; dfs(nxt, now); sz[now] += sz[nxt]; dsum[now] += dsum[nxt]; dsum[now] %= mod; ddsum[now] += ddsum[nxt]; ddsum[now] %= mod; } } void get_tree_info() { dep = vector<int>(N, 0); sz = vector<int>(N, 0); par = vector<vector<int> >(19, vector<int>(N, -1)); dist = vector<long long int>(N, 0); dsum = vector<long long int>(N, 0); ddsum = vector<long long int>(N, 0); dfs(0, -1); } int lca(int a, int b) { if (dep[a] < dep[b]) swap(a, b); int diff = dep[a] - dep[b]; for (int i = 0; i < 19; i++) { if ((diff >> i) & 1) a = par[i][a]; } if (a == b) return a; for (int i = 19; i--;) { if (par[i][a] != par[i][b]) { a = par[i][a]; b = par[i][b]; } } return par[0][a]; } vector<long long int> dp, dp2, dp3; void dfs2(int now, int bf) { for (int i = 0; i < adj[now].size(); i++) { int nxt = adj[now][i].first; int d = adj[now][i].second; if (nxt == bf) continue; dp[nxt] = (dp[now] - dist[now] * (long long int)sz[nxt] % mod + dist[nxt] * (long long int)sz[nxt] % mod) % mod; dp[nxt] = (dp[nxt] + mod) % mod; dp2[nxt] = (dp2[now] - (dist[now] * dist[now] % mod) * (long long int)sz[nxt] % mod + (dist[nxt] * dist[nxt] % mod) * (long long int)sz[nxt] % mod) % mod; dp2[nxt] = (dp2[nxt] + mod) % mod; dp3[nxt] = (dp3[now] - dist[now] * dsum[nxt] % mod + dist[nxt] * dsum[nxt] % mod) % mod; dp3[nxt] = (dp3[nxt] + mod) % mod; dfs2(nxt, now); } } void get_dp() { dp = vector<long long int>(N, 0); dp2 = vector<long long int>(N, 0); dp3 = vector<long long int>(N, 0); dfs2(0, -1); } int main() { scanf("%d", &N); adj.resize(N); for (int i = 0; i < N - 1; i++) { int a, b, c; scanf("%d %d %d", &a, &b, &c); a--; b--; adj[a].push_back(pair<int, int>(b, c)); adj[b].push_back(pair<int, int>(a, c)); } get_tree_info(); get_dp(); int Q; scanf("%d", &Q); for (int i = 0; i < Q; i++) { int u, v; scanf("%d %d", &u, &v); u--; v--; int x = lca(u, v); long long int t2 = ((long long int)sz[0] * dist[u] % mod) * dist[u] % mod; t2 += ddsum[0]; t2 %= mod; t2 += 4 * (dp2[u] - dp2[0] + ((long long int)sz[0] * dist[0] % mod) * dist[0] % mod); t2 %= mod; t2 += 2 * dist[u] * dsum[0] % mod; t2 %= mod; t2 -= 4 * dist[u] * (dp[u] - dp[0] + (long long int)sz[0] * dist[0] % mod) % mod; t2 %= mod; t2 -= 4 * (dp3[u] - dp3[0] + dsum[0] * dist[0] % mod) % mod; t2 %= mod; t2 = (t2 + mod) % mod; if (x == v) { long long int t = ((long long int)sz[v] * dist[u] % mod) * dist[u] % mod; t += ddsum[v]; t %= mod; t += 4 * (dp2[u] - dp2[v] + ((long long int)sz[v] * dist[v] % mod) * dist[v] % mod); t %= mod; t += 2 * dist[u] * dsum[v] % mod; t %= mod; t -= 4 * dist[u] * (dp[u] - dp[v] + (long long int)sz[v] * dist[v] % mod) % mod; t %= mod; t -= 4 * (dp3[u] - dp3[v] + dsum[v] * dist[v] % mod) % mod; t %= mod; t = (t + mod) % mod; long long int ans = (2 * t - t2) % mod; ans = (ans + mod) % mod; printf("%I64d\n", ans); } else { long long int t = ((long long int)sz[v] * dist[u] % mod) * dist[u] % mod; t += ddsum[v]; t %= mod; t += (4 * (long long int)sz[v] * dist[x] % mod) * dist[x] % mod; t %= mod; t += 2 * dist[u] * dsum[v] % mod; t %= mod; t -= (4 * (long long int)sz[v] * dist[u] % mod) * dist[x] % mod; t %= mod; t -= 4 * dsum[v] * dist[x] % mod; t %= mod; t = (t + mod) % mod; long long int ans = (2 * t - t2) % mod; ans = (ans + mod) % mod; printf("%I64d\n", ans); } } }
#include <bits/stdc++.h> long long mo(long long x) { return x % 1000000007ll; } struct edge { int to, nex; long long v; } e[200010]; long long dsum[100010], dsum2[100010], alld[100010], alld2[100010], siz[100010], dis[100010]; int h[100010], fa[100010][17], dep[100010], tot, n; void add(int a, int b, long long c) { tot++; e[tot].to = b; e[tot].v = c; e[tot].nex = h[a]; h[a] = tot; } void dfs(int x) { siz[x] = 1; for (int i = h[x]; i; i = e[i].nex) { if (e[i].to != fa[x][0]) { dis[e[i].to] = mo(dis[x] + e[i].v); fa[e[i].to][0] = x; dep[e[i].to] = dep[x] + 1; dfs(e[i].to); siz[x] += siz[e[i].to]; dsum[x] = mo(dsum[x] + dsum[e[i].to] + siz[e[i].to] * e[i].v); dsum2[x] = mo(dsum2[x] + mo(e[i].v * e[i].v) * siz[e[i].to] + 2ll * e[i].v * dsum[e[i].to] + dsum2[e[i].to]); } } } void dfs2(int x) { for (int i = h[x]; i; i = e[i].nex) { if (e[i].to != fa[x][0]) { alld[e[i].to] = mo(alld[x] + (n - 2ll * siz[e[i].to]) * e[i].v); alld2[e[i].to] = mo(alld2[x] + 2ll * e[i].v * mo(alld[x] - 2ll * dsum[e[i].to] - siz[e[i].to] * e[i].v) + (n - 2ll * siz[e[i].to]) * mo(e[i].v * e[i].v)); dfs2(e[i].to); } } } void swap(int& a, int& b) { int c = a; a = b; b = c; } int lca(int x, int y) { if (dep[x] < dep[y]) swap(x, y); int i; for (i = 16; i >= 0; i--) { if (dep[fa[x][i]] >= dep[y]) x = fa[x][i]; } if (x == y) return x; for (i = 16; i >= 0; i--) { if (fa[x][i] != fa[y][i]) { x = fa[x][i]; y = fa[y][i]; } } return fa[x][0]; } int main() { int q, i, j, u, v, uv; long long w; scanf("%d", &n); for (i = 1; i < n; i++) { scanf("%d%d%I64d", &u, &v, &w); add(u, v, w); add(v, u, w); } dep[1] = 1; dfs(1); alld[1] = dsum[1]; alld2[1] = dsum2[1]; dfs2(1); for (j = 1; j < 17; j++) { for (i = 1; i <= n; i++) fa[i][j] = fa[fa[i][j - 1]][j - 1]; } scanf("%d", &q); while (q--) { scanf("%d%d", &u, &v); uv = lca(u, v); if (uv == v) { w = mo(dis[u] - dis[v]); w = mo((n - siz[v]) * mo(w * w) + 2ll * w * (alld[v] - dsum[v]) + alld2[v] - dsum2[v]); w = mo(alld2[u] - 2ll * w); } else { w = mo(dis[u] + dis[v] - 2ll * dis[uv]); w = mo(siz[v] * mo(w * w) + 2ll * w * dsum[v] + dsum2[v]); w = mo(2ll * w - alld2[u]); } printf("%I64d\n", mo(w + 1000000007ll)); } }
#include <bits/stdc++.h> using namespace std; const int N = 1e5 + 10; const int S = 17; vector<pair<int, int> > g[N]; int fa[N][S + 1], deep[N]; int dis[N]; int n, m; struct node { int v2, v, sum; } f[N], h[N]; const int mod = 1e9 + 7; int add(int x, int y) { x += y; return x >= mod ? x - mod : x; } int sub(int x, int y) { x -= y; return x < 0 ? x + mod : x; } int mul(int x, int y) { return 1ll * x * y % mod; } int calc(int x, int y) { int z = 1; while (y) { if (y & 1) z = mul(z, x); x = mul(x, x), y >>= 1; } return z; } node operator+(node a, node b) { a.v2 = add(a.v2, b.v2); a.v = add(a.v, b.v); a.sum = add(a.sum, b.sum); return a; } node operator-(node a, node b) { a.v2 = sub(a.v2, b.v2); a.v = sub(a.v, b.v); a.sum = sub(a.sum, b.sum); return a; } node link(node a, int x) { a.v2 = add(a.v2, add(mul(mul(2, a.v), x), mul(a.sum, mul(x, x)))); a.v = add(a.v, mul(x, a.sum)); return a; } void dfs(int x) { deep[x]++; for (int i = 0; fa[fa[x][i]][i]; i++) fa[x][i + 1] = fa[fa[x][i]][i]; f[x].sum = 1; for (auto u : g[x]) if (u.first != fa[x][0]) { fa[u.first][0] = x; deep[u.first] = deep[x]; dis[u.first] = add(dis[x], u.second); dfs(u.first); f[x] = f[x] + link(f[u.first], u.second); } } int up(int x, int y) { for (int i = S; i >= 0; i--) if (y >= (1 << i)) y -= (1 << i), x = fa[x][i]; return x; } int getlca(int x, int y) { if (deep[x] < deep[y]) swap(x, y); x = up(x, deep[x] - deep[y]); for (int i = S; i >= 0; i--) if (fa[x][i] != fa[y][i]) x = fa[x][i], y = fa[y][i]; return x != y ? fa[x][0] : x; } void dfs(int x, node up) { h[x] = f[x] + up; for (auto u : g[x]) if (u.first != fa[x][0]) { dfs(u.first, link(up + f[x] - link(f[u.first], u.second), u.second)); } } int main() { scanf("%d", &n); for (int i = 1; i < n; i++) { int x, y, z; scanf("%d %d %d", &x, &y, &z); g[x].push_back({y, z}); g[y].push_back({x, z}); } dfs(1); dfs(1, node{0, 0, 0}); scanf("%d", &m); while (m--) { int x, y; scanf("%d %d", &x, &y); if (x == y) { int a = h[x].v2, b = f[x].v2; printf("%d\n", sub(mul(b, 2), a)); } else { int lca = getlca(x, y); int v = sub(add(dis[x], dis[y]), mul(dis[lca], 2)); if (lca == y) { int a = h[x].v2, b = link(h[y] - f[y], v).v2; printf("%d\n", sub(a, mul(b, 2))); } else { int a = h[x].v2, b = link(f[y], v).v2; printf("%d\n", sub(mul(b, 2), a)); } } } return 0; }
#include <bits/stdc++.h> using namespace std; const int maxn = 1e5 + 100; const int mod = 1e9 + 7; long long sum1[maxn], sum2[maxn], size[maxn]; int dfn[maxn], dfncnt, f[maxn][20], d[maxn][20], n, dep[maxn]; vector<int> side[maxn], w[maxn]; int trans(int u, int val) { return (sum2[u] + size[u] * val % mod * val % mod + 2 * val * sum1[u] % mod) % mod; } void dfs1(int u, int fa) { f[u][0] = fa; dfn[u] = ++dfncnt; size[u] = 1; dep[u] = dep[fa] + 1; for (int i = 0; i < side[u].size(); i++) { int v = side[u][i]; if (v == fa) continue; dfs1(v, u); size[u] += size[v]; d[v][0] = w[u][i]; sum1[u] = (sum1[u] + sum1[v] + w[u][i] * size[v] % mod) % mod; sum2[u] = (sum2[u] + trans(v, w[u][i])) % mod; } } void init() { for (int i = (1), iend = (19); i <= iend; i++) for (int j = (1), jend = (n); j <= jend; j++) f[j][i] = f[f[j][i - 1]][i - 1]; for (int i = (1), iend = (19); i <= iend; i++) for (int j = (1), jend = (n); j <= jend; j++) d[j][i] = (d[j][i - 1] + d[f[j][i - 1]][i - 1]) % mod; } int get_dis(int u, int v) { long long ans = 0; if (dep[u] < dep[v]) swap(u, v); for (int i = 19; i >= 0; i--) if (dep[f[u][i]] >= dep[v]) ans = (ans + d[u][i]) % mod, u = f[u][i]; if (u == v) return ans; for (int i = 19; i >= 0; i--) if (f[u][i] != f[v][i]) ans = (1ll * ans + d[u][i] + d[v][i]) % mod, u = f[u][i], v = f[v][i]; return (1ll * ans + d[u][0] + d[v][0]) % mod; } struct Query { int u, v, idx; bool insubtree; } q[maxn]; int ans[maxn]; bool cmp(Query a, Query b) { return dfn[a.u] < dfn[b.u]; } int now = 1, t; void dfs2(int u, int fa) { while (now <= t && q[now].u == u) { int v = q[now].v, idx = q[now].idx; if (q[now].insubtree) { ans[idx] = (sum2[u] - 2 * trans(f[v][0], get_dis(f[v][0], u))) % mod; ans[idx] = (ans[idx] + mod) % mod; } else { ans[idx] = (2 * trans(v, get_dis(u, v)) - sum2[u]) % mod; ans[idx] = (ans[idx] + mod) % mod; } now++; } for (int i = 0; i < side[u].size(); i++) { int v = side[u][i]; if (v == fa) continue; long long bku1 = sum1[u], bku2 = sum2[u], bku3 = size[u]; long long bkv1 = sum1[v], bkv2 = sum2[v], bkv3 = size[v]; int tmp1 = trans(v, w[u][i]), tmp2 = trans(u, w[u][i]) - trans(v, 2 * w[u][i] % mod); tmp2 = (tmp2 % mod + mod) % mod; sum1[u] = (bku1 - (bkv1 + w[u][i] * bkv3) % mod) % mod; sum1[u] = (sum1[u] % mod + mod) % mod; sum1[v] = ((bku1 - (bkv1 + w[u][i] * bkv3) % mod) + (bku3 - bkv3) * w[u][i] % mod + bkv1) % mod; sum1[v] = (sum1[v] % mod + mod) % mod; sum2[u] = (bku2 - tmp1) % mod; sum2[u] = (sum2[u] % mod + mod) % mod; sum2[v] = tmp2 + bkv2; sum2[v] = (sum2[v] % mod + mod) % mod; size[u] = bku3 - bkv3; size[v] = bku3; dfs2(v, u); sum1[u] = bku1, sum2[u] = bku2, size[u] = bku3; sum1[v] = bkv1, sum2[v] = bkv2, size[v] = bkv3; } } int main() { ios::sync_with_stdio(0); cin >> n; for (int i = (1), iend = (n - 1); i <= iend; i++) { int u, v, val; cin >> u >> v >> val; side[u].push_back(v); w[u].push_back(val); side[v].push_back(u); w[v].push_back(val); } dfs1(1, 0); init(); cin >> t; for (int i = (1), iend = (t); i <= iend; i++) { cin >> q[i].u >> q[i].v; q[i].idx = i; if (dfn[q[i].v] <= dfn[q[i].u] && dfn[q[i].u] <= dfn[q[i].v] + size[q[i].v] - 1) q[i].insubtree = 1; } sort(q + 1, q + 1 + t, cmp); dfs2(1, 0); for (int i = (1), iend = (t); i <= iend; i++) { cout << (ans[i] % mod + mod) % mod << endl; } return 0; }
