text
stringlengths
49
983k
#include <bits/stdc++.h> using namespace std; const int N = 200000 + 9; int n, p[N], deg[N]; vector<int> G[N]; unordered_set<int> ust[N][2]; int dfs(int u, int p) { int sz = 1; for (int v : G[u]) if (v != p) { int tmp = dfs(v, u); ust[u][tmp & 1].insert(v); sz += tmp; } if (p) ust[u][(n - sz) & 1].insert(p); return sz; } bool vis[N]; void solve() { scanf("%d", &n); for (int i = 1; i <= n; ++i) { scanf("%d", p + i); if (!p[i]) continue; G[p[i]].push_back(i); G[i].push_back(p[i]); } dfs(1, 0); queue<int> Q; vector<int> vc; for (int i = 1; i <= n; ++i) { if (ust[i][0].empty() && (~ust[i][1].size() & 1u)) { Q.push(i); vis[i] = true; } } while (!Q.empty()) { int u = Q.front(); Q.pop(); vc.push_back(u); for (int v : G[u]) if (!vis[v]) { ust[v][0].erase(u); ust[v][1].erase(u); if (ust[v][0].empty() && (~ust[v][1].size() & 1u)) { Q.push(v); vis[v] = true; } } } if ((int)vc.size() == n) { printf("YES\n"); for (int u : vc) printf("%d\n", u); } else { printf("NO\n"); } } int main() { int T = 1; while (T--) solve(); return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 2e5 + 5; vector<int> e[N]; int n, cnt[N]; void dfs(int x, int fa) { cnt[x] = 1; int len = e[x].size(); for (int i = 0; i < len; i++) { if (e[x][i] == fa) continue; dfs(e[x][i], x); cnt[x] += cnt[e[x][i]]; } } void solve(int x, int fa) { int len = e[x].size(); for (int i = 0; i < len; i++) { if (e[x][i] == fa) continue; if (cnt[e[x][i]] % 2 == 0) { solve(e[x][i], x); } } printf("%d\n", x); for (int i = 0; i < len; i++) { if (e[x][i] == fa) continue; if (cnt[e[x][i]] % 2 == 1) { solve(e[x][i], x); } } } int main() { cin >> n; for (int i = 1; i <= n; i++) { int x; scanf("%d", &x); if (x == 0) continue; e[i].push_back(x); e[x].push_back(i); } dfs(1, 0); if (cnt[1] & 1) { printf("YES\n"); solve(1, 0); } else { printf("NO"); } return 0; }
#include <bits/stdc++.h> using namespace std; int nextInt() { int x; scanf("%d", &x); return x; } string nextString() { string s; cin >> s; return s; } const int MAXN = 2e5; vector<int> G[MAXN + 10]; int num[MAXN + 10]; int f[MAXN + 10]; vector<int> order; void dfs(int v) { for (auto u : G[v]) { dfs(u); } order.push_back(v); } int main() { int n = nextInt(); int root = -1; for (int i = (1); i <= (n); ++i) { int x = nextInt(); if (x == 0) root = i; else num[i]++, num[x]++; G[x].push_back(i); f[i] = x; } dfs(root); vector<int> ans0; vector<int> ans1; for (auto i : order) { if (num[i] & 1) { if (i == root) { cout << "NO\n"; return 0; } ans1.push_back(i); } else { num[f[i]]--; ans0.push_back(i); } } reverse(begin(ans1), end(ans1)); ans0.insert(ans0.end(), begin(ans1), end(ans1)); cout << "YES\n"; for (auto i : ans0) { cout << i << endl; } }
#include <bits/stdc++.h> using namespace std; const int N = 2 * 100000 + 100; vector<int> e[N]; bool mark[N], del[N]; int n, cnt, par[N]; void destruct(int v) { del[v] = true; cout << v + 1 << endl; for (int i = 0; i < e[v].size(); i++) { int u = e[v][i]; if (u != par[v] && !del[u]) destruct(u); } } int dfs(int v) { mark[v] = true; int s = 0, d = 0; for (int i = 0; i < e[v].size(); i++) { int u = e[v][i]; if (!mark[u]) { par[u] = v; int x = dfs(u); s += x; } } if (s % 2) destruct(v); return s + 1; } int main() { cin >> n; if (n % 2 == 0) { cout << "NO\n"; return 0; } cout << "YES\n"; for (int i = 0; i < n; i++) { int v; cin >> v; if (v == 0) continue; v--; e[v].push_back(i); e[i].push_back(v); } dfs(0); destruct(0); }
#include <bits/stdc++.h> using namespace std; vector<int> graf[200005], stek; bool mark[200005]; int root; void dfsd(int s) { if (mark[s]) return; mark[s] = true; stek.push_back(s); for (int i = 0; i < graf[s].size(); i++) dfsd(graf[s][i]); } void dfs(int s) { int deg = 0; if (s != root) deg++; for (int i = 0; i < graf[s].size(); i++) { dfs(graf[s][i]); if (!mark[graf[s][i]]) deg++; } if (deg % 2 == 0) dfsd(s); } int main() { int n; scanf("%d", &n); for (int i = 1; i <= n; i++) { int t; scanf("%d", &t); graf[t].push_back(i); if (t == 0) root = i; } dfs(root); if (stek.size() < n) printf("NO"); else { printf("YES\n"); for (int i = 0; i < n; i++) printf("%d\n", stek[i]); } }
#include <bits/stdc++.h> using namespace std; stack<int> s; int deg[200005]; int vis[200005]; int p[200005]; vector<int> ne[200005]; vector<int> ans; void dfs(int u) { s.push(u); for (int i = 0; i < ne[u].size(); i++) { dfs(ne[u][i]); } } void dfs2(int u) { vis[u] = 1; ans.push_back(u); for (int i = 0; i < ne[u].size(); i++) { int v = ne[u][i]; deg[v]--; if (!vis[v] && deg[v] % 2 == 0) { dfs2(v); } } deg[p[u]]--; } int main() { int n; cin >> n; for (int i = 1; i <= n; i++) { deg[i] = 0; } for (int i = 1; i <= n; i++) { vis[i] = 0; cin >> p[i]; ne[p[i]].push_back(i); if (p[i]) { deg[i]++; deg[p[i]]++; } } if (n % 2 == 0) { cout << "NO" << endl; return 0; } cout << "YES" << endl; int root = ne[0][0]; dfs(root); while (!s.empty()) { int u = s.top(); s.pop(); if (!vis[u] && deg[u] % 2 == 0) { dfs2(u); } } for (int i = 0; i < n; i++) { printf("%d\n", ans[i]); } return 0; }
#include <bits/stdc++.h> using namespace std; int read() { int xx = 0, ff = 1; char ch = getchar(); while (ch > '9' || ch < '0') { if (ch == '-') ff = -1; ch = getchar(); } while (ch >= '0' && ch <= '9') { xx = xx * 10 + ch - '0'; ch = getchar(); } return xx * ff; } const int maxn = 200010; int N, root; int lin[maxn], len, deg[maxn]; struct edge { int y, next; } e[maxn << 1]; inline void insert(int xx, int yy) { e[++len].next = lin[xx]; lin[xx] = len; e[len].y = yy; deg[xx]++; } bool v[maxn]; int cnt[maxn][2]; bool dfs(int x, int fa) { for (int i = lin[x]; i; i = e[i].next) if (e[i].y != fa) cnt[x][dfs(e[i].y, x)]++; if ((deg[x] - cnt[x][1]) % 2 == 0) v[x] = 1; else v[x] = 0; return v[x]; } void print(int x, int fa) { for (int i = lin[x]; i; i = e[i].next) if (e[i].y != fa) if (v[e[i].y]) print(e[i].y, x); printf("%d\n", x); for (int i = lin[x]; i; i = e[i].next) if (e[i].y != fa) if (!v[e[i].y]) print(e[i].y, x); } int main() { N = read(); for (int i = 1; i <= N; i++) { int temp = read(); if (!temp) root = i; else insert(i, temp), insert(temp, i); } if (dfs(root, 0)) { puts("YES"); print(root, 0); } else puts("NO"); return 0; }
#include <bits/stdc++.h> using namespace std; int p[200002], d[200002]; vector<int> ch[200002]; vector<int> ans, buf; void bfs(int pos) { for (int c : ch[pos]) bfs(c); if (d[pos] & 1) { buf.push_back(pos); } else { ans.push_back(pos); d[p[pos]]--; } } int main() { int n; cin >> n; int root = 0; for (int i = 1; i <= n; i++) { cin >> p[i]; if (p[i] == 0) { root = i; } else { ch[p[i]].push_back(i); } d[i]++; d[p[i]]++; } if (n % 2 == 0) { cout << "NO" << endl; return 0; } cout << "YES" << endl; bfs(root); for (int a : ans) cout << a << endl; reverse(buf.begin(), buf.end()); for (int b : buf) cout << b << endl; return 0; }
#include <bits/stdc++.h> using namespace std; const int inf = 0x3f3f3f3f; int tot, z; int head[1000010]; struct node { int from; int to; int w; int next; } edge[1000010]; void add(int from, int to, int w) { edge[tot].from = from; edge[tot].to = to; edge[tot].w = w; edge[tot].next = head[from]; head[from] = tot++; } int vis[200100]; int deg[200100]; int ans[200100]; int n, tt, root; void des(int p, int pre) { vis[p] = 1; ans[tt++] = p; for (int i = head[p]; i != -1; i = edge[i].next) { int v = edge[i].to; deg[v]--; if (v == pre) continue; if (vis[v] == 0) { if (deg[v] % 2 == 0) { des(v, p); } } } } bool dfs(int Q, int P) { bool Ok = deg[Q] & 1; for (int i = head[Q]; i != -1; i = edge[i].next) { int v = edge[i].to; if (v != P) Ok ^= dfs(v, Q); } if (!Ok) des(Q, P); return !Ok; } int main() { memset(head, -1, sizeof(head)); tot = 0; tt = 0; memset(ans, 0, sizeof(ans)); memset(deg, 0, sizeof(deg)); memset(vis, 0, sizeof(vis)); cin >> n; if (n % 2 == 0) { cout << "NO" << endl; return 0; } for (int i = 1; i <= n; i++) { int aa; cin >> aa; if (aa == 0) { root = i; continue; } add(aa, i, 0); add(i, aa, 0); deg[aa]++; deg[i]++; } cout << "YES" << endl; dfs(root, 0); for (int i = 0; i < tt; i++) cout << ans[i] << endl; return 0; }