#include <bits/stdc++.h> using namespace std; template <class S> inline void read(S& arg) { cin >> arg; } template <class S> inline void readA(S Lptr, S Rptr) { while (Lptr != Rptr) { read(*Lptr); Lptr++; } } template <class S, class... T> inline void read(S& arg, T&... rest) { read(arg); read(rest...); } char delimiter = ' '; template <class S> inline void write(S arg) { cout << arg << '\n'; } template <class S, class... T> inline void write(S arg, T... rest) { cout << arg << delimiter; write(rest...); } template <class S> inline void writeA(S Lptr, S Rptr) { while (Lptr != Rptr) { cout << *Lptr; Lptr++; if (Lptr != Rptr) cout << delimiter; } cout << '\n'; } template <class T, class S> inline bool smin(T& a, S b) { return (T)b < a ? a = b, 1 : 0; } template <class T, class S> inline bool smax(T& a, S b) { return a < (T)b ? a = b, 1 : 0; } constexpr long long MOD = 1e9 + 7; constexpr long long N = 1e5 + 10; template <typename T> inline T mod(T& v) { return v = (v % MOD + MOD) % MOD; } template <typename T> inline long long dom(T v) { return (v % MOD + MOD) % MOD; } template <typename S, typename T> inline S add(S& l, T r) { return mod(l += r); } long long po(long long v, long long u) { return u ? po(v * v % MOD, u >> 1) * (u & 1 ? v : 1) % MOD : 1; } long long n, a[N], b[N], A[N], B[N], q; long long c[N], res[N]; vector<long long> adj[N], qu[N]; long long mul[N << 2], sum[N << 2], lazy[N << 2]; void shift(long long id, long long len) { add(mul[id], 2 * lazy[id] * sum[id] + dom(lazy[id] * lazy[id]) * len); add(sum[id], lazy[id] * len); if (len == 1) return lazy[id] = 0, void(); add(lazy[id << 1], lazy[id]); add(lazy[id << 1 | 1], lazy[id]); lazy[id] = 0; } void segAdd(long long s, long long t, long long val, long long l = 0, long long r = n, long long id = 1) { shift(id, r - l); if (l >= t || r <= s) return; if (l >= s && r <= t) { add(lazy[id], val); shift(id, r - l); return; } long long mid = l + r >> 1; segAdd(s, t, val, l, mid, id << 1); segAdd(s, t, val, mid, r, id << 1 | 1); mul[id] = dom(mul[id << 1] + mul[id << 1 | 1]); sum[id] = dom(sum[id << 1] + sum[id << 1 | 1]); } long long segGet(long long s, long long t, long long l = 0, long long r = n, long long id = 1) { shift(id, r - l); if (l >= t || r <= s) return 0; if (l >= s && r <= t) return mul[id]; long long mid = l + r >> 1; return dom(segGet(s, t, l, mid, id << 1) + segGet(s, t, mid, r, id << 1 | 1)); } long long st[N], en[N], TM; long long d[N]; void dfs1(long long v = 0, long long par = 0) { st[v] = TM++; for (auto e : adj[v]) { long long u = a[e] ^ b[e] ^ v; if (u ^ par) { segAdd(TM, TM + 1, d[v] + c[e]); add(d[u], d[v] + c[e]); dfs1(u, v); } } en[v] = TM; } void dfs2(long long v = 0, long long par = 0) { for (auto e : qu[v]) { long long u = B[e]; add(res[e], -segGet(0, n) + 2 * segGet(st[u], en[u])); } for (auto e : adj[v]) { long long u = a[e] ^ b[e] ^ v; if (u ^ par) { segAdd(0, n, c[e]); segAdd(st[u], en[u], MOD - 2 * c[e]); dfs2(u, v); segAdd(0, n, MOD - c[e]); segAdd(st[u], en[u], 2 * c[e]); } } } int32_t main() { ios::sync_with_stdio(0); cin.tie(0); cout.tie(0); read(n); for (long long i = 1; i < (long long)n; i++) { read(a[i], b[i], c[i]); a[i]--, b[i]--; adj[a[i]].push_back(i); adj[b[i]].push_back(i); } read(q); for (long long i = 0; i < (long long)q; i++) { read(A[i], B[i]); A[i]--, B[i]--; qu[A[i]].push_back(i); } dfs1(); dfs2(); delimiter = '\n'; writeA(res, res + q); return 0; }
#include <bits/stdc++.h> using namespace std; int father[20][300005], lv[300005], n; long long dis[300005]; vector<int> e[300005], ev[300005]; void init(int x, int lt) { father[0][x] = lt; for (int i = 0; i < ((int)(e[x]).size()); ++i) { int y = e[x][i]; if (y != lt) { dis[y] = dis[x] + ev[x][i]; lv[y] = lv[x] + 1; init(y, x); } } } int adv(int x, int v) { for (int i = 0; (1 << i) <= v; i++) { if ((v >> i) & 1) x = father[i][x]; } return x; } int lca(int x, int y) { if (lv[x] > lv[y]) x = adv(x, lv[x] - lv[y]); else y = adv(y, lv[y] - lv[x]); if (x == y) return x; for (int i = 19; i >= 0; i--) if (father[i][x] != father[i][y]) { x = father[i][x]; y = father[i][y]; } return father[0][x]; } void build() { init(1, 1); for (int i = (1); i < (20); ++i) { for (int x = (1); x < (n + 1); ++x) father[i][x] = father[i - 1][father[i - 1][x]]; } } int num[300005], sum[300005], sum2[300005], all_sum[300005], all_sum2[300005]; void add(int &x, long long v) { x = (x + v) % 1000000007; } void dfs0(int x, int lt) { num[x] = 1; for (int i = 0; i < ((int)(e[x]).size()); ++i) { int y = e[x][i]; if (y == lt) continue; dfs0(y, x); num[x] += num[y]; sum[x] = (sum[x] + sum[y] + (long long)num[y] * ev[x][i]) % 1000000007; sum2[x] = (sum2[x] + sum2[y] + (long long)sum[y] * 2 * ev[x][i] + (long long)ev[x][i] * ev[x][i] % 1000000007 * num[y]) % 1000000007; } } void dfs1(int x, int lt, long long v1, long long v2) { v1 %= 1000000007; v2 %= 1000000007; if (v1 < 0) v1 += 1000000007; if (v2 < 0) v2 += 1000000007; all_sum[x] = sum[x]; all_sum2[x] = sum2[x]; add(all_sum[x], v1); add(all_sum2[x], v2); for (int i = 0; i < ((int)(e[x]).size()); ++i) { int y = e[x][i]; if (y == lt) continue; dfs1(y, x, v1 + (long long)(n - num[y]) * ev[x][i] % 1000000007 + sum[x] - sum[y] - (long long)num[y] * ev[x][i] % 1000000007, all_sum2[x] - sum2[y] - sum[y] * 2LL * ev[x][i] % 1000000007 - (long long)ev[x][i] * ev[x][i] % 1000000007 * num[y] + (long long)(n - num[y]) * ev[x][i] % 1000000007 * ev[x][i] % 1000000007 + 2LL * ev[x][i] * (v1 + sum[x] - sum[y] - (long long)num[y] * ev[x][i] % 1000000007) % 1000000007); } } int main() { scanf("%d", &n); for (int i = (1); i < (n); ++i) { int x, y, v; scanf("%d%d%d", &x, &y, &v); e[x].push_back(y); ev[x].push_back(v); e[y].push_back(x); ev[y].push_back(v); } build(); dfs0(1, 1); dfs1(1, 1, 0, 0); int Q; scanf("%d", &Q); while (Q--) { int u, v; scanf("%d%d", &u, &v); int me = lca(u, v); int an = 0; long long dd = dis[u] + dis[v] - 2 * dis[me]; dd %= 1000000007; if (me != v) { an = -all_sum2[u] % 1000000007; add(an, (sum2[v] + dd * dd % 1000000007 * num[v] % 1000000007 + dd * 2LL * sum[v] % 1000000007) * 2); } else { an = all_sum2[u]; add(an, (all_sum2[v] - sum2[v] + dd * dd % 1000000007 * (n - num[v]) % 1000000007 + dd * 2LL * (all_sum[v] - sum[v]) % 1000000007) * -2); } if (an < 0) an += 1000000007; printf("%d\n", an); } }
#include <bits/stdc++.h> using namespace std; typedef struct node { long long lazy; long long sum, sumsq; } node; vector<pair<int, long long> > G[100100]; vector<int> queries[100100]; map<pair<int, long long>, long long> M; int uq[100100]; int vq[100100]; int lft[100100]; int rgt[100100]; int sz[100100]; node S[4 * 100100]; int idx, n; node ZERO; void push(int x, int l, int r) { long long v = S[x].lazy; int mid = (l + r) / 2; long long siz1 = mid - l + 1, siz2 = r - (mid + 1) + 1; S[x * 2].lazy = (S[x * 2].lazy + v) % 1000000007; S[x * 2].sumsq = (S[x * 2].sumsq + 2 * ((v * S[x * 2].sum) % 1000000007) + (siz1 * ((v * v) % 1000000007)) % 1000000007) % 1000000007; S[x * 2].sum = (S[x * 2].sum + (siz1 * v) % 1000000007) % 1000000007; S[x * 2 + 1].lazy = (S[x * 2 + 1].lazy + v) % 1000000007; S[x * 2 + 1].sumsq = (S[x * 2 + 1].sumsq + 2 * ((v * S[x * 2 + 1].sum) % 1000000007) + (siz2 * ((v * v) % 1000000007)) % 1000000007) % 1000000007; S[x * 2 + 1].sum = (S[x * 2 + 1].sum + (siz2 * v) % 1000000007) % 1000000007; S[x].lazy = 0; } void update(int x, int l, int r, int i, int j, long long v) { if ((j < l) or (r < i)) return; if ((i <= l) and (r <= j)) { S[x].lazy = (S[x].lazy + v) % 1000000007; long long siz = r - l + 1; S[x].sumsq = (S[x].sumsq + 2 * ((v * S[x].sum) % 1000000007) + (siz * ((v * v) % 1000000007)) % 1000000007) % 1000000007; S[x].sum = (S[x].sum + (siz * v) % 1000000007) % 1000000007; return; } push(x, l, r); int mid = (l + r) / 2; update(x * 2, l, mid, i, j, v); update(x * 2 + 1, mid + 1, r, i, j, v); node Q1 = S[x * 2]; node Q2 = S[x * 2 + 1]; S[x].sum = (Q2.sum + Q1.sum) % 1000000007; S[x].sumsq = (Q2.sumsq + Q1.sumsq) % 1000000007; } node query(int x, int l, int r, int i, int j) { if ((j < l) or (r < i)) return ZERO; if ((i <= l) and (r <= j)) return S[x]; push(x, l, r); int mid = (l + r) / 2; node Q1 = query(x * 2, l, mid, i, j); node Q2 = query(x * 2 + 1, mid + 1, r, i, j); Q2.sum = (Q2.sum + Q1.sum) % 1000000007; Q2.sumsq = (Q2.sumsq + Q1.sumsq) % 1000000007; return Q2; } void dfs0(int x, int pi, long long dist) { idx++; lft[x] = idx, rgt[x] = idx; update(1, 1, n, idx, idx, dist); sz[x] = 1; for (int j = (0); j < (G[x].size()); j++) { int y = G[x][j].first; long long w = G[x][j].second; if (y == pi) continue; dfs0(y, x, (dist + w) % 1000000007); lft[x] = (((lft[x]) < (lft[y])) ? (lft[x]) : (lft[y])); rgt[x] = (((rgt[x]) > (rgt[y])) ? (rgt[x]) : (rgt[y])); sz[x] += sz[y]; } } void dfs1(int x, int pi) { node Q = query(1, 1, n, 1, n); for (int j = (0); j < (queries[x].size()); j++) { int y = queries[x][j]; long long T = S[1].sumsq; node Q = query(1, 1, n, lft[y], rgt[y]); long long ans = (2 * Q.sumsq - T + 1000000007) % 1000000007; M[make_pair(x, y)] = ans; } for (int j = (0); j < (G[x].size()); j++) { int y = G[x][j].first; long long w = G[x][j].second; if (y == pi) continue; update(1, 1, n, 1, n, w); update(1, 1, n, lft[y], rgt[y], (2 * 1000000007 - 2 * w) % 1000000007); dfs1(y, x); update(1, 1, n, lft[y], rgt[y], (2 * w) % 1000000007); update(1, 1, n, 1, n, 1000000007 - w); } } int main() { ZERO.sum = 0; ZERO.sumsq = 0; int x, y, u, v; idx = 0; scanf("%d", &n); long long w; for (int j = (1); j <= (n - 1); j++) { scanf("%d %d %I64d", &x, &y, &w); G[x].push_back(make_pair(y, w)); G[y].push_back(make_pair(x, w)); } for (int j = (0); j < (4 * 100100); j++) { S[j].sum = 0; S[j].sumsq = 0; } dfs0(1, -1, 0); int q; cin >> q; for (int j = (1); j <= (q); j++) { scanf("%d %d", &uq[j], &vq[j]); queries[uq[j]].push_back(vq[j]); } dfs1(1, -1); for (int j = (1); j <= (q); j++) { printf("%I64d\n", M[make_pair(uq[j], vq[j])]); } }