#include <bits/stdc++.h> using namespace std; inline int nxt() { int x; scanf("%d", &x); return x; } const int N = 222222; vector<int> a[N]; int sz[N]; int par[N]; void dfsSize(int v, int p = -1) { for (int x : a[v]) { if (x == p) { continue; } dfsSize(x, v); sz[v] += sz[x]; } par[v] = p; ++sz[v]; } vector<int> ans; void dfs(int v) { for (int x : a[v]) { if (x == par[v]) { continue; } if (sz[x] % 2 == 0) { dfs(x); } } ans.push_back(v); for (int x : a[v]) { if (x == par[v]) { continue; } if (sz[x] % 2) { dfs(x); } } } int main() { mt19937 rng(chrono::steady_clock::now().time_since_epoch().count()); int n = nxt(); for (int i = 0; i < n; ++i) { int u = nxt() - 1, v = i; if (u == -1) { continue; } a[u].push_back(v); a[v].push_back(u); } if (n % 2 == 0) { cout << "NO\n"; return 0; } dfsSize(0); dfs(0); printf("YES\n"); for (int x : ans) { printf("%d\n", x + 1); } return 0; }
#include <bits/stdc++.h> using namespace std; long long modexpo(long long x, long long p) { long long res = 1; x = x % 1000000007; while (p) { if (p % 2) res = res * x; p >>= 1; x = x * x % 1000000007; res %= 1000000007; } return res; } struct compare { bool operator()(const pair<long long, long long> a, const pair<long long, long long> b) const { return a.first < b.first; } }; const long long nax = 2e5 + 5; vector<long long> g[nax]; long long deg[nax]; long long n, root; vector<long long> ans; set<long long> s; void topdowndfs(long long x, long long p) { ans.push_back(x); s.insert(x); for (long long i : g[x]) { if (i != p && s.find(i) == s.end()) { topdowndfs(i, x); } } } void dfs(long long x, long long p) { for (long long i : g[x]) { if (i != p) { dfs(i, x); } } if (deg[x] % 2 == 0) { topdowndfs(x, p); deg[p]--; } } int32_t main() { ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0); cin >> n; for (long long i = 1; i <= n; i++) { long long x; cin >> x; if (x == 0) { root = i; } else { g[i].push_back(x); g[x].push_back(i); deg[i]++; deg[x]++; } } dfs(root, root); if (ans.size() == n) { cout << "YES\n"; for (long long i : ans) { cout << i << " "; } cout << "\n"; } else { cout << "NO" << "\n"; } }
#include <bits/stdc++.h> using namespace std; int n; unordered_set<int> g[200005]; bool gone[200005]; void dfs1(int u, int p) { printf("%d\n", u); gone[u] = true; for (auto v : g[u]) { if (v == p) continue; dfs1(v, u); } } void dfs(int u, int p) { if (gone[u]) return; for (auto itr = g[u].begin(); itr != g[u].end();) { int v = *itr; auto nitr = next(itr); if (v == p) { itr = nitr; continue; } dfs(v, u); itr = nitr; } if (g[u].size() && (g[u].size() & 1) == 0) { printf("%d\n", u); gone[u] = true; for (auto itr = g[u].begin(); itr != g[u].end();) { int v = *itr; auto nitr = next(itr); g[u].erase(v); g[v].erase(u); if (v != p) { dfs1(v, u); } itr = nitr; } } } int main() { memset(gone, 0, sizeof(gone)); scanf("%d", &n); for (int i = 1; i <= n; i++) { int u = i; int v; scanf("%d", &v); if (v == 0) continue; g[u].insert(v); g[v].insert(u); } if ((n & 1) == 0) { printf("NO\n"); return (0); } printf("YES\n"); dfs(1, 0); for (int i = 1; i <= n; i++) { if (gone[i] == false) printf("%d\n", i); } return (0); }
#include <bits/stdc++.h> using namespace std; const int N = 2e5 + 10; vector<int> g[N]; bool seen[N][2], dp[N][2]; vector<pair<int, int> > bk[N][2]; bool solve(int i, bool p, int par); void back(int i, bool p); int main() { int n; cin >> n; int root = -1; for (int i = 1; i <= n; ++i) { int p; cin >> p; if (!p) { root = i; } else { g[i].push_back(p); g[p].push_back(i); } } if (solve(root, 0, 0)) { cout << "YES\n"; back(root, 0); } else { cout << "NO\n"; } } bool solve(int i, bool p, int par) { if (seen[i][p]) { return dp[i][p]; } seen[i][p] = true; int tot = 0, codd = 0, ceven = 0, both = 0; for (auto &j : g[i]) { if (j == par) { continue; } else { ++tot; int o = solve(j, 1, i); int e = solve(j, 0, i); if (!o and !e) { dp[i][p] = false; return false; } codd += o; ceven += e; } } if (tot % 2 == p) { if ((tot - ceven) % 2) { dp[i][p] = false; } else { dp[i][p] = true; for (auto &j : g[i]) { if (j != par and !solve(j, 0, i)) { bk[i][p].push_back({j, 1}); } } bk[i][p].push_back({i, p}); for (auto &j : g[i]) { if (j != par and solve(j, 0, i)) { bk[i][p].push_back({j, 0}); } } } } else { if (!codd) { dp[i][p] = false; } else if ((codd - both) % 2) { dp[i][p] = true; for (auto &j : g[i]) { if (j != par and !solve(j, 0, i)) { bk[i][p].push_back({j, 1}); } } bk[i][p].push_back({i, p}); for (auto &j : g[i]) { if (j != par and solve(j, 0, i)) { bk[i][p].push_back({j, 0}); } } } else if (both) { dp[i][p] = true; int k = 0; for (auto &j : g[i]) { if (j != par and solve(j, 0, i) and solve(j, 1, i)) { bk[i][p].push_back({j, 1}); k = j; break; } } for (auto &j : g[i]) { if (j != par and !solve(j, 0, i)) { bk[i][p].push_back({j, 1}); } } bk[i][p].push_back({i, p}); for (auto &j : g[i]) { if (j != par and solve(j, 0, i) and j != k) { bk[i][p].push_back({j, 0}); } } } else { dp[i][p] = false; } } return dp[i][p]; } void back(int i, bool p) { for (auto &cur : bk[i][p]) { if (cur.first == i) { cout << i << '\n'; } else { back(cur.first, cur.second); } } }
#include <bits/stdc++.h> #pragma GCC optimize("-O2") using namespace std; void err(istream_iterator<string> it) {} template <typename T, typename... Args> void err(istream_iterator<string> it, T a, Args... args) { cerr << *it << " = " << a << endl; err(++it, args...); } const int LIM = 2e5 + 5, MOD = 1e9 + 7; int t, n, m, k, x, y; vector<vector<int> > v; vector<int> deg; vector<int> nchild; int dfs(int i, int par) { int ans = 1; for (auto &it : v[i]) if (it != par) ans += dfs(it, i); return nchild[i] = ans; } bool vs[LIM]; void solve(int i, int par) { if (vs[i]) return; if (deg[i] == 0) { cout << i + 1 << endl; vs[i] = 1; return; } int neven = 0; for (auto &it : v[i]) if (!vs[it] && it != par && !(nchild[it] & 1)) neven++; if (neven == 0 && !(deg[i] & 1)) { cout << i + 1 << endl; vs[i] = 1; deg[i] = 0; for (auto &it : v[i]) deg[it]--; for (auto &it : v[i]) if (!vs[it] && it != par) solve(it, i); } else { for (auto &it : v[i]) if (!vs[it] && it != par) solve(it, i); neven = 0; for (auto &it : v[i]) if (!vs[it] && it != par && !(nchild[it] & 1)) neven++; if (neven == 0 && !(deg[i] & 1)) { cout << i + 1 << endl; vs[i] = 1; deg[i] = 0; for (auto &it : v[i]) deg[it]--; for (auto &it : v[i]) if (!vs[it] && it != par) solve(it, i); } else { return; } } } int main() { cin >> n; if (!(n & 1)) { cout << "NO" << endl; return 0; } v.assign(n, vector<int>(0)); deg.assign(n, 0); nchild.assign(n, 0); for (int i = 0; i < n; i++) { cin >> x; if (x == 0) continue; x--; deg[x]++; deg[i]++; v[x].push_back(i); v[i].push_back(x); } dfs(0, -1); cout << "YES\n"; solve(0, -1); return 0; }
#include <bits/stdc++.h> using namespace std; const long long mod = 1e9 + 7; const double PI = acos(-1); int n, i, j, k, t; vector<int> adj[200002], ans; bool deleted[200002]; int sz[200002]; void dfs(int v, int p) { for (int x : adj[v]) { if (x == p) continue; if (sz[x] % 2 == 0) { dfs(x, v); deleted[x] = true; } } ans.push_back(v); for (int x : adj[v]) { if (x == p || deleted[x]) continue; dfs(x, v); } } void getsz(int v, int p) { sz[v] = 1; for (int x : adj[v]) { if (x == p) continue; getsz(x, v); sz[v] += sz[x]; } } int main() { memset(deleted, false, sizeof deleted); scanf("%d", &n); for (i = 1; i <= n; ++i) { scanf("%d", &t); if (t) { adj[t].push_back(i); adj[i].push_back(t); } } if (n % 2 == 0) { puts("NO"); return 0; } getsz(1, 1); dfs(1, 1); puts("YES"); for (int x : ans) printf("%d\n", x); return 0; }
#include <bits/stdc++.h> using namespace std; inline int Read() { char c = getchar(); int num = 0; while ('0' > c || c > '9') c = getchar(); while ('0' <= c && c <= '9') num = num * 10 + c - '0', c = getchar(); return (num); } vector<int> e[400010]; vector<pair<int, int> > s[400010][2]; int f[400010][2], d[400010], n, m; inline void Dp(int x, int y) { for (int i = 0; i < e[x].size(); i++) s[x][1].push_back(make_pair(-1, -1)), s[x][0].push_back(make_pair(-1, -1)); if (d[x] == 1 && y) { f[x][0] = 1; return; } int g0 = -1, g1 = -1; for (int i = 0; i < e[x].size(); i++) if (e[x][i] != y) { Dp(e[x][i], x); if (g0 == -1) { if (f[e[x][i]][0]) g0 = 1, s[x][0][i] = make_pair(0, 0); if (f[e[x][i]][1]) g1 = 1, s[x][1][i] = make_pair(1, 1); if (g0 == -1) g0 = 0; if (g1 == -1) g1 = 0; continue; } int g0_ = g0, g1_ = g1; g0 = g1 = 0; if (g0_ && f[e[x][i]][1]) g1 = 1, s[x][1][i] = make_pair(0, 1); if (g1_ && f[e[x][i]][0]) g1 = 1, s[x][1][i] = make_pair(1, 0); if (g1_ && f[e[x][i]][1]) g0 = 1, s[x][0][i] = make_pair(1, 1); if (g0_ && f[e[x][i]][0]) g0 = 1, s[x][0][i] = make_pair(0, 0); } if (x == 1) { if (d[x] % 2 == 0) f[x][0] = g0; else f[x][0] = g1; } else { if (d[x] % 2 == 0) f[x][0] = g1, f[x][1] = g0; else f[x][0] = g0, f[x][1] = g1; } } inline void Write(int x, int y, int w) { if (x == 1) { if (d[x] % 2 == 1) w ^= 1; } else { if (d[x] % 2 == 0) w ^= 1; } int w0 = w; for (int i = e[x].size() - 1; i >= 0; i--) if (e[x][i] != y) { if (s[x][w][i].second == 1) Write(e[x][i], x, s[x][w][i].second); w = s[x][w][i].first; } printf("%d\n", x); if (x == 4) int deb = 0; w = w0; for (int i = e[x].size() - 1; i >= 0; i--) if (e[x][i] != y) { if (s[x][w][i].second == 0) Write(e[x][i], x, s[x][w][i].second); w = s[x][w][i].first; } } int p[400010]; int main() { n = Read(); for (int i = 1; i <= n; i++) { p[i] = Read(); if (p[i]) { e[i].push_back(p[i]), e[p[i]].push_back(i); d[p[i]]++, d[i]++; } } Dp(1, 0); if (!f[1][0]) { puts("NO"); return (0); } puts("YES"); Write(1, 0, 0); }
#include <bits/stdc++.h> using namespace std; int arr[1000050], d[1000050], tim[1000050], ind[1000050]; set<int> e[1000050]; vector<int> g[1000050]; priority_queue<pair<int, int>, vector<pair<int, int> >, greater<pair<int, int> > > q; int main() { int n, i, x, vs, curx, curd, next, size; pair<int, int> pa; scanf("%d", &n); for (i = 1; i <= n; i++) { scanf("%d", &x); if (x) { e[x].insert(i); e[i].insert(x); d[x]++; d[i]++; } } for (i = 1; i <= n; i++) q.push(make_pair(d[i], i)); for (; !q.empty();) { pa = q.top(); curx = pa.second; curd = pa.first; q.pop(); if (d[curx] != curd) continue; arr[++vs] = curx; if (d[curx]) { next = *e[curx].begin(); d[curx]--; d[next]--; e[curx].erase(next); e[next].erase(curx); q.push(make_pair(d[next], next)); if (tim[curx] % 2 == 0) { tim[next]++; g[next].push_back(curx); ind[curx]++; } else { g[curx].push_back(next); ind[next]++; } } else if (tim[curx] & 1) { printf("NO\n"); return 0; } } printf("YES\n"); for (; !q.empty(); q.pop()) ; for (i = 1; i <= n; i++) q.push(make_pair(ind[i], i)); for (; !q.empty();) { pa = q.top(); curx = pa.second; curd = pa.first; q.pop(); if (ind[curx] != curd) continue; printf("%d\n", curx); size = g[curx].size(); for (i = 0; i < size; i++) { ind[g[curx][i]]--; q.push(make_pair(ind[g[curx][i]], g[curx][i])); } } return 0; }
#include <bits/stdc++.h> using namespace std; int n, root, p[200001]; vector<int> ans, ch[200001], before[200001], after[200001]; bool vis[200001], par[200001]; void dfs(int u) { if (ch[u].size() == 0) { par[u] = false; return; } for (int c : ch[u]) { dfs(c); if (par[c]) before[u].push_back(c); else after[u].push_back(c); } par[u] = after[u].size() % 2; } void get_ans(int u) { for (int c : before[u]) get_ans(c); ans.push_back(u); for (int c : after[u]) get_ans(c); } int main() { scanf("%d", &n); for (int i = 0; i < n; i++) { ch[i] = vector<int>(); before[i] = vector<int>(); after[i] = vector<int>(); } for (int i = 0; i < n; i++) { scanf("%d", &p[i]); p[i]--; if (p[i] >= 0) ch[p[i]].push_back(i); else root = i; } dfs(root); if (par[root]) { printf("NO\n"); return 0; } ans = vector<int>(); get_ans(root); printf("YES\n%d", ans[0] + 1); for (int i = 1; i < n; i++) printf(" %d", ans[i] + 1); printf("\n"); }