#include <bits/stdc++.h> using namespace std; struct node { long long t, d, g, h, s, ds, dq, dis, sum; } A[100100]; int p[100100], nxt[2 * 100100], C[2 * 100100], V[2 * 100100], f[100100], g[100100][19], n, q, i, ed; int gi() { int s = 0; char c = getchar(); while (c < '0' || c > '9') c = getchar(); while (c >= '0' && c <= '9') s = s * 10 + c - '0', c = getchar(); return s; } void Add(int u, int v, int c) { V[++ed] = v, C[ed] = c, nxt[ed] = p[u], p[u] = ed; } long long sqr(long long x) { return (x * x) % 1000000007; }; long long Mul(long long x, long long y) { return ((x % 1000000007) * y) % 1000000007; } void Dfs(int x, int fa) { f[x] = fa, A[x].s = 1, A[x].t = A[f[x]].t + 1; for (int i = p[x]; i != -1; i = nxt[i]) { int v = V[i]; if (v == fa) continue; A[v].d = (A[x].d + C[i]) % 1000000007; A[v].g = (A[x].g + A[v].d) % 1000000007; A[v].h = (A[x].h + sqr(A[v].d)) % 1000000007; Dfs(v, x); A[x].s = (A[x].s + A[v].s) % 1000000007; A[x].ds = (A[x].ds + A[v].ds + A[v].s * C[i]) % 1000000007; A[x].dq = (A[x].dq + A[v].dq + Mul(A[v].s, sqr(C[i])) + 2LL * Mul(A[v].ds, C[i])) % 1000000007; } } void Calc(int x, long long c) { A[x].dis = (A[f[x]].dis - Mul(A[x].s, c) + Mul((n - A[x].s), c)) % 1000000007; A[x].sum = (A[f[x]].sum + Mul(n, sqr(c))) % 1000000007; A[x].sum = (A[x].sum - 2LL * Mul(A[x].ds + Mul(A[x].s, c), c)) % 1000000007; A[x].sum = (A[x].sum + 2LL * Mul(A[x].dis - A[x].ds - Mul(n - A[x].s, c), c)) % 1000000007; for (int i = p[x]; i != -1; i = nxt[i]) if (V[i] != f[x]) Calc(V[i], C[i]); } int Lca(int u, int v) { if (A[u].t < A[v].t) swap(u, v); for (int i = 18; i >= 0; i--) if (A[g[u][i]].t >= A[v].t) u = g[u][i]; if (u == v) return u; for (int i = 18; i >= 0; i--) if (g[u][i] != g[v][i]) u = g[u][i], v = g[v][i]; return f[u]; } int find(int u) { for (int i = 18; i >= 0; i--) if (A[g[u][i]].t >= 2) u = g[u][i]; return u; } int main() { memset(p, -1, sizeof(p)); scanf("%d", &n); for (i = 1; i < n; i++) { int u = gi(), v = gi(), c = gi(); Add(u, v, c), Add(v, u, c); } Dfs(1, 0); for (i = 1; i <= n; i++) g[i][0] = f[i]; for (i = 1; i <= 17; i++) for (int j = 1; j <= n; j++) g[j][i] = g[g[j][i - 1]][i - 1]; for (i = 1; i <= n; i++) A[1].sum += sqr(A[i].d), A[1].dis += A[i].d; A[1].sum %= 1000000007, A[1].dis %= 1000000007; for (i = p[1]; i != -1; i = nxt[i]) Calc(V[i], C[i]); scanf("%d", &q); for (i = 1; i <= q; i++) { int u = gi(), v = gi(); int z = Lca(u, v); long long ans, o, h, b; if (z == v && u != v) { o = (A[v].d - A[f[v]].d) % 1000000007; b = (A[u].d - A[f[v]].d) % 1000000007; h = (A[f[v]].dis - A[v].ds - Mul(o, A[v].s)) % 1000000007; ans = (A[f[v]].sum - A[v].dq - Mul(A[v].s, sqr(o)) - 2LL * Mul(A[v].ds, o)) % 1000000007; ans = (ans + Mul(n - A[v].s, sqr(b)) + 2LL * Mul(h, b)) % 1000000007; ans = (A[u].sum - 2 * ans) % 1000000007; if (v == 1) ans = A[u].sum; } else { long long det = (A[u].d + A[v].d - 2LL * A[z].d) % 1000000007; ans = (A[v].dq + Mul(A[v].s, sqr(det))) % 1000000007; o = (2LL * Mul(A[v].ds, det)) % 1000000007; ans = (2LL * (ans + o) - A[u].sum) % 1000000007; } printf("%I64d\n", (1000000007 + ans) % 1000000007); } }
#include <bits/stdc++.h> #pragma comment(linker, "/STACK:1024000000,1024000000") using namespace std; long long tot[100010]; int sz[100010], p[100010][20], d[100010], a[100010], b[100010], f[100010], h[100010], l[100010], aa[100010], bb[100010]; vector<pair<int, int> > g[100010]; void dfs(int u, int fa, int w = 0) { sz[u] = 1; p[u][0] = fa; d[u] = (d[fa] + w) % 1000000007; l[u] = l[fa] + 1; for (int i = 0; i < g[u].size(); i++) { int j = g[u][i].first, w = g[u][i].second; if (j == fa) continue; dfs(j, u, w); sz[u] += sz[j]; long long v = (a[j] + 1LL * sz[j] * w % 1000000007 * w % 1000000007 + 1LL * w * b[j] % 1000000007 * 2) % 1000000007; a[u] = (a[u] + v) % 1000000007; f[j] = v; v = b[j] + 1LL * sz[j] * w % 1000000007; v %= 1000000007; b[u] = (b[u] + v) % 1000000007; h[j] = v; } } void go(int u, int fa, int w = 0, int first = 0, int second = 0) { if (u > 1) { first = (a[fa] - f[u] + first) % 1000000007; if (first < 0) first += 1000000007; second = (b[fa] - h[u] + second) % 1000000007; if (second < 0) second += 1000000007; tot[u] = (first + 1LL * (sz[1] - sz[u]) * w % 1000000007 * w % 1000000007 + 1LL * w * second % 1000000007 * 2) % 1000000007; first = tot[u]; second = (second + 1LL * (sz[1] - sz[u]) * w % 1000000007) % 1000000007; tot[u] = (tot[u] + a[u]) % 1000000007; aa[u] = first, bb[u] = second; } else tot[1] = a[1]; for (int i = 0; i < g[u].size(); i++) { int j = g[u][i].first, w = g[u][i].second; if (j == fa) continue; go(j, u, w, first, second); } } int lca(int a, int b) { if (l[a] < l[b]) swap(a, b); int h = l[a] - l[b]; for (int i = 0; i < 18; i++) if (h >> i & 1) a = p[a][i]; if (a == b) return a; for (int i = 17; i >= 0; i--) if (p[a][i] != p[b][i]) a = p[a][i], b = p[b][i]; return p[a][0]; } int main() { int T, i, j, m, n, ca = 0, k, now = 0; scanf("%d", &n); for (i = 1; i < n; i++) { int w; scanf("%d%d%d", &j, &k, &w); g[j].push_back(make_pair(k, w)); g[k].push_back(make_pair(j, w)); } dfs(1, 0); go(1, 0); for (i = 1; i < 19; i++) for (j = 1; j <= n; j++) p[j][i] = p[p[j][i - 1]][i - 1]; scanf("%d", &m); while (m--) { int u, v, t = 1; scanf("%d%d", &u, &v); int fa = lca(u, v); long long ans = 0; if (v == fa) { long long w = d[u] - d[v], first = aa[v], second = bb[v], z = sz[1] - sz[v]; if (w < 0) w += 1000000007; ans = first + z * w % 1000000007 * w % 1000000007 + w * second % 1000000007 * 2; ans %= 1000000007; t = -1; } else { long long w = d[u] - d[fa] + d[v] - d[fa], first = a[v], second = b[v], z = sz[v]; w %= 1000000007; if (w < 0) w += 1000000007; ans = first + z * w % 1000000007 * w % 1000000007 + w * second % 1000000007 * 2; ans %= 1000000007; } if (ans < 0) ans += 1000000007; ans = 2LL * ans - tot[u]; ans *= t; ans %= 1000000007; if (ans < 0) ans += 1000000007; printf("%d\n", ans); } }
#include <bits/stdc++.h> using namespace std; const int MAXN = 100 * 1000 + 23, D = 1000 * 1000 * 1000 + 7, MXLN = 17 + 3; int mul() { return 1; } template <typename... T> int mul(int x, T... a) { return 1ll * x * mul(a...) % D; } int add() { return 0; } template <typename... T> int add(int x, T... a) { return (x + add(a...)) % D; } int n, e[MAXN], w[MAXN], sum[MAXN], sum2[MAXN], up[MAXN], up2[MAXN], sz[MAXN], h[MAXN], par[MXLN][MAXN], dis[MAXN], q; vector<int> g[MAXN]; void dfs(int v = 0, int p = -1) { for (auto i : g[v]) { int u = v ^ e[i]; if (u == p) continue; h[u] = h[v] + 1; dis[u] = add(dis[v], w[i]); par[0][u] = v; dfs(u, v); sz[v] += sz[u]; sum[v] = add(sum[v], sum[u], mul(sz[u], w[i])); sum2[v] = add(sum2[v], mul(w[i], w[i], sz[u]), sum2[u], mul(2, w[i], sum[u])); } sz[v]++; } void ufs(int v = 0, int p = -1) { int tmp = up[v], tmp2 = up2[v]; for (auto i : g[v]) { int u = v ^ e[i]; if (u == p) continue; tmp = add(tmp, sum[u], mul(sz[u], w[i])); tmp2 = add(tmp2, mul(w[i], w[i], sz[u]), sum2[u], mul(2, w[i], sum[u])); } for (auto i : g[v]) { int u = v ^ e[i]; if (u == p) continue; up[u] = add(tmp, D - sum[u], D - mul(sz[u], w[i]), mul(w[i], (n - sz[u]))); up2[u] = add(tmp2, D - mul(w[i], w[i], sz[u]), D - sum2[u], D - mul(2, w[i], sum[u]), mul(w[i], w[i], n - sz[u]), mul(2, w[i], add(tmp, D - sum[u], D - mul(sz[u], w[i])))); ufs(u, v); } } int lca(int u, int v) { if (h[u] < h[v]) swap(u, v); for (int i = MXLN - 1; ~i; i--) if (h[par[i][u]] >= h[v]) u = par[i][u]; if (u == v) return v; for (int i = MXLN - 1; ~i; i--) if (par[i][u] != par[i][v]) { u = par[i][u]; v = par[i][v]; } return par[0][v]; } int main() { cin >> n; for (int i = 1; i < n; i++) { int a, b, c; cin >> a >> b >> c; g[--a].push_back(i), g[--b].push_back(i); e[i] = a ^ b; w[i] = c; } dfs(), ufs(); for (int i = 1; i < MXLN; i++) for (int j = 0; j < n; j++) par[i][j] = par[i - 1][par[i - 1][j]]; cin >> q; while (q--) { int u, v; cin >> u >> v; int x = lca(--u, --v); if (x == v) { int fas = add(dis[u], D - dis[v]), tmp = D - add(up2[v], mul(fas, fas, (n - sz[v])), mul(2, fas, up[v])); cout << add(sum2[u], up2[u], tmp, tmp) << '\n'; } else { int fas = ((x == u) ? add(dis[v], D - dis[u]) : add(dis[u], dis[v], D - dis[x], D - dis[x])), tmp = add(mul(fas, fas, sz[v]), sum2[v], mul(2, fas, sum[v])); cout << add(tmp, D - sum2[u], D - up2[u], tmp) << '\n'; } } }
#include <bits/stdc++.h> using namespace std; const int inf = 1e9 + 100500; const int mod = 1000000007; const int maxn = 100500; int add(int x, int y) { return (x + y) % mod; } int add(int x, int y, int z) { return add(x, add(y, z)); } int mul(int x, int y) { return (long long)x * y % mod; } int sub(int x, int y) { x -= y; if (x < 0) x += mod; return x; } int n; vector<pair<int, int> > e[maxn]; int p[maxn][20], wp[maxn], h[maxn], H[maxn]; int cd[maxn], cu[maxn], sd[maxn], su[maxn], sd2[maxn], su2[maxn]; int tin[maxn], tout[maxn], dtime; inline bool anc(int u, int v) { return tin[u] <= tin[v] && tout[u] >= tout[v]; } int getr1(int u, int w) { return add(sd[u], mul(w, add(cd[u], 1))); } int getr2(int u, int w) { return add(sd2[u], mul(2, mul(w, sd[u])), mul(cd[u] + 1, mul(w, w))); } void buildlca() { for (int k = 0; k < (int)(20); ++k) if (k) { for (int i = 0; i < (int)(n); ++i) p[i][k] = p[p[i][k - 1]][k - 1]; } } int lca(int u, int v) { if (H[u] < H[v]) swap(u, v); for (int k = 0; k < (int)(20); ++k) if ((H[u] - H[v]) & (1 << k)) { u = p[u][k]; } assert(H[u] == H[v]); if (u == v) return u; for (int k = (int)(20) - 1; k >= 0; --k) { if (p[u][k] != p[v][k]) { u = p[u][k]; v = p[v][k]; } } return p[v][0]; } int dist(int u, int v) { int l = lca(u, v); return sub(add(h[u], h[v]), mul(2, h[l])); } void dfs1(int v, int anc) { tin[v] = dtime++; for (auto X : e[v]) { int u = X.first, w = X.second; if (u == anc) continue; wp[u] = w; h[u] = add(h[v], w); H[u] = H[v] + 1; p[u][0] = v; dfs1(u, v); cd[v] += cd[u] + 1; sd[v] = add(sd[v], getr1(u, w)); sd2[v] = add(sd2[v], getr2(u, w)); } cu[v] = n - cd[v] - 1; tout[v] = dtime++; } void dfs2(int v, int anc) { int u = anc; int w = wp[v]; if (v != 0) { int c = cu[u] + cd[u] - (cd[v] + 1); int s = sub(add(su[u], sd[u]), getr1(v, w)); int s2 = sub(add(su2[u], sd2[u]), getr2(v, w)); su[v] = add(s, mul(w, add(c, 1))); su2[v] = add(s2, mul(2, mul(w, s)), mul(c + 1, mul(w, w))); } for (auto X : e[v]) { int u = X.first; if (u != anc) { dfs2(u, v); } } } void scan() { scanf("%d", &n); for (int i = 0; i < (int)(n - 1); ++i) { int u, v, c; scanf("%d%d%d", &u, &v, &c); e[--u].push_back(make_pair(--v, c)); e[v].push_back(make_pair(u, c)); } } int query(int u, int v) { int res = add(sd2[u], su2[u]); if (anc(v, u)) { int W = sub(h[u], h[v]); int C = cu[v]; int S = su[v]; int S2 = su2[v]; int radd = add(S2, mul(2, mul(S, W)), mul(C, mul(W, W))); return sub(res, mul(2, radd)); } else { int W = dist(u, v); int C = cd[v] + 1; int S = sd[v]; int S2 = sd2[v]; int radd = add(S2, mul(2, mul(S, W)), mul(C, mul(W, W))); return sub(mul(2, radd), res); } } void gen_tree(int n) { ::n = n; for (int i = (int)(1); i <= (int)(n - 1); ++i) { int j = rand() % i; int c = rand() % 10 + 1; e[j].push_back(make_pair(i, c)); e[i].push_back(make_pair(j, c)); } } void dfs(int v, int anc, int cd, vector<int>& a) { a.push_back(cd); for (int i = 0; i < (int)(e[v].size()); ++i) if (anc != e[v][i].first) { dfs(e[v][i].first, v, cd + e[v][i].second, a); } } void solved() { dfs1(0, -1); dfs2(0, -1); for (int i = 0; i < (int)(n); ++i) { vector<int> a; dfs(i, -1, 0, a); int s = 0; for (auto x : a) s += x * x; if (s != sd2[i] + su2[i]) { cout << "fail" << endl; for (int v = 0; v < (int)(n); ++v) { for (auto to : e[v]) cout << to.first << " "; cout << endl; } exit(0); } else { cout << s << " " << sd2[i] << " " << su2[i] << endl; } } } void solve() { dfs1(0, -1); dfs2(0, -1); buildlca(); int q; scanf("%d", &q); for (int i = 0; i < (int)(q); ++i) { int u, v; scanf("%d%d", &u, &v); printf("%d\n", query(u - 1, v - 1)); } } int main() { scan(); solve(); return 0; }