#include <bits/stdc++.h> #pragma GCC optimize("O3") using namespace std; template <typename T> void _R(T& x) { cin >> x; } template <typename T> void _R(vector<T>& x) { for (auto it = x.begin(); it != x.end(); it++) { _R(*it); } } void R() {} template <typename T, typename... K> void R(T& head, K&... tail) { _R(head); R(tail...); } template <typename T> void _W(const T& x, const char c) { cout << x; } template <typename T> void _W(const vector<T>& x, const char c) { for (auto it = x.cbegin(); it != x.cend(); it++) { if (it != x.cbegin()) putchar(c); _W(*it, c); } } void W() {} template <typename T, typename... K> void W(const T& head, const K&... tail) { _W(head, ' '); cout << (sizeof...(tail) ? ' ' : '\n') << flush; W(tail...); } const double PI = 3.14159265358979323846264338327950288419716939937510582097494459230; template <typename T> inline T gcd(T a, T b) { if (a == 0) return b; return gcd(b % a, a); } template <typename T> inline void amin(T& x, T y) { if (x > y) x = y; } template <typename T> inline void amax(T& x, T y) { if (x < y) x = y; } template <typename A, typename B> class comp { public: bool operator()(const pair<A, B>& a, const pair<A, B>& b) { if (a.first != b.first) return a.first < b.first; else return a.first > b.first; } }; long long fast_exp(long long a, long long b) { long long res = 1; while (b) { if (b & 1LL) { res *= a; res %= 1000000007; } b >>= 1LL; a *= a; a %= 1000000007; } return res; } const int N = 200005; int n; vector<int> g[N]; vector<int> a; bool b[N]; map<int, bool> m[N]; void preprocess(void) { return; } bool dfs(int u, int p) { int cnt = 0; for (auto v : (g[u])) { if (v == p) continue; bool f = dfs(v, u); m[u][v] = f; if (f) cnt++; } if (p == -1) { if ((cnt)&1) return false; else return true; } cnt++; if (cnt & 1) return true; else return false; } void answ(int u, int p) { for (auto v : (g[u])) { if (v == p) continue; if (!m[u][v]) { answ(v, u); } } a.push_back(u); for (auto v : (g[u])) { if (v == p) continue; if (m[u][v]) { answ(v, u); } } } signed main(int argc, char* argv[], char* envp[]) { ios_base::sync_with_stdio(false); cin.tie(NULL); cout.precision(20); preprocess(); int teeee; teeee = 1; for (int zeeee = (1); zeeee <= (teeee); zeeee++) { cin >> n; for (int i = (0); i <= ((int)(n)-1); i++) { int p; cin >> p; if (p == 0) continue; p--; g[i].push_back(p); g[p].push_back(i); } fill(b, b + n, false); bool ans = dfs(0, -1); if (ans) { cout << "YES\n"; answ(0, -1); for (auto v : a) { cout << v + 1 << "\n"; } } else { cout << "NO\n"; } } cerr << (((double)clock()) / ((double)CLOCKS_PER_SEC)) << endl; return 0; }
#include <bits/stdc++.h> using namespace std; vector<long long> adj[200005]; bool vis[200005] = {false}; long long degree[200005] = {0}; vector<long long> ans; long long dfs(long long s) { vis[s] = true; long long i, ans = 0; for (i = 0; i < adj[s].size(); i++) { if (!vis[adj[s][i]]) ans += dfs(adj[s][i]); } degree[s] = ans + 1; return degree[s]; } void dfs1(long long s) { vis[s] = true; long long i; for (i = 0; i < adj[s].size(); i++) { if (!vis[adj[s][i]] && degree[adj[s][i]] % 2 == 0) dfs1(adj[s][i]); } ans.push_back(s); for (i = 0; i < adj[s].size(); i++) { if (!vis[adj[s][i]] && degree[adj[s][i]] % 2 == 1) dfs1(adj[s][i]); } } int main() { long long n, i, j, temp; cin >> n; for (i = 1; i <= n; i++) { cin >> temp; if (temp == 0) continue; adj[i].push_back(temp); adj[temp].push_back(i); } if (n % 2 == 0) { cout << "NO" << "\n"; return 0; } dfs(1); for (i = 1; i <= n; i++) vis[i] = false; dfs1(1); cout << "YES" << "\n"; for (i = 0; i < ans.size(); i++) cout << ans[i] << "\n"; }