#include <bits/stdc++.h> using namespace std; const int MaxN = 100010; const int MOD = 1000000007; struct Node { int v; long long c; Node *nxt; } pool[MaxN << 1], *tail = pool, *g[MaxN]; struct Pack { long long s, s2, cnt; Pack() {} Pack(long long _s, long long _s2, long long _cnt) : s(_s), s2(_s2), cnt(_cnt) {} Pack operator*(long long t) { t %= MOD; return Pack(s + cnt * t % MOD, (s2 + 2 * s * t % MOD + cnt * t % MOD * t) % MOD, cnt); } Pack operator+(const Pack &t) { return Pack((s + t.s) % MOD, (s2 + t.s2) % MOD, cnt + t.cnt); } Pack operator-(const Pack &t) { return Pack((s - t.s) % MOD, (s2 - t.s2) % MOD, cnt - t.cnt); } Pack operator+=(const Pack &t) { return *this = *this + t; } Pack operator-=(const Pack &t) { return *this = *this - t; } } d[MaxN], up[MaxN]; int n, q; int h[MaxN]; long long len[MaxN]; int fa[20][MaxN]; void dfs(int u) { d[u].cnt = 1; for (Node *p = g[u]; p; p = p->nxt) if (p->v != fa[0][u]) fa[0][p->v] = u, h[p->v] = h[u] + 1, len[p->v] = len[u] + p->c, dfs(p->v), d[u] += d[p->v] * p->c; } void dfs2(int u) { for (Node *p = g[u]; p; p = p->nxt) if (p->v != fa[0][u]) up[p->v] = (d[u] - d[p->v] * p->c + up[u]) * p->c, dfs2(p->v); } int lca(int u, int v) { if (h[u] < h[v]) u ^= v ^= u ^= v; for (int i = 19; i >= 0; i--) if (h[fa[i][u]] >= h[v]) u = fa[i][u]; if (u == v) return u; for (int i = 19; i >= 0; i--) if (fa[i][u] != fa[i][v]) u = fa[i][u], v = fa[i][v]; return fa[0][u]; } int main() { scanf("%d", &n); for (int i = 1; i < n; i++) { int u, v, c; scanf("%d%d%d", &u, &v, &c); tail->v = v; tail->c = c; tail->nxt = g[u]; g[u] = tail++; tail->v = u; tail->c = c; tail->nxt = g[v]; g[v] = tail++; } h[1] = 1; dfs(1); dfs2(1); for (int i = 1; i < 20; i++) for (int j = 1; j <= n; j++) fa[i][j] = fa[i - 1][fa[i - 1][j]]; scanf("%d", &q); for (int i = 1; i <= q; i++) { int u, v; scanf("%d%d", &u, &v); int w = lca(u, v); long long tl = len[u] + len[v] - len[w] * 2; Pack s1 = up[u] + d[u], s2 = w == v ? d[u] + up[u] - up[v] * tl : d[v] * tl; printf("%I64d\n", ((s2.s2 * 2 - s1.s2) % MOD + MOD) % MOD); } return 0; }
#include <bits/stdc++.h> using namespace std; const int md = 1000000007; int n, a[200009], b[200009], c[200009], used[100009], cnt[100009], s1[100009], s1c[100009], s2[100009], s2c[100009], par[19][100009]; int val[19][100009], q, dep[100009]; vector<int> adj[100009]; inline void Dfs1(int x) { used[x] = 1; cnt[x] = 1; for (int i = 0; i < adj[x].size(); i++) { int id = adj[x][i]; if (!used[b[id]]) { par[0][b[id]] = x; val[0][b[id]] = c[id]; dep[b[id]] = dep[x] + 1; Dfs1(b[id]); cnt[x] += cnt[b[id]]; s1c[x] = (s1c[x] + s1c[b[id]] + (long long)c[id] * cnt[b[id]]) % md; s2c[x] = (s2c[x] + s2c[b[id]] + (long long)c[id] * c[id] % md * cnt[b[id]] + 2ll * c[id] * s1c[b[id]]) % md; } } used[x] = 0; } inline void Dfs2(int x) { used[x] = 1; for (int i = 0; i < adj[x].size(); i++) { int id = adj[x][i]; if (!used[b[id]]) { int tmpcnt = n - cnt[b[id]]; int tmp1 = (s1[x] - s1c[b[id]] - (long long)c[id] * cnt[b[id]]) % md; int tmp2 = (s2[x] - s2c[b[id]] - (long long)c[id] * c[id] % md * cnt[b[id]] - 2ll * c[id] * s1c[b[id]]) % md; s1[b[id]] = (s1c[b[id]] + tmp1 + (long long)c[id] * tmpcnt) % md; s2[b[id]] = (s2c[b[id]] + tmp2 + (long long)c[id] * c[id] % md * tmpcnt + 2ll * c[id] * tmp1) % md; Dfs2(b[id]); } } used[x] = 0; } pair<int, int> Lca(int x, int y) { if (dep[x] < dep[y]) { swap(x, y); } int sum = 0; for (int i = 17; i >= 0; i--) { if (dep[par[i][x]] >= dep[y]) { sum = (sum + val[i][x]) % md; x = par[i][x]; } } if (x == y) { return make_pair(x, sum); } for (int i = 17; i >= 0; i--) { if (par[i][x] != par[i][y]) { sum = (sum + val[i][x]) % md; sum = (sum + val[i][y]) % md; x = par[i][x]; y = par[i][y]; } } sum = (sum + val[0][x]) % md; sum = (sum + val[0][y]) % md; return make_pair(par[0][x], sum); } int main() { ios_base::sync_with_stdio(0); cin.tie(NULL); cin >> n; for (int i = 1; i < n; i++) { cin >> a[i] >> b[i] >> c[i]; a[i + n - 1] = b[i]; b[i + n - 1] = a[i]; c[i + n - 1] = c[i]; adj[a[i]].push_back(i); adj[b[i]].push_back(i + n - 1); } dep[1] = 1; Dfs1(1); s1[1] = s1c[1]; s2[1] = s2c[1]; Dfs2(1); for (int i = 1; i <= 17; i++) { for (int j = 1; j <= n; j++) { par[i][j] = par[i - 1][par[i - 1][j]]; val[i][j] = (val[i - 1][j] + val[i - 1][par[i - 1][j]]) % md; } } cin >> q; for (int iQ = 1; iQ <= q; iQ++) { int x, y; cin >> x >> y; pair<int, int> l = Lca(x, y); if (l.first == y) { cout << ((s2[x] - 2ll * l.second * l.second % md * (n - cnt[y]) - 2ll * (s2[y] - s2c[y]) - 4ll * l.second * (s1[y] - s1c[y])) % md + md) % md << "\n"; } else { cout << ((-s2[x] + 2ll * l.second * l.second % md * cnt[y] + 2ll * s2c[y] + 4ll * l.second * s1c[y]) % md + md) % md << "\n"; } } return 0; }
#include <bits/stdc++.h> using namespace std; template <typename T> void chkmax(T &x, T y) { if (x < y) x = y; } template <typename T> void chkmin(T &x, T y) { if (x > y) x = y; } inline int read() { int x = 0; char c = getchar(); bool f = 0; while (c < 48) f |= c == '-', c = getchar(); while (c > 47) x = x * 10 + (c ^ 48), c = getchar(); return f ? -x : x; } const int maxn = 1e5 + 10, P = 1e9 + 7; int Inc(int x, int y) { return x + y < P ? x + y : x + y - P; } int Dec(int x, int y) { return x < y ? x - y + P : x - y; } void Add(int &x, int y) { x += y; if (x >= P) x -= P; } void Sub(int &x, int y) { x -= y; if (x < 0) x += P; } int qp(int a, int k) { int res = 1; for (; k; k >>= 1, a = 1ll * a * a % P) if (k & 1) res = 1ll * res * a % P; return res; } int n, q; int ecnt = 1, h[maxn]; struct edges { int nxt, to, w; } E[maxn << 1]; void addline(int u, int v, int w) { E[++ecnt] = {h[u], v, w}, h[u] = ecnt; } int sum1[maxn], sum2[maxn]; int fa[maxn], sz[maxn], dep[maxn], son[maxn], top[maxn], dis[maxn], dfn[maxn]; void dfs1(int u, int f) { fa[u] = f, sz[u] = 1, dep[u] = dep[f] + 1; for (int i = h[u]; i; i = E[i].nxt) { int v = E[i].to; if (v != f) { dis[v] = Inc(dis[u], E[i].w), dfs1(v, u); if (sz[son[u]] < sz[v]) son[u] = v; sz[u] += sz[v], Add(sum1[u], (sum1[v] + 1ll * sz[v] * E[i].w) % P), Add(sum2[u], (sum2[v] + 2ll * sum1[v] * E[i].w % P + 1ll * E[i].w * E[i].w % P * sz[v] % P) % P); } } } int dp1[maxn], dp2[maxn]; void dfs2(int u, int tp) { for (int i = h[u]; i; i = E[i].nxt) { int v = E[i].to; if (v != fa[u]) { dp1[v] = (dp1[u] + 1ll * E[i].w * (n - sz[v] * 2 + P) % P) % P; dp2[v] = (dp2[u] - (1ll * E[i].w * E[i].w % P * sz[v] % P + 2ll * E[i].w * sum1[v] % P) % P + 1ll * E[i].w * E[i].w % P * (n - sz[v]) % P + 2ll * E[i].w % P * (dp1[u] - sum1[v] - 1ll * E[i].w * sz[v] % P + P + P) % P) % P; } } static int now; dfn[u] = ++now, top[u] = tp; if (son[u]) dfs2(son[u], tp); for (int i = h[u]; i; i = E[i].nxt) { int v = E[i].to; if (v != fa[u] && v != son[u]) dfs2(v, v); } } int qlca(int u, int v) { for (; top[u] != top[v]; u = fa[top[u]]) { if (dep[top[u]] < dep[top[v]]) swap(u, v); } return dep[u] < dep[v] ? u : v; } struct ZZH { int c[maxn]; void ins(int u, int x) { Add(c[dfn[u]], x), Sub(c[dfn[u] + sz[u]], x); } void build() { for (int i = (2), iend = (n + 1); i <= iend; ++i) Add(c[i], c[i - 1]); } int query(int u, int v) { return Dec(c[dfn[u]], c[dfn[v]]); } } B1_sz, B2_sz, B1_s1, B2_s1, B1_y, B2_y, B_w; void solve() { cin >> n; for (int i = (2), iend = (n); i <= iend; ++i) { int u = read(), v = read(), w = read(); addline(u, v, w), addline(v, u, w); } dfs1(1, 0), dp1[1] = sum1[1], dp2[1] = sum2[1], dfs2(1, 1); for (int i = (2), iend = (n); i <= iend; ++i) { B1_sz.ins(i, 1ll * dis[fa[i]] * (sz[fa[i]] - sz[i]) % P); B2_sz.ins(i, 1ll * dis[fa[i]] * dis[fa[i]] % P * (sz[fa[i]] - sz[i]) % P); int w = Dec(dis[i], dis[fa[i]]); B_w.ins(i, (1ll * w * w % P * sz[i] % P + 2ll * w * sum1[i] % P) % P); int tp = (sum1[fa[i]] - sum1[i] - 1ll * w * sz[i] % P + P + P) % P; B1_y.ins(i, tp); B2_y.ins(i, 1ll * dis[fa[i]] * tp % P); } for (int i = (1), iend = (n); i <= iend; ++i) { B1_s1.ins(i, sum1[i]); B2_s1.ins(i, 1ll * dis[i] * sum1[i] % P); } B1_sz.build(), B2_sz.build(), B_w.build(); B1_s1.build(), B2_s1.build(), B1_y.build(), B2_y.build(); cin >> q; while (q--) { int u = read(), v = read(), res = 0; if (dfn[u] < dfn[v] || dfn[u] >= dfn[v] + sz[v]) { int l = (dis[u] + dis[v] - 2ll * dis[qlca(u, v)] % P + P) % P; res = (1ll * l * l % P * sz[v] % P + 2ll * l * sum1[v] % P + sum2[v]) % P; } else { res = (sum2[v] + 1ll * dis[u] * dis[u] % P * (sz[v] - sz[u]) % P) % P; res = (res + B2_sz.query(u, v) - 2ll * dis[u] * B1_sz.query(u, v) % P + P) % P; res = (res - B_w.query(u, v) + P) % P; res = (res + 2ll * (1ll * dis[u] * B1_y.query(u, v) % P - B2_y.query(u, v) + P) % P + P) % P; } res = (res * 2ll - dp2[u] + P) % P; printf("%d\n", res); } } signed main() { solve(); return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 1e5 + 10; const int mod = 1e9 + 7; long long mark[N], st[N], ft[N], lzy[4 * N], ans[N], n, t; pair<long long, long long> seg[4 * N]; vector<pair<long long, long long> > adj[N], qry[N]; void add(int id, int l, int r, long long x) { seg[id].first = (seg[id].first + 2LL * seg[id].second * x + (x * x) % mod * 1LL * (r - l)) % mod; seg[id].second = (seg[id].second + x * (r - l)) % mod; lzy[id] = (lzy[id] + x) % mod; } void shift(int id, int l, int r) { int md = (l + r) >> 1; add(id << 1, l, md, lzy[id]); add(id << 1 | 1, md, r, lzy[id]); lzy[id] = 0; } void upd(int l, int r, long long x, int s = 0, int e = n, int id = 1) { if (e <= l || r <= s) return; if (l <= s && e <= r) { add(id, s, e, x); return; } shift(id, s, e); int md = (s + e) >> 1; upd(l, r, x, s, md, id << 1); upd(l, r, x, md, e, id << 1 | 1); seg[id].first = (seg[id << 1].first + seg[id << 1 | 1].first) % mod; seg[id].second = (seg[id << 1].second + seg[id << 1 | 1].second) % mod; } long long get(int l, int r, int s = 0, int e = n, int id = 1) { if (e <= l || r <= s) return 0; if (l <= s && e <= r) return seg[id].first; shift(id, s, e); int md = (s + e) >> 1; return (get(l, r, s, md, id << 1) + get(l, r, md, e, id << 1 | 1)) % mod; } void preDFS(int v, long long d = 0) { mark[v] = 1; st[v] = t++; upd(st[v], st[v] + 1, d % mod); for (pair<long long, long long> e : adj[v]) if (!mark[e.first]) preDFS(e.first, d + e.second); ft[v] = t; } void DFS(int v) { mark[v] = 1; for (pair<long long, long long> p : qry[v]) { int u = p.first, id = p.second; ans[id] = (2LL * get(st[u], ft[u]) - seg[1].first) % mod; } for (pair<long long, long long> e : adj[v]) { int u = e.first, w = e.second; if (mark[u]) continue; upd(0, n, w); upd(st[u], ft[u], -2 * w); DFS(u); upd(st[u], ft[u], 2 * w); upd(0, n, -w); } } int main() { ios::sync_with_stdio(0); cin.tie(0); cout.tie(0); cin >> n; for (int i = 1; i < n; i++) { int u, v, w; cin >> u >> v >> w; adj[u].push_back(make_pair(v, w)); adj[v].push_back(make_pair(u, w)); } int q; cin >> q; for (int i = 0; i < q; i++) { int u, v; cin >> u >> v; qry[u].push_back(make_pair(v, i)); } preDFS(1); memset(mark, 0, sizeof mark); DFS(1); for (int i = 0; i < q; i++) cout << (ans[i] + mod) % mod << '\n'; return 0; }
#include <bits/stdc++.h> using namespace std; inline int in() { int x; scanf("%d", &x); return x; } const long double EPS = 1e-12; const int INF = 1e9 + 10; const long long LINF = 1000ll * 1000 * 1000 * 1000 * 1000 * 1000 + 100; const int MN = 1e5 + 10; const int MOD = 1e9 + 7; int n, q; vector<pair<int, int> > adj[MN], qr[MN]; int ans[MN]; long long mul[4 * MN], seg[4 * MN], lz[4 * MN]; int Time, st[MN], ft[MN]; long long d_tmp[MN]; int rev[MN]; void input() { scanf("%d", &n); for (int i = 0; i < n - 1; ++i) { int a, b, c; scanf("%d%d%d", &a, &b, &c); --a, --b; adj[a].push_back(pair<int, int>(b, c)), adj[b].push_back(pair<int, int>(a, c)); } scanf("%d", &q); for (int i = 0; i < q; ++i) { int u, v; scanf("%d%d", &u, &v); --u, --v; qr[u].push_back(pair<int, int>(v, i)); } } void dfs_prep(int s, int pr, long long cur) { st[s] = Time++; rev[st[s]] = s; d_tmp[s] = cur; for (int i = 0; i < ((int)(adj[s]).size()); ++i) { int v = adj[s][i].first; if (v == pr) continue; dfs_prep(v, s, (cur + adj[s][i].second) % MOD); } ft[s] = Time; } void change(int segnum, int val, int left, int right) { int t = right - left + 1, mid = (left + right) >> 1; mul[segnum] = (1ll * mul[segnum] + ((1ll * val * val) % MOD * (1ll * t * (t - 1) / 2)) % MOD) % MOD; mul[segnum] = (1ll * mul[segnum] + ((seg[segnum] * (t - 1)) % MOD * val) % MOD) % MOD; if (mul[segnum] < 0) mul[segnum] += MOD; seg[segnum] = (1ll * seg[segnum] + 1ll * val * t) % MOD; if (seg[segnum] < 0) seg[segnum] += MOD; } void shift(int segnum, int left, int right) { int mid = (left + right) >> 1; change(2 * segnum, lz[segnum], left, mid); change(2 * segnum + 1, lz[segnum], mid + 1, right); lz[2 * segnum] += lz[segnum], lz[2 * segnum + 1] += lz[segnum]; lz[2 * segnum] %= MOD, lz[2 * segnum + 1] %= MOD, lz[segnum] = 0; } void build(int segnum, int left, int right) { if (left == right) { seg[segnum] = d_tmp[rev[left]]; return; } int mid = (left + right) >> 1; build(2 * segnum, left, mid), build(2 * segnum + 1, mid + 1, right); seg[segnum] = (seg[2 * segnum] + seg[2 * segnum + 1]) % MOD; mul[segnum] = (mul[2 * segnum] + mul[2 * segnum + 1]) % MOD; mul[segnum] = (mul[segnum] + seg[2 * segnum] * seg[2 * segnum + 1]) % MOD; } void upd(int segnum, int left, int right, int l, int r, int val) { if (r < left || right < l) return; if (l <= left && right <= r) { change(segnum, val, left, right); lz[segnum] = (lz[segnum] + val) % MOD; return; } shift(segnum, left, right); int mid = (left + right) >> 1; upd(2 * segnum, left, mid, l, r, val), upd(2 * segnum + 1, mid + 1, right, l, r, val); seg[segnum] = (seg[2 * segnum] + seg[2 * segnum + 1]) % MOD; mul[segnum] = (mul[2 * segnum] + mul[2 * segnum + 1]) % MOD; mul[segnum] = (mul[segnum] + (seg[2 * segnum] * seg[2 * segnum + 1]) % MOD) % MOD; } long long get(int segnum, int left, int right, int l, int r) { if (r < left || right < l) return 0; if (l <= left && right <= r) return ((seg[segnum] * seg[segnum]) % MOD - (2ll * mul[segnum]) % MOD + MOD) % MOD; int mid = (left + right) >> 1; shift(segnum, left, right); return (get(2 * segnum, left, mid, l, r) + get(2 * segnum + 1, mid + 1, right, l, r)) % MOD; } void dfs(int s, int pr, int c) { for (int i = 0; i < ((int)(qr[s]).size()); ++i) { int v = qr[s][i].first; long long val1 = get(1, 0, n - 1, st[v], ft[v] - 1); long long val2 = get(1, 0, n - 1, 0, n - 1); ans[qr[s][i].second] = (2ll * val1 - val2 + MOD) % MOD; } for (int i = 0; i < ((int)(adj[s]).size()); ++i) { int v = adj[s][i].first, w = adj[s][i].second; if (v == pr) continue; upd(1, 0, n - 1, 0, n - 1, w); upd(1, 0, n - 1, st[v], ft[v] - 1, -2 * w); dfs(v, s, w); } if (pr != -1) { upd(1, 0, n - 1, 0, n - 1, -c); upd(1, 0, n - 1, st[s], ft[s] - 1, 2 * c); } } int main() { ios_base ::sync_with_stdio(false), cin.tie(0), cout.tie(0); input(); dfs_prep(0, -1, 0); build(1, 0, n - 1); dfs(0, -1, 0); for (int i = 0; i < q; ++i) printf("%d\n", ans[i]); return 0; }
#include <bits/stdc++.h> const int MAXN = 1e5 + 10; const int MOD = 1e9 + 7; int n, q; struct Edge { int v, w, next; } edge[MAXN << 1]; int head[MAXN], tail; void insert(int u, int v, int w) { edge[++tail] = (Edge){v, w, head[u]}; head[u] = tail; } namespace { inline int add(int x) { return x >= MOD ? x - MOD : x; } inline int sub(int x) { return x < 0 ? x + MOD : x; } inline int mul(int x, int y) { return (long long)x * y % MOD; } } // namespace namespace solver1 { int son_w2[MAXN], son_w[MAXN], up_w2[MAXN], up_w[MAXN], sz[MAXN]; int anc[MAXN][21], len[MAXN], dep[MAXN]; void dfs(int u, int fa) { dep[u] = dep[fa] + 1; sz[u] = 1; anc[u][0] = fa; for (int i = 1; i <= 20; i++) anc[u][i] = anc[anc[u][i - 1]][i - 1]; for (int i = head[u]; i; i = edge[i].next) { int v = edge[i].v; if (v == fa) continue; len[v] = add(len[u] + edge[i].w); dfs(v, u); sz[u] += sz[v]; son_w2[u] = add(son_w2[u] + add(son_w2[v] + add(mul(edge[i].w * 2, son_w[v]) + mul(mul(edge[i].w, edge[i].w), sz[v])))); son_w[u] = add(son_w[u] + add(son_w[v] + mul(edge[i].w, sz[v]))); } } void dfs2(int u, int fa, int w2, int w) { up_w2[u] = w2; up_w[u] = w; for (int i = head[u]; i; i = edge[i].next) { int v = edge[i].v; if (v == fa) continue; int ww2 = add( w2 + sub(son_w2[u] - add(son_w2[v] + add(mul(edge[i].w * 2, son_w[v]) + mul(mul(edge[i].w, edge[i].w), sz[v]))))); int ww = add(w + sub(son_w[u] - add(son_w[v] + mul(edge[i].w, sz[v])))); dfs2(v, u, add(ww2 + add(mul(edge[i].w * 2, ww) + mul(mul(edge[i].w, edge[i].w), n - sz[v]))), add(ww + mul(edge[i].w, n - sz[v]))); } } int lca(int x, int y) { if (dep[x] < dep[y]) std::swap(x, y); int k = dep[x] - dep[y]; for (int i = 20; i >= 0; i--) { if (k & (1 << i)) { x = anc[x][i]; } } if (x == y) return x; for (int i = 20; i >= 0; i--) { if (anc[x][i] != anc[y][i]) { x = anc[x][i]; y = anc[y][i]; } } return anc[x][0]; } void main() { dfs(1, 0); dfs2(1, 0, 0, 0); while (q--) { int u, v; scanf("%d%d", &u, &v); int l = lca(u, v); int w = sub(add(len[u] + len[v]) - add(len[l] + len[l])); int part2 = add(son_w2[u] + up_w2[u]), part1; if (l != v) { part1 = add(son_w2[v] + add(mul(w * 2, son_w[v]) + mul(mul(w, w), sz[v]))); } else { part1 = sub( add(son_w2[u] + up_w2[u]) - add(add(mul(mul(w, w), n - sz[v]) + up_w2[v]) + mul(w * 2, up_w[v]))); } printf("%d\n", sub(add(part1 * 2) - part2)); } } } // namespace solver1 int main() { scanf("%d", &n); for (int i = 1; i < n; i++) { int u, v, w; scanf("%d%d%d", &u, &v, &w); insert(u, v, w); insert(v, u, w); } scanf("%d", &q); solver1::main(); }
#include <bits/stdc++.h> using namespace std; const int MAXN = 1e6 + 100; const int MOD = 1e9 + 7; long long T = 0; long long st[MAXN], fn[MAXN]; vector<pair<long long, long long>> ver[MAXN]; pair<long long, long long> q[MAXN]; vector<long long> query[MAXN]; long long d[MAXN]; long long s[MAXN]; long long sum[MAXN * 4], lazy[MAXN * 4], seg[MAXN * 4]; long long res[MAXN], n; inline void calc(long long id, long long xl, long long xr, long long qv) { long long sqr = qv * qv % MOD; seg[id] = (2 * sum[id] * qv + sqr * (xr - xl) + seg[id]) % MOD; sum[id] = (sum[id] + qv * (xr - xl)) % MOD; lazy[id] = (lazy[id] + qv) % MOD; } inline void shift(long long id, long long xl, long long xr) { if (!lazy[id]) return; long long mid = (xl + xr) / 2; calc(2 * id + 1, xl, mid, lazy[id]); calc(2 * id + 2, mid, xr, lazy[id]); lazy[id] = 0; } void upd(long long ql, long long qr, long long qv, long long xl = 0, long long xr = MAXN, long long id = 0) { if (ql <= xl && xr <= qr) return calc(id, xl, xr, qv); if (qr <= xl || xr <= ql) return; shift(id, xl, xr); long long mid = (xl + xr) / 2; upd(ql, qr, qv, xl, mid, 2 * id + 1); upd(ql, qr, qv, mid, xr, 2 * id + 2); seg[id] = (seg[2 * id + 1] + seg[2 * id + 2]) % MOD; sum[id] = (sum[2 * id + 1] + sum[2 * id + 2]) % MOD; } long long get(long long ql, long long qr, long long xl = 0, long long xr = MAXN, long long id = 0) { if (ql >= qr) return 0; if (ql <= xl && xr <= qr) return seg[id]; if (qr <= xl || xr <= ql) return 0; shift(id, xl, xr); long long mid = (xl + xr) / 2; return (get(ql, qr, xl, mid, 2 * id + 1) + get(ql, qr, mid, xr, 2 * id + 2)) % MOD; } void build(long long xl = 0, long long xr = MAXN, long long id = 0) { if (xr - xl == 1) { sum[id] = s[xl]; seg[id] = s[xl] * s[xl] % MOD; return; } long long mid = (xl + xr) / 2; build(xl, mid, 2 * id + 1); build(mid, xr, 2 * id + 2); sum[id] = (sum[2 * id + 1] + sum[2 * id + 2]) % MOD; seg[id] = (seg[2 * id + 1] + seg[2 * id + 2]) % MOD; } void pre_dfs(long long v, long long par = 0) { st[v] = T++; for (auto e : ver[v]) { long long u = e.first; long long w = e.second; if (u == par) continue; d[u] = (d[v] + w) % MOD; pre_dfs(u, v); } fn[v] = T; } void dfs(long long v, long long w = 0, long long par = 0) { for (auto u : query[v]) { long long k = q[u].second; res[u] = (2 * get(st[k], fn[k]) - seg[0] + MOD) % MOD; } for (auto e : ver[v]) { long long u = e.first; long long z = e.second; if (u == par) continue; upd(0, n, +z); upd(st[u], fn[u], (2 * MOD - 2 * z) % MOD); dfs(u, z, v); } upd(0, n, MOD - w); upd(st[v], fn[v], 2 * w % MOD); } int32_t main() { ios_base::sync_with_stdio(0); cin.tie(0), cout.tie(0); cin >> n; for (long long i = 1; i < n; i++) { long long x, y, z; cin >> x >> y >> z; ver[x].push_back({y, z}); ver[y].push_back({x, z}); } pre_dfs(1); for (long long i = 1; i <= n; i++) s[st[i]] = d[i]; build(); long long nq; cin >> nq; for (long long i = 0; i < nq; i++) { cin >> q[i].first >> q[i].second; query[q[i].first].push_back(i); } dfs(1); for (long long i = 0; i < nq; i++) cout << res[i] << '\n'; }
#include <bits/stdc++.h> using namespace std; const int N = 1e5 + 9; const int mod = 1e9 + 7; int s[N], st[N], ed[N], n, tot, ans[N]; long long sq[N << 2], sum[N << 2], ch[N << 2]; vector<pair<int, int> > adj[N]; vector<int> qu[N]; int rend(int v, int b, int e, int x) { ch[v] = (ch[v] + x) % mod; sq[v] = (sq[v] + (x * 1LL * x % mod) * (e - b) + sum[v] * x * 2) % mod; sum[v] = (x * 1LL * (e - b) + sum[v]) % mod; } void spread(int v, int b, int e) { int mid = b + e >> 1, l = v << 1, r = l | 1; rend(l, b, mid, ch[v]); rend(r, mid, e, ch[v]); ch[v] = 0; } void renew(int v) { int l = v << 1, r = l | 1; sq[v] = (sq[l] + sq[r]) % mod; sum[v] = (sum[l] + sum[r]) % mod; } void update(int i, int j, int x, int v = 1, int b = 0, int e = n) { if (i >= e || b >= j) return; if (i <= b && e <= j) { rend(v, b, e, x); return; } int mid = b + e >> 1, l = v << 1, r = l | 1; spread(v, b, e); update(i, j, x, l, b, mid); update(i, j, x, r, mid, e); renew(v); } int query(int i, int j, int v = 1, int b = 0, int e = n) { if (i >= e || b >= j) return 0; if (i <= b && e <= j) return sq[v]; int mid = b + e >> 1, l = v << 1, r = l | 1; spread(v, b, e); return (query(i, j, l, b, mid) + query(i, j, r, mid, e)) % mod; } void dfs_init(int v, int p = -1, int d = 0) { st[v] = tot++; update(st[v], st[v] + 1, d); for (int i = 0; i < (int)adj[v].size(); i++) if (adj[v][i].first != p) { int u = adj[v][i].first, w = adj[v][i].second; dfs_init(u, v, (d + w) % mod); } ed[v] = tot; } void dfs_ans(int v, int p = -1) { for (int i = 0; i < (int)adj[v].size(); i++) if (adj[v][i].first != p) { int u = adj[v][i].first, w = adj[v][i].second; update(st[0], ed[0], w); update(st[u], ed[u], (-2 * w + 2 * mod) % mod); dfs_ans(u, v); update(st[0], ed[0], (-w + mod) % mod); update(st[u], ed[u], 2 * w % mod); } for (int i = 0; i < (int)qu[v].size(); i++) { int id = qu[v][i], u = s[id]; ans[id] = (0LL + -query(st[0], ed[0]) + 2 * query(st[u], ed[u]) + 100 * 1LL * mod) % mod; } return; } int main() { ios_base::sync_with_stdio(0); cin >> n; for (int i = 0; i < n - 1; i++) { int u, v, w; cin >> u >> v >> w; u--, v--; adj[u].push_back({v, w}); adj[v].push_back({u, w}); } int q; cin >> q; for (int i = 0; i < q; i++) { int u, v; cin >> u >> v; u--, v--; s[i] = v; qu[u].push_back(i); } dfs_init(0); dfs_ans(0); for (int i = 0; i < q; i++) cout << ans[i] << '\n'; return 0; }