#include <bits/stdc++.h> using namespace std; const double PI = acos(-1.0); const double eps = 1e-6; const int INF = 0x3f3f3f3f; const int maxn = 2e5 + 11; int N, M, T, P, Q; list<int> G[maxn]; bool ok = 1; int deg[maxn]; bool dele[maxn]; list<int> ans; void del(int u, int pu) { if (dele[u]) return; dele[u] = 1; ans.push_back(u); for (int v : G[u]) { if (v == pu) continue; del(v, u); } } void dfs(int u = 1, int pu = -1) { for (int v : G[u]) { if (v == pu) continue; dfs(v, u); if (dele[v]) deg[u]--; } if (deg[u] % 2 == 0) del(u, pu); } int main() { cin >> N; for (int i = 1, j; i <= N; i++) { scanf("%d", &j); if (j) G[i].push_back(j), G[j].push_back(i); } for (int i = 1; i <= N; i++) deg[i] = G[i].size(); dfs(); if (ans.size() < N) puts("NO"); else { puts("YES"); for (int x : ans) printf("%d\n", x); } return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 2e5 + 7; vector<int> g[N]; int sz[N]; bool vis[N]; int lvl[N]; void dfs(int node, int par) { for (int nxt : g[node]) { if (nxt == par) continue; lvl[nxt] = lvl[node] + 1; dfs(nxt, node); } } int main() { ios_base::sync_with_stdio(false); cin.tie(NULL); int n; cin >> n; int root; for (int i = 1; i <= n; i++) { int x; cin >> x; if (!x) { root = i; continue; } g[x].push_back(i); g[i].push_back(x); } memset(sz, 0, sizeof(sz)); memset(vis, 0, sizeof(vis)); memset(lvl, 0, sizeof(lvl)); dfs(root, 0); set<pair<int, int> > ss; for (int i = 1; i <= n; i++) { sz[i] = g[i].size(); if (sz[i] % 2 == 0) { ss.insert(make_pair(lvl[i], i)); } } vector<int> vec; while (ss.size()) { pair<int, int> p = *ss.rbegin(); int node = p.second; vec.push_back(node); vis[node] = true; ss.erase(prev(ss.end())); for (int nxt : g[node]) { if (vis[nxt]) continue; sz[nxt]--; if (sz[nxt] & 1) { ss.erase(make_pair(lvl[nxt], nxt)); } else ss.insert(make_pair(lvl[nxt], nxt)); } } if (vec.size() != n) { cout << "NO\n"; return 0; } cout << "YES\n"; for (int x : vec) { cout << x << endl; } return 0; }
#include <bits/stdc++.h> using namespace std; int sz[200001]; bool mark[200001]; set<int> tree[200001]; vector<int> destroy; void predfs(int u, int p) { sz[u] = 1; for (int v : tree[u]) { if (v != p) { predfs(v, u); sz[u] += sz[v]; } } } void dfs(int u, int p) { vector<int> rest; for (int v : tree[u]) { if (mark[v]) continue; if (v != p && sz[v] % 2 == 0) { dfs(v, u); } else if (v != p) { rest.push_back(v); } } mark[u] = true; destroy.push_back(u); for (int v : rest) { dfs(v, -1); } } int main() { int n, p; cin >> n; for (int i = 1; i <= n; ++i) { cin >> p; if (p) { tree[i].insert(p); tree[p].insert(i); } } if (n % 2 == 0) { cout << "NO" << endl; return 0; } fill(mark, mark + n + 1, false); predfs(1, -1); dfs(1, -1); cout << "YES" << endl; for (int u : destroy) { cout << u << endl; } return 0; }
#include <bits/stdc++.h> using namespace std; int N; set<int> E[202020]; set<int> cand; int C[202020]; vector<int> V; int dfs(int cur, int pre) { C[cur] = 1; for (auto& e : E[cur]) if (e != pre) C[cur] += dfs(e, cur); return C[cur]; } void dfs2(int cur, int pre) { if (C[cur] % 2 == 1) { for (auto& e : E[cur]) if (e != pre) { if (C[e] % 2 == 0) dfs2(e, cur); } V.push_back(cur); for (auto& e : E[cur]) if (e != pre) { if (C[e] % 2 == 1) dfs2(e, cur); } } else { for (auto& e : E[cur]) if (e != pre) { if (C[e] % 2 == 0) dfs2(e, cur); } V.push_back(cur); for (auto& e : E[cur]) if (e != pre) { if (C[e] % 2 == 1) dfs2(e, cur); } } } void solve() { int i, j, k, l, r, x, y; string s; cin >> N; if (N % 2 == 0) return (void)printf("NO\n"); for (i = 1; i <= N; i++) { cin >> x; if (x) { E[i].insert(x); E[x].insert(i); } } dfs(1, 1); dfs2(1, 1); cout << "YES" << endl; for (auto& v : V) cout << v << endl; } int main(int argc, char** argv) { string s; int i; if (argc == 1) ios::sync_with_stdio(false), cin.tie(0); for (i = 0; i < (argc - 1); i++) s += argv[i + 1], s += '\n'; for (i = 0; i < (s.size()); i++) ungetc(s[s.size() - 1 - i], stdin); cout.tie(0); solve(); return 0; }