#include <bits/stdc++.h> using namespace std; const long long MOD = 1000000007; const int MAXN = 100010; int n; struct edge { int t; long long w; edge *next; } epool[MAXN * 2], *e[MAXN]; int psz; int dep[MAXN], fa[MAXN][21]; long long dis[MAXN]; struct S { long long size, sum, sum2; S() {} S(long long size, long long sum, long long sum2) : size(size), sum(sum), sum2(sum2) {} S operator+(long long d) const { return S(size, (sum + d * size % MOD) % MOD, (sum2 + 2 * d * sum % MOD + d * d % MOD * size % MOD) % MOD); } S &operator+=(const S &b) { size += b.size, sum += b.sum, sum2 += b.sum2; size %= MOD, sum %= MOD, sum2 %= MOD; return *this; } S &operator-=(const S &b) { size += MOD - b.size, sum += MOD - b.sum, sum2 += MOD - b.sum2; size %= MOD, sum %= MOD, sum2 %= MOD; return *this; } } f[MAXN], g[MAXN]; void addedge(int u, int v, long long w) { epool[psz] = (edge){v, w, e[u]}; e[u] = epool + psz++; } void init() { psz = 0, memset(e, 0, sizeof(e)); scanf("%d", &n); for (int i = 1; i < n; ++i) { int u, v, w; scanf("%d%d%d", &u, &v, &w); addedge(u, v, w % MOD); addedge(v, u, w % MOD); } } void dfs1(int u) { f[u] = S(1, 0, 0); for (int i = 0; i < 20; ++i) fa[u][i + 1] = fa[fa[u][i]][i]; for (edge *i = e[u]; i; i = i->next) { int v = i->t; if (v == fa[u][0]) continue; fa[v][0] = u; dep[v] = dep[u] + 1; dis[v] = (dis[u] + i->w) % MOD; dfs1(v); f[u] += f[v] + i->w; } } void dfs2(int u) { for (edge *i = e[u]; i; i = i->next) { int v = i->t; if (v == fa[u][0]) continue; g[v] = g[u] + i->w; g[v] += f[u] + i->w; g[v] -= f[v] + i->w * 2 % MOD; dfs2(v); } } int lca(int u, int v) { if (dep[u] < dep[v]) swap(u, v); for (int i = 20; i >= 0; --i) { if (dep[fa[u][i]] >= dep[v]) u = fa[u][i]; } if (u == v) return u; for (int i = 20; i >= 0; --i) { if (fa[u][i] != fa[v][i]) u = fa[u][i], v = fa[v][i]; } return fa[u][0]; } void solve() { int q; scanf("%d", &q); while (q--) { int u, v; scanf("%d%d", &u, &v); int w = lca(u, v); long long d = ((dis[u] + dis[v] - dis[w] * 2) % MOD + MOD) % MOD; S s1, s2; if (w == v) { s2 = g[v] + d; s1 = f[u]; s1 += g[u]; s1 -= s2; } else { s1 = f[v] + d; s2 = f[u]; s2 += g[u]; s2 -= s1; } s1 -= s2; printf("%d\n", (int)s1.sum2); } } int main() { init(); dep[1] = 1, dis[1] = 0; dfs1(1); dfs2(1); solve(); }
#include <bits/stdc++.h> using namespace std; const long long N = 1e5 + 300; const long long mod = 1e9 + 7; const long long NN = 20 + 1; vector<pair<long long, long long> > a[N]; long long p[N][NN], t[N], dp[N], dp2[N], sum[N], h[N], dp3[N], dp4[N], n; void dfs2(long long v, long long par = -1, long long col = -1) { dp3[v] = dp[v]; dp4[v] = dp2[v]; if (par != -1) { dp4[v] = 0; dp3[v] = (dp3[par] + ((n - 2 * t[v] + 2 * mod) * col) % mod) % mod; dp4[v] = (dp4[par] + (((col * col) % mod) * (n - 1)) % mod + 2 * (col * dp3[par]) % mod) % mod; dp4[v] += 2 * mod - (4 * dp[v] * col) % mod - (t[v] * 4 * ((col * col) % mod)) % mod + (col * col) % mod; dp4[v] %= mod; } for (long long i = 0, u, c; i < a[v].size(); i++) { u = a[v][i].first, c = a[v][i].second; if (u != par) { dfs2(u, v, c); } } } void dfs(long long v, long long par = -1) { p[v][0] = par; for (long long i = 1; i < NN; i++) { if (p[v][i - 1] != -1) p[v][i] = p[p[v][i - 1]][i - 1]; } t[v] = 1; for (long long i = 0, u, c; i < a[v].size(); i++) { u = a[v][i].first, c = a[v][i].second; if (u != par) { sum[u] = (sum[v] + c) % mod; h[u] = h[v] + 1; dfs(u, v); t[v] += t[u]; dp[v] += (dp[u] + c * t[u]) % mod; dp[v] %= mod; dp2[v] += (dp2[u] + (t[u] * ((c * c) % mod)) % mod) % mod; dp2[v] %= mod; dp2[v] += 2 * ((c * dp[u]) % mod); dp2[v] %= mod; } } } long long getp(long long v, long long k) { for (long long i = 0; i < NN; i++) { if ((k & (1 << i)) != 0) v = p[v][i]; } return v; } long long lca(long long v, long long u) { if (h[u] > h[v]) swap(u, v); v = getp(v, h[v] - h[u]); if (u == v) return v; for (long long i = NN - 1; i >= 0; i--) { if (p[u][i] != p[v][i]) u = p[u][i], v = p[v][i]; } return p[u][0]; } int32_t main() { ios::sync_with_stdio(0); cin.tie(0); memset(p, -1, sizeof(p)); cin >> n; for (long long i = 0, u, v, c; i < n - 1; i++) { cin >> u >> v >> c; u--; v--; a[u].push_back(make_pair(v, c)); a[v].push_back(make_pair(u, c)); } dfs(0); dfs2(0); long long m; cin >> m; for (long long _ = 0, u, v; _ < m; _++) { cin >> u >> v; u--; v--; long long l = lca(u, v); long long x = sum[u] + sum[v] - 2 * sum[l] + 2 * mod; x %= mod; long long ans = dp2[v] + (t[v] * ((x * x) % mod)) % mod + 2 * ((dp[v] * x) % mod); if (v == l) { long long h = (dp4[v] - dp2[v] + mod) % mod + ((n - t[v]) * ((x * x) % mod)) % mod + (2 * (((dp3[v] - dp[v]) * x) % mod) % mod); h %= mod; ans = dp4[u] - h + mod; } ans %= mod; ans *= 2; ans += mod - dp4[u]; ans %= mod; cout << ans << "\n"; } return 0; }
#include <bits/stdc++.h> using namespace std; const double pi = acos(-1); const int mo = 1e9 + 7; struct Val { int x2, x1, x0; friend Val operator+(const Val &a, const Val &b) { return Val{(a.x2 + b.x2) % mo, (a.x1 + b.x1) % mo, (a.x0 + b.x0) % mo}; } friend Val operator-(const Val &a, const Val &b) { return Val{(a.x2 - b.x2) % mo, (a.x1 - b.x1) % mo, (a.x0 - b.x0) % mo}; } friend Val operator*(const Val &a, const int d) { Val c; c.x2 = (a.x2 + 2ll * d * a.x1 + (long long)d * d % mo * a.x0) % mo; c.x1 = (a.x1 + 1ll * d * a.x0) % mo; c.x0 = a.x0; return c; } } f[120000], g[120000], sum[120000]; int w[120000], ff[21][120000], dep[120000], Q, n; vector<pair<int, int> > E[120000]; int LCA(int x, int y) { if (dep[x] < dep[y]) swap(x, y); for (int i = 20; i >= 0; --i) if (dep[x] - dep[y] >= 1 << i) x = ff[i][x]; if (x == y) return x; for (int i = 20; i >= 0; --i) if (ff[i][x] != ff[i][y]) x = ff[i][x], y = ff[i][y]; return ff[0][x]; } void dfs(int x, int fa) { ff[0][x] = fa; for (int i = 1; i <= 20; ++i) ff[i][x] = ff[i - 1][ff[i - 1][x]]; f[x].x2 = f[x].x1 = 0; f[x].x0 = 1; for (auto e : E[x]) if (e.first != fa) { dep[e.first] = dep[x] + 1; w[e.first] = (w[x] + e.second) % mo; dfs(e.first, x); f[x] = f[x] + f[e.first] * e.second; } } void dp(int x, int fa) { Val tmp = {0, 0, 1}; for (auto e : E[x]) if (e.first != fa) tmp = tmp + f[e.first] * e.second; for (auto e : E[x]) if (e.first != fa) { int y = e.first; sum[y] = (sum[x] + (tmp - f[y] * e.second)) * e.second; g[y] = (tmp + g[x] - f[y] * e.second) * e.second; dp(y, x); } } int main() { scanf("%d", &n); for (int i = 1; i <= n - 1; ++i) { int x, y, k; scanf("%d%d%d", &x, &y, &k); E[x].push_back(make_pair(y, k)); E[y].push_back(make_pair(x, k)); } dfs(1, 0); dp(1, 0); scanf("%d", &Q); for (int _ = 1; _ <= Q; ++_) { int u, v; scanf("%d%d", &u, &v); int lca = LCA(u, v), dist = ((long long)w[u] + w[v] - 2 * w[lca]) % mo, ans; if (lca == v) ans = (2ll * (f[u].x2 + (sum[u] - sum[v] * dist).x2) - (f[u] + g[u]).x2) % mo; else ans = (2ll * (f[v] * dist).x2 - (f[u] + g[u]).x2) % mo; printf("%d\n", (ans + mo) % mo); } }
#include <bits/stdc++.h> using namespace std; const int MAXN = 1e5 + 6.66; const int LOGMAXN = 20; const long long mod = 1e9 + 7; vector<pair<int, long long>> tree[MAXN]; int par[MAXN]; long long upedge[MAXN]; int sz[MAXN]; int h[MAXN]; int lca[LOGMAXN][MAXN]; long long sum[LOGMAXN][MAXN]; long long down[MAXN]; long long down2[MAXN]; long long up[MAXN]; long long up2[MAXN]; long long tot[MAXN]; void lca_init_dfs(int v = 1, int p = 0, int hei = 0, int wei = 0) { par[v] = p; h[v] = hei; upedge[v] = wei; for (auto x : tree[v]) if (x.first != p) lca_init_dfs(x.first, v, hei + 1, x.second); } void init_lca(int n) { lca_init_dfs(); for (int i = 1; i <= n; i++) lca[0][i] = par[i], sum[0][i] = upedge[i]; for (int i = 1; i < LOGMAXN; i++) for (int j = 1; j <= n; j++) lca[i][j] = lca[i - 1][lca[i - 1][j]], sum[i][j] = sum[i - 1][j] + sum[i - 1][lca[i - 1][j]]; } int get_par(int v, int x) { for (; x; x ^= x & -x) v = lca[__builtin_ctz(x)][v]; return v; } bool is_anc(int v, int u) { if (h[v] > h[u]) return false; return get_par(u, h[u] - h[v]) == v; } int get_lca(int v, int u) { if (h[v] > h[u]) swap(u, v); u = get_par(u, h[u] - h[v]); if (u == v) return v; for (int i = LOGMAXN - 1; i > -1; i--) if ((1 << i) <= h[v] && lca[i][v] != lca[i][u]) u = lca[i][u], v = lca[i][v]; return lca[0][u]; } long long get_path_par(int v, int p) { long long ans = 0; for (int i = LOGMAXN - 1; i > -1; i--) if (h[v] - (1 << i) >= h[p]) (ans += sum[i][v]) %= mod, v = lca[i][v]; return ans; } long long get_path(int v, int u) { int lc = get_lca(u, v); return (get_path_par(u, lc) + get_path_par(v, lc)) % mod; } long long pow2_sum(long long sw2, long long sw, long long x, long long s) { sw2 %= mod, sw %= mod, x %= mod, s %= mod; if (sw2 < 0) sw2 += mod; if (sw < 0) sw += mod; if (x < 0) x += mod; return (sw2 + 2LL * x * sw % mod + 1LL * x * x % mod * s % mod) % mod; } void dfs_up(int v = 1, int p = 0) { sz[v] = 1; for (auto x : tree[v]) if (x.first != p) { dfs_up(x.first, v); sz[v] += sz[x.first]; (down[v] += down[x.first] + x.second * sz[x.first]) %= mod; (down2[v] += pow2_sum(down2[x.first], down[x.first], x.second, sz[x.first])) %= mod; } } void dfs_down(int v = 1, int p = 0, long long upp = 0, long long upp2 = 0) { upp %= mod, upp2 %= mod; up[v] = upp; up2[v] = upp2; tot[v] = (up2[v] + down2[v]) % mod; for (auto x : tree[v]) if (x.first != p) { long long ss = upp + down[v] - down[x.first] + 2LL * mod + 1LL * (sz[1] - 2 * sz[x.first]) * x.second % mod; ss %= mod; long long ss2 = pow2_sum( upp2 + down2[v] + mod - pow2_sum(down2[x.first], down[x.first], x.second, sz[x.first]), upp + down[v] - down[x.first] - sz[x.first] * x.second % mod + 2LL * mod, x.second, (sz[1] - sz[x.first])); dfs_down(x.first, v, ss, ss2); } } void initiate(int& n) { scanf("%d", &n); for (int i = 1; i < n; i++) { int x, y; long long z; scanf("%d %d %lld", &x, &y, &z); tree[x].push_back({y, z}); tree[y].push_back({x, z}); } init_lca(n); dfs_up(); dfs_down(); } int main() { int n; initiate(n); int q; scanf("%d", &q); while (q--) { int u, v; scanf("%d %d", &u, &v); long long ans = 0; if (u == v) ans = (down2[v] - up2[v] + mod) % mod; else if (is_anc(v, u)) { long long xx = pow2_sum(up2[v], up[v], get_path_par(u, v), sz[1] - sz[v]); (ans = tot[u] - 2LL * xx + 2LL * mod) %= mod; } else { long long x1 = pow2_sum(down2[v], down[v], get_path(u, v), sz[v]); (ans = 2LL * x1 - tot[u] + 2LL * mod) %= mod; } printf("%lld\n", ans); } return 0; }
#include <bits/stdc++.h> using namespace std; mt19937 rng(chrono::steady_clock::now().time_since_epoch().count()); const long long N = 1e5 + 100; const long long LOG = 19; const long long MOD = 1e9 + 7; vector<pair<long long, long long>> g[N]; long long up[N][LOG], tin[N], tout[N], d0[N], d1[N], d2[N], sizes[N], ans[N], ans1[N], ans2[N]; long long timer = 0; long long n; long long add(long long a, long long b) { a += b; a %= MOD; if (a < 0) { a += MOD; } return a; } long long mul(long long a, long long b) { return 1ll * a * b % MOD; } void dfs0(long long v, long long p) { tin[v] = timer++; sizes[v] = 1; for (long long i = 1; i < LOG; i++) { up[v][i] = up[up[v][i - 1]][i - 1]; } for (long long i = 0; i < (long long)g[v].size(); i++) { if (g[v][i].first == p) { g[v].erase(g[v].begin() + i); break; } } for (auto i : g[v]) { assert(i.first != p); up[i.first][0] = v; d0[i.first] = add(d0[v], i.second); dfs0(i.first, v); sizes[v] += sizes[i.first]; } tout[v] = timer; } long long anc(long long a, long long b) { return tin[a] <= tin[b] && tout[b] <= tout[a]; } long long lca(long long v, long long u) { if (anc(v, u)) { return v; } if (anc(u, v)) { return u; } for (long long i = LOG - 1; i >= 0; i--) { if (!anc(up[v][i], u)) { v = up[v][i]; } } return up[v][0]; } long long getDist(long long v, long long u) { long long w = lca(v, u); long long ret = add(d0[v], d0[u]); ret = add(ret, mul(-2, d0[w])); return ret; } long long get_cost(long long d, long long d1, long long d2, long long n) { long long ret = mul(mul(d, d), n); ret = add(ret, mul(2 * d, d1)); ret = add(ret, d2); return ret; } void dfs1(long long v) { for (auto i : g[v]) { long long u = i.first, c = i.second; dfs1(u); d2[v] = add(d2[v], get_cost(c, d1[u], d2[u], sizes[u])); d1[v] = add(d1[v], mul(c, sizes[u])); d1[v] = add(d1[v], d1[u]); } } void dfs2(long long v, long long a, long long b) { ans[v] = add(ans[v], d2[v]); ans[v] = add(ans[v], b); ans1[v] = a; ans2[v] = b; a = add(a, d1[v]); b = add(b, d2[v]); for (auto i : g[v]) { long long u = i.first, c = i.second; long long ta = a; ta = add(ta, -d1[u]); ta = add(ta, -mul(c, sizes[u])); long long tb = b; tb = add(tb, -get_cost(c, d1[u], d2[u], sizes[u])); tb = get_cost(c, ta, tb, n - sizes[u]); ta = add(ta, mul(c, n - sizes[u])); dfs2(u, ta, tb); } } long long stupid(long long v) { long long ret = 0; for (long long i = 0; i < n; i++) { long long D = getDist(v, i); ret = add(ret, mul(D, D)); } return ret; } long long solve(long long v, long long u) { swap(v, u); long long ret = 0; long long D = getDist(v, u); if (anc(v, u)) { ret = ans[u]; long long cur = get_cost(D, ans1[v], ans2[v], n - sizes[v]); ret = add(ret, -mul(2, cur)); } else { ret = add(0, -ans[u]); long long cur = 0; cur = get_cost(D, d1[v], d2[v], sizes[v]); ret = add(ret, mul(2, cur)); } return ret; } signed main() { ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0); cin >> n; for (long long i = 1; i < n; i++) { long long v, u, c; cin >> v >> u >> c; v--; u--; g[v].emplace_back(u, c); g[u].emplace_back(v, c); } dfs0(0, -1); dfs1(0); dfs2(0, 0, 0); long long q; cin >> q; while (q--) { long long v, u; cin >> v >> u; v--; u--; cout << solve(v, u) << '\n'; } }
#include <bits/stdc++.h> using namespace std; const int MX = 100005, LG = 18, mod = 1000000007; int n, p[MX][LG], lvl[MX], q; long long d[MX], d2[MX], sz[MX], sd[MX], sd2[MX], tor[MX]; vector<pair<int, long long> > adj[MX]; int LCA(int u, int v) { if (lvl[u] < lvl[v]) swap(u, v); for (int j = 0; j < LG; j++) if (lvl[u] - lvl[v] & (1 << j)) u = p[u][j]; if (u == v) return u; for (int j = LG - 1; j >= 0; j--) if (p[u][j] != p[v][j]) { u = p[u][j]; v = p[v][j]; } return p[u][0]; } void pre(int u) { sz[u] = 1; for (pair<int, long long> &v : adj[u]) if (v.first != p[u][0]) { lvl[v.first] = lvl[u] + 1; p[v.first][0] = u; tor[v.first] = (tor[u] + v.second) % mod; pre(v.first); sz[u] += sz[v.first]; (sd[u] += (sd[v.first] + sz[v.first] * v.second)) %= mod; (sd2[u] += (sd2[v.first] + 2 * sd[v.first] * v.second + v.second * v.second % mod * sz[v.first])) %= mod; } } void dfs(int u) { for (pair<int, long long> &v : adj[u]) if (v.first != p[u][0]) { d[v.first] = (d[u] + v.second * (n - 2 * sz[v.first])) % mod; d2[v.first] = (d2[u] + 2 * v.second * (d[u] - 2 * (sd[v.first] + v.second * sz[v.first]) % mod) % mod + v.second * v.second % mod * n) % mod; dfs(v.first); } } int main() { ios_base::sync_with_stdio(0); cin.tie(0); cin >> n; for (int i = 0; i < n - 1; i++) { int a, b, c; cin >> a >> b >> c; adj[a].emplace_back(b, c); adj[b].emplace_back(a, c); } p[1][0] = 1; pre(1); for (int j = 1; j < LG; j++) for (int i = 1; i <= n; i++) p[i][j] = p[p[i][j - 1]][j - 1]; d[1] = sd[1]; d2[1] = sd2[1]; dfs(1); cin >> q; while (q--) { int u, v; cin >> u >> v; int lca = LCA(u, v); long long res = lca == v ? d2[u] : -d2[u]; long long dis = (tor[u] + tor[v] - 2 * tor[lca]) % mod; if (lca == v) { (res -= 2 * (((d2[v] - sd2[v]) + 2 * (d[v] - sd[v]) * dis + dis * dis % mod * (n - sz[v])) % mod)) %= mod; } else { (res += 2 * ((sd2[v] + 2 * sd[v] * dis + dis * dis % mod * sz[v]) % mod)) %= mod; } cout << ((((res) % (mod)) + (mod)) % (mod)) << '\n'; } return 0; }
#include <bits/stdc++.h> using namespace std; class sp { public: int q; long long w, t, t1, t2; sp *e, *r; sp(int q1, long long w1, sp *e1) { q = q1; w = w1; e = e1; t = t1 = t2 = 0; } }; sp *a[100000], *s1[100000]; int s[100000], s2[100000], d[100000], d1[100000], d2[100000], p = 1000000007; int u = 0, d3[100000], *f[100000], *f1[100000], h[100000], h1[100000]; int d00[100000], d01[100000], d02[100000]; long long m(long long w, long long e) { if (w < 0) w += p; if (e < 0) e += p; return (w * e) % p; } void l(int q, sp *w) { sp *c; if (s[q] == -1) { s[q] = 0; s1[q] = w; if (w == 0) s[q] = -2; for (c = a[q]; c; c = c->e) if (c != w) { l(c->q, c->r); d[q] += c->t; d1[q] = (d1[q] + c->t1) % p; d2[q] = (d2[q] + c->t2) % p; } } if (s[q] == 0) if (s1[q] == w) { w->r->t = d[q]; w->r->t1 = (d[q] * (w->w) + d1[q]) % p; w->r->t2 = (m(w->w, w->w) * d[q] + 2 * m(w->w, d1[q]) + d2[q]) % p; return; } else { s[q] = -2; l(s1[q]->q, s1[q]->r); d[q] = d[q] + s1[q]->t; d1[q] = (d1[q] + s1[q]->t1) % p; d2[q] = (d2[q] + s1[q]->t2) % p; } if ((s[q] == -2) && (w != 0)) { w->r->t = d[q] - w->t; w->r->t1 = (m(d[q] - w->t, w->w) + d1[q] - w->t1 + p) % p; w->r->t2 = (m(m(w->w, w->w), d[q] - w->t) + 2 * m(w->w, d1[q] - w->t1) + d2[q] - w->t2 + p) % p; } } void l1(int q, sp *w, int t) { sp *c; h[q] = u; u++; s[t] = q; s2[t] = 0; if (w != 0) s2[t] = (s2[t - 1] + w->w) % p; for (c = a[q]; c; c = c->e) if (c != w) l1(c->q, c->r, t + 1); h1[q] = u - 1; if (w != 0) { d[q] = d[q] - w->t; d1[q] = (d1[q] - w->t1 + p) % p; d3[q] = (d2[q] - w->t2 + p) % p; d00[q] = w->t; d01[q] = w->t1; d02[q] = w->t2; } int e, r; for (e = 0, r = 1; e < 17; e++, r <<= 1) if (t >= r) { f[q][e] = s[t - r]; f1[q][e] = s2[t] - s2[t - r]; if (f1[q][e] < 0) f1[q][e] += p; } else f[q][e] = -1; } int k(int q, int w) { int e, c; long long t = 0; c = q; for (e = 16; e >= 0; e--) if (f[c][e] >= 0) if (!((h[f[c][e]] <= h[w]) && (h[w] <= h1[f[c][e]]))) { t += f1[c][e]; c = f[c][e]; } if (f[c][0] >= 0) if (!((h[c] <= h[w]) && (h[w] <= h1[c]))) t += f1[c][0]; c = w; for (e = 16; e >= 0; e--) if (f[c][e] >= 0) if (!((h[f[c][e]] <= h[q]) && (h[q] <= h1[f[c][e]]))) { t += f1[c][e]; c = f[c][e]; } if (f[c][0] >= 0) if (!((h[c] <= h[q]) && (h[q] <= h1[c]))) t += f1[c][0]; return t % p; } int main() { int q, w, e, r; long long t, c; cin >> q; for (w = 0; w < q; w++) { s[w] = -1; d[w] = 1; d1[w] = d2[w] = 0; a[w] = 0; f[w] = new int[17]; f1[w] = new int[17]; } for (w = 1; w < q; w++) { scanf("%d%d%I64d", &e, &r, &t); e--; r--; a[e] = new sp(r, t, a[e]); a[r] = new sp(e, t, a[r]); a[e]->r = a[r]; a[r]->r = a[e]; } for (w = 0; w < q; w++) if (s[w] != -2) l(w, 0); d00[0] = d01[0] = d02[0] = 0; d3[0] = d2[0]; l1(0, 0, 0); for (cin >> w; w; w--) { scanf("%d%d", &e, &r); e--; r--; t = k(e, r); if ((h[r] <= h[e]) && (h[e] <= h1[r])) { c = (m(d00[r], m(t, t)) + 2 * m(t, d01[r]) + d02[r]) % p; c = (d2[e] - ((c * 2) % p) + p) % p; printf("%d\n", c); } else { c = (m(d[r], m(t, t)) + 2 * m(t, d1[r]) + d3[r]) % p; c = (-(d2[e] - ((c * 2) % p)) + p) % p; printf("%d\n", c); } } return 0; }
#include <bits/stdc++.h> using namespace std; int n; int q; struct st { long long int lazy; long long int sum1; long long int sum2; long long int cnt; st() { cnt = lazy = sum1 = sum2 = 0; } }; vector<pair<int, long long int> > v[100002]; long long int dist[100002]; bool use[100002]; int siz; int star[100002]; int en[100002]; int ar[100002]; inline void dfs(int b, long long int D = 0) { if (D >= 1000000007LL) { D %= 1000000007LL; } dist[b] = D; use[b] = true; star[b] = siz; ar[siz] = b; siz++; for (int i = 0; i < v[b].size(); i++) { if (use[v[b][i].first] == false) { dfs(v[b][i].first, D + v[b][i].second); } } en[b] = siz; } st seg[100002 * 4]; st merge(st a, st b) { st r; r.sum1 = a.sum1 + b.sum1; r.sum2 = a.sum2 + b.sum2; r.cnt = a.cnt + b.cnt; r.sum1 %= 1000000007LL; r.sum2 %= 1000000007LL; return r; } void update(int b) { if (seg[b].lazy != 0) { if (seg[b].lazy >= 1000000007LL) { seg[b].lazy %= 1000000007LL; } if (b * 2 + 2 < 100002 * 4) { seg[b * 2 + 1].lazy += seg[b].lazy; if (seg[b * 2 + 1].lazy >= 1000000007LL) { seg[b * 2 + 1].lazy %= 1000000007LL; } seg[b * 2 + 2].lazy += seg[b].lazy; if (seg[b * 2 + 2].lazy >= 1000000007LL) { seg[b * 2 + 2].lazy %= 1000000007LL; } } seg[b].sum2 += (((seg[b].lazy * seg[b].lazy) % 1000000007LL) * seg[b].cnt); if (seg[b].sum2 >= 1000000007LL) { seg[b].sum2 %= 1000000007LL; } seg[b].sum2 += 2LL * seg[b].lazy * seg[b].sum1; if (seg[b].sum2 >= 1000000007LL) { seg[b].sum2 %= 1000000007LL; } seg[b].sum1 += seg[b].cnt * seg[b].lazy; seg[b].sum1 %= 1000000007LL; seg[b].lazy = 0; } } inline void init(int b, int l, int r) { seg[b].cnt = r - l; if (l + 1 == r) { seg[b].sum2 = dist[ar[l]] * dist[ar[l]]; if (seg[b].sum2 >= 1000000007LL) { seg[b].sum2 %= 1000000007LL; } seg[b].sum1 = dist[ar[l]]; if (seg[b].sum1 >= 1000000007LL) { seg[b].sum1 %= 1000000007LL; } return; } init(b * 2 + 1, l, (l + r) >> 1); init(b * 2 + 2, (l + r) >> 1, r); seg[b] = merge(seg[b * 2 + 1], seg[b * 2 + 2]); } long long int ans[100002]; vector<pair<int, int> > vv[100002]; inline void add(int b, int l, int r, int ll, int rr, long long int x) { if (x >= 1000000007LL) { x %= 1000000007LL; } update(b); if (r <= ll || rr <= l) { return; } if (ll <= l && r <= rr) { seg[b].lazy += (long long int)(x); update(b); return; } add(b * 2 + 1, l, (l + r) >> 1, ll, rr, x); add(b * 2 + 2, (l + r) >> 1, r, ll, rr, x); seg[b] = merge(seg[b * 2 + 1], seg[b * 2 + 2]); } inline st query(int b, int l, int r, int ll, int rr) { update(b); if (ll <= l && r <= rr) { return seg[b]; } if (rr <= l || r <= ll) { return st(); } return merge(query(b * 2 + 1, l, (l + r) >> 1, ll, rr), query(b * 2 + 2, (l + r) >> 1, r, ll, rr)); } inline void dfs2(int b) { use[b] = false; for (int i = 0; i < v[b].size(); i++) { if (use[v[b][i].first] == true) { add(0, 0, siz, 0, siz, v[b][i].second); add(0, 0, siz, star[v[b][i].first], en[v[b][i].first], (1000000007LL - v[b][i].second) * 2LL); dfs2(v[b][i].first); add(0, 0, siz, 0, siz, 1000000007LL - v[b][i].second); add(0, 0, siz, star[v[b][i].first], en[v[b][i].first], v[b][i].second * 2LL); } } long long int D = query(0, 0, siz, 0, siz).sum2; D %= 1000000007LL; D = 1000000007LL - D; D %= 1000000007LL; for (int i = 0; i < vv[b].size(); i++) { ans[vv[b][i].second] = 2LL * query(0, 0, siz, star[vv[b][i].first], en[vv[b][i].first]).sum2 + D; ans[vv[b][i].second] %= 1000000007LL; } } int main() { scanf("%d", &n); for (int i = 1; i < n; i++) { int a, b, c; scanf("%d%d%d", &a, &b, &c); a--; b--; v[a].push_back(make_pair(b, c)); v[b].push_back(make_pair(a, c)); } cin >> q; dfs(0); init(0, 0, n); for (int i = 0; i < q; i++) { int a, b; scanf("%d%d", &a, &b); a--; b--; vv[a].push_back(make_pair(b, i)); } dfs2(0); for (int i = 0; i < q; i++) { printf("%lld\n", ans[i]); } return 0; }
#include <bits/stdc++.h> using namespace std; template <class T> inline void umax(T &a, T b) { if (a < b) a = b; } template <class T> inline void umin(T &a, T b) { if (a > b) a = b; } template <class T> inline T abs(T a) { return a > 0 ? a : -a; } template <class T> inline T gcd(T a, T b) { return __gcd(a, b); } template <class T> inline T lcm(T a, T b) { return a / gcd(a, b) * b; } const int inf = 1e9 + 143; const long long longinf = 1e18 + 143; inline int read() { int x; scanf(" %d", &x); return x; } const int N = 101001; const int LOG = 17; const int mod = 1e9 + 7; inline int add(int x, int y) { return (x + y >= mod) ? x + y - mod : x + y; } inline int mul(int x, int y) { return (long long)x * y % mod; } struct info { int a, b, c; info() : a(0), b(0), c(0) {} info(int _a, int _b, int _c) : a(_a), b(_b), c(_c) {} info operator+(const info &other) { return info(add(a, other.a), add(b, other.b), add(c, other.c)); } info operator-(const info &other) { return info(add(a, mod - other.a), add(b, mod - other.b), add(c, mod - other.c)); } info operator*(const int &x) { info res; res.a = add(a, mul(b, mul(2, x))); res.a = add(res.a, mul(c, mul(x, x))); res.b = add(b, mul(c, x)); res.c = c; return res; } void newnode() { ++c; } }; vector<pair<int, int> > g[N]; info down[N], up[N]; int d[N], de[N]; int anc[N][LOG]; void dfs1(int u, int p) { anc[u][0] = p; for (int i = 1; i < LOG; i++) anc[u][i] = anc[anc[u][i - 1]][i - 1]; for (__typeof((g[u]).begin()) it = (g[u]).begin(); it != (g[u]).end(); it++) { int v = it->first; int c = it->second; if (v != p) { d[v] = add(d[u], c); de[v] = de[u] + 1; dfs1(v, u); down[u] = down[u] + (down[v] * c); } } down[u].newnode(); } void dfs2(int u, int p) { info sum; for (__typeof((g[u]).begin()) it = (g[u]).begin(); it != (g[u]).end(); it++) { int v = it->first; int c = it->second; if (v != p) { sum = sum + (down[v] * c); } } for (__typeof((g[u]).begin()) it = (g[u]).begin(); it != (g[u]).end(); it++) { int v = it->first; int c = it->second; if (v != p) { up[v] = sum - (down[v] * c) + up[u]; up[v].newnode(); up[v] = up[v] * c; dfs2(v, u); } } } int getlca(int u, int v) { if (de[u] < de[v]) swap(u, v); for (int i = 0; i < LOG; i++) { if ((de[u] - de[v]) & (1 << i)) u = anc[u][i]; } if (u == v) return u; for (int i = LOG - 1; i >= 0; i--) if (anc[u][i] != anc[v][i]) { u = anc[u][i]; v = anc[v][i]; } return anc[u][0]; } int main() { int n = read(); for (int i = 1; i < n; i++) { int u = read(), v = read(), c = read(); g[u].push_back(pair<int, int>(v, c)); g[v].push_back(pair<int, int>(u, c)); } dfs1(1, 0); dfs2(1, 0); int q = read(); while (q--) { int u = read(), v = read(); int lca = getlca(u, v); int dist = add(d[u], add(d[v], mod - mul(2, d[lca]))); if (lca == v) { info toall = up[u] + down[u]; info unsub = up[v] * dist; 0; printf("%d\n", add(toall.a, mod - mul(2, unsub.a))); } else { info toall = up[u] + down[u]; info sub = down[v] * dist; 0; printf("%d\n", mod - add(toall.a, mod - mul(2, sub.a))); } } return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 1e5 + 7; const int inf = 0x3f3f3f3f; const long long INF = 0x3f3f3f3f3f3f3f3f; const int mod = 1e9 + 7; const double eps = 1e-8; const double PI = acos(-1); template <class T, class S> inline void add(T& a, S b) { a += b; if (a >= mod) a -= mod; } template <class T, class S> inline void sub(T& a, S b) { a -= b; if (a < 0) a += mod; } template <class T, class S> inline bool chkmax(T& a, S b) { return a < b ? a = b, true : false; } template <class T, class S> inline bool chkmin(T& a, S b) { return a > b ? a = b, true : false; } int n, q; int pa[N][20], len[N][20], depth[N]; int allDis2[N]; vector<pair<int, int> > G[N]; struct dpNode { dpNode() { cnt = sumDis = sumDis2 = 0; } dpNode(int cnt, int sumDis, int sumDis2) : cnt(cnt), sumDis(sumDis), sumDis2(sumDis2) {} int cnt, sumDis, sumDis2; void print() { printf("cnt: %d sumDis: %d sumDis2: %d\n", cnt, sumDis, sumDis2); } } dp[N], dp2[N], INIT(1, 0, 0); dpNode mergeTwo(dpNode a, dpNode b, int w, int op) { if (op > 0) { a.cnt += b.cnt; add(a.sumDis, b.sumDis); add(a.sumDis, 1LL * b.cnt * w % mod); add(a.sumDis2, b.sumDis2); add(a.sumDis2, 1LL * b.sumDis * 2 * w % mod); add(a.sumDis2, 1LL * w * w % mod * b.cnt % mod); } else { a.cnt -= b.cnt; sub(a.sumDis, b.sumDis); sub(a.sumDis, 1LL * b.cnt * w % mod); sub(a.sumDis2, b.sumDis2); sub(a.sumDis2, 1LL * b.sumDis * 2 * w % mod); sub(a.sumDis2, 1LL * w * w % mod * b.cnt % mod); } return a; } void dfs(int u, int fa, int disTofa) { depth[u] = depth[fa] + 1; pa[u][0] = fa; len[u][0] = disTofa; dp[u].cnt = 1; for (int i = 1; i < 20; i++) { pa[u][i] = pa[pa[u][i - 1]][i - 1]; len[u][i] = (len[u][i - 1] + len[pa[u][i - 1]][i - 1]) % mod; } for (auto& e : G[u]) { int v = e.second; if (v == fa) continue; dfs(v, u, e.first); dp[u] = mergeTwo(dp[u], dp[v], e.first, 1); } } pair<int, int> getLca(int u, int v) { if (depth[u] < depth[v]) swap(u, v); int dis = depth[u] - depth[v]; int ret = 0; for (int i = 19; i >= 0; i--) if (dis >> i & 1) add(ret, len[u][i]), u = pa[u][i]; if (u == v) return make_pair(ret, u); for (int i = 19; i >= 0; i--) { if (pa[u][i] != pa[v][i]) { add(ret, len[u][i]); add(ret, len[v][i]); u = pa[u][i]; v = pa[v][i]; } } add(ret, len[u][0]); add(ret, len[v][0]); return make_pair(ret, pa[u][0]); } void dfs2(int u, int fa, dpNode up) { dp2[u] = up; dp2[u].cnt--; allDis2[u] = (dp[u].sumDis2 + up.sumDis2) % mod; for (auto& e : G[u]) { if (e.second == fa) continue; up = mergeTwo(up, dp[e.second], e.first, 1); } for (auto& e : G[u]) { if (e.second == fa) continue; up = mergeTwo(up, dp[e.second], e.first, -1); dfs2(e.second, u, mergeTwo(INIT, up, e.first, 1)); up = mergeTwo(up, dp[e.second], e.first, 1); } } int main() { scanf("%d", &n); for (int i = 1; i < n; i++) { int u, v, w; scanf("%d%d%d", &u, &v, &w); G[u].push_back(make_pair(w, v)); G[v].push_back(make_pair(w, u)); } dfs(1, 0, 0); dfs2(1, 0, INIT); getLca(4, 3); scanf("%d", &q); while (q--) { int u, v; scanf("%d%d", &u, &v); pair<int, int> ret = getLca(u, v); int lca = ret.second, dis = ret.first; int ans = 0; if (lca != v) { int x = mergeTwo(INIT, dp[v], dis, 1).sumDis2; int z = allDis2[u]; ans = ((2 * x - z) % mod + mod) % mod; } else { int y = mergeTwo(INIT, dp2[v], dis, 1).sumDis2; int z = allDis2[u]; ans = ((z - 2 * y) % mod + mod) % mod; } printf("%d\n", ans); } return 0; }
#include <bits/stdc++.h> using namespace std; const long long N = 100100; vector<pair<long long, long long> > G[N]; long long n, ht[N], dist[N], sum[N], sum2[N], all2[N], size[N], all[N]; long long parent[N], p[N][20]; static bool vis[N][2], vis_[N]; void dfs(long long v) { vis_[v] = true; long long i, sz = G[v].size(); size[v] = 1; for (i = 0; i < sz; i++) if (!vis_[G[v][i].first]) { dfs(G[v][i].first); size[v] += size[G[v][i].first]; sum[v] = (sum[v] + (size[G[v][i].first] * G[v][i].second) % 1000000007 + sum[G[v][i].first] % 1000000007) % 1000000007; sum2[v] = (sum2[v] + sum2[G[v][i].first] + (2LL * sum[G[v][i].first] * G[v][i].second) % 1000000007 + (size[G[v][i].first] * ((G[v][i].second * G[v][i].second) % 1000000007)) % 1000000007) % 1000000007; } } void bfs(long long v) { long long i, sz, h; vis[v][0] = vis[v][1] = true; parent[v] = dist[v] = ht[v] = 0; queue<long long> q; q.push(v); while (!q.empty()) { h = q.front(); sz = G[h].size(); for (i = 0; i < sz; i++) if (!vis[G[h][i].first][0]) { dist[G[h][i].first] = (dist[h] + G[h][i].second) % 1000000007; ht[G[h][i].first] = ht[h] + 1; parent[G[h][i].first] = h; vis[G[h][i].first][0] = true; q.push(G[h][i].first); } q.pop(); } for (long long i = 1; i <= n; i++) all[v] = (all[v] + dist[i]) % 1000000007, all2[v] = (all2[v] + (dist[i] * dist[i]) % 1000000007) % 1000000007; q.push(v); while (!q.empty()) { h = q.front(); sz = G[h].size(); for (i = 0; i < sz; i++) if (!vis[G[h][i].first][1]) { all[G[h][i].first] = ((all[h] + (n - 2LL * size[G[h][i].first]) * G[h][i].second) % 1000000007 + 1000000007) % 1000000007; all2[G[h][i].first] = ((all2[h] - (n * ((G[h][i].second * G[h][i].second) % 1000000007) % 1000000007) + 2LL * (all[G[h][i].first] - 2LL * sum[G[h][i].first]) * G[h][i].second) % 1000000007 + 1000000007) % 1000000007; vis[G[h][i].first][1] = true; q.push(G[h][i].first); } q.pop(); } } void init() { long long i, j; for (i = 1; i < n + 1; i++) p[i][0] = parent[i]; for (j = 1; (1 << j) < n; j++) for (i = 1; i < n + 1; i++) p[i][j] = p[p[i][j - 1]][j - 1]; } long long lca(long long u, long long v) { if (ht[u] < ht[v]) swap(u, v); long long log, i; for (log = 1; (1 << log) <= ht[u]; log++) ; log--; for (i = log; i >= 0; i--) if (ht[u] - (1 << i) >= ht[v]) u = p[u][i]; if (u == v) return u; for (i = log; i >= 0; i--) if (p[u][i] and (p[u][i] != p[v][i])) u = p[u][i], v = p[v][i]; return p[u][0]; } int main() { ios_base::sync_with_stdio(false); cin >> n; long long a, b, c, i, q; for (i = 1; i < n; i++) { cin >> a >> b >> c; G[a].push_back(make_pair(b, c)); G[b].push_back(make_pair(a, c)); } dfs(1); bfs(1); init(); cin >> q; while (q--) { cin >> a >> b; long long k = lca(a, b), ans; if (k != b) { long long d = ((dist[a] + dist[b] - 2LL * dist[k]) % 1000000007 + 1000000007) % 1000000007; long long c = size[b], s = sum[b], s2 = sum2[b], A = all2[a]; ans = (((2LL * c * ((d * d) % 1000000007)) % 1000000007 + (4LL * d * s) % 1000000007 + 2LL * s2 - A) % 1000000007 + 1000000007) % 1000000007; } else { long long d = (dist[a] - dist[b] + 1000000007) % 1000000007; long long c = size[b], s = sum[b], s2 = sum2[b]; long long A2a = all2[a], A2b = all2[b], Ab = all[b]; ans = ((A2a - (2LL * ((d * d) % 1000000007) * (n - c + 1000000007)) % 1000000007 - 4LL * (d * (Ab - s + 1000000007)) % 1000000007 - 2LL * (A2b - s2 + 1000000007) % 1000000007) % 1000000007 + 1000000007) % 1000000007; } cout << ans << '\n'; } return 0; }