#include <bits/stdc++.h> using namespace std; template <class c> struct rge { c b, e; }; template <class c> rge<c> range(c i, c j) { return {i, j}; } struct printer { ~printer() { cerr << endl; } template <class c> printer& operator,(c x) { cerr << boolalpha << x; return *this; } printer& operator,(string x) { cerr << x; return *this; } template <class c, class d> printer& operator,(pair<c, d> x) { return *this, "(", x.first, ", ", x.second, ")"; } template <class... d, template <class...> class c> printer& operator,(c<d...> x) { return *this, range(begin(x), end(x)); } template <class c> printer& operator,(rge<c> x) { *this, "["; for (auto it = x.b; it != x.e; ++it) *this, (it == x.b ? "" : ", "), *it; return *this, "]"; } }; mt19937 rng(chrono::steady_clock::now().time_since_epoch().count()); int my_rand(int l, int r) { return uniform_int_distribution<int>(l, r)(rng); } const int N = 200009; vector<int> vec[N]; int ar[N], degree[N], level[N]; struct node { int u, lv, id; bool operator<(const node& p) const { return p.lv > lv; } }; void dfs(int u, int par, int lv) { level[u] = lv; int v, i, sz = vec[u].size(); for (i = 0; i < sz; i++) { v = vec[u][i]; if (v != par) { dfs(v, u, lv + 1); } } } int main() { int n, i, r; scanf("%d", &n); for (i = 1; i <= n; i++) { scanf("%d", &r); if (r == 0) continue; vec[i].push_back(r); vec[r].push_back(i); degree[r]++; degree[i]++; } if (n % 2 == 0) { printf("NO\n"); return 0; } for (i = 1; i <= n; i++) { if (degree[i] == 1) { dfs(i, -1, 0); break; } } priority_queue<node> pq; for (i = 1; i <= n; i++) { if (degree[i] % 2 == 0) pq.push({i, level[i], 0}); } vector<int> ans; while (!pq.empty()) { node top = pq.top(); pq.pop(); if (top.id != ar[top.u]) continue; ans.push_back(top.u); int sz = vec[top.u].size(); for (i = 0; i < sz; i++) { int v = vec[top.u][i]; if (degree[v] > 0) { degree[v]--; ar[v]++; if (degree[v] == 0) ans.push_back(v); else if (degree[v] % 2 == 0) { pq.push({v, level[v], ar[v]}); } } } degree[top.u] = 0; } int sz = ans.size(); printf("YES\n"); for (i = 0; i < sz; i++) { printf("%d\n", ans[i]); } return 0; }
#include <bits/stdc++.h> using namespace std; const int maxn = 2e5 + 10; const int maxm = 1e6 + 10; const int INF = 0x3f3f3f3f; int casn, n, m, k; int st, pre[maxn], deg[maxn]; int to[maxn], nex[maxn], head[maxn], nume; int dfn[maxn], cnt, ans1[maxn], ans2[maxn], cnt2; void dfs(int now) { for (int i = head[now]; i; i = nex[i]) { if (to[i] != now) dfs(to[i]); } dfn[++cnt] = now; } int main() { ios::sync_with_stdio(false); cin.tie(0); cout.tie(0); cin >> n; for (int i = 1; i <= n; i++) { cin >> pre[i]; deg[pre[i]]++; if (pre[i]) { deg[i]++; to[++nume] = i; nex[nume] = head[pre[i]]; head[pre[i]] = nume; } else st = i; } dfs(st); cnt = 0; for (int i = 1; i < n; i++) { if (deg[dfn[i]] & 1) { ans2[++cnt2] = dfn[i]; } else ans1[++cnt] = dfn[i], deg[pre[dfn[i]]]--; } if (deg[dfn[n]] & 1) cout << "NO\n"; else { ans1[++cnt] = dfn[n]; cout << "YES\n"; for (int i = 1; i <= cnt; i++) cout << ans1[i] << '\n'; for (int i = cnt2; i; i--) cout << ans2[i] << '\n'; } return 0; }
#include <bits/stdc++.h> using namespace std; const int maxn = 200050; vector<int> graf[maxn]; int dp[2][maxn]; vector<int> data[maxn]; int n, root; vector<int> v; void bejar(int start) { for (int s : graf[start]) { if (dp[1][s]) { bejar(s); } } v.push_back(start); for (int s : graf[start]) { if (dp[0][s]) { bejar(s); } } return; } int main() { ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL); cin >> n; for (int i = 0; i < n; i++) { int z; cin >> z; z--; if (z >= 0) { graf[z].push_back(i); } else { root = i; } } vector<int> sor; vector<int> apa; sor.push_back(root); int it = 0; while (it < sor.size()) { int akt = sor[it]; for (int s : graf[akt]) { sor.push_back(s); } it++; } reverse(sor.begin(), sor.end()); for (int i = 0; i < n; i++) { int akt = sor[i]; if (graf[akt].size() == 0) { dp[0][akt] = true; dp[1][akt] = false; } else { int with_akt = 0; for (int s : graf[akt]) { if (dp[0][s]) { with_akt++; } } if (with_akt % 2 == 0) { dp[0][akt] = true; dp[1][akt] = false; } else { dp[0][akt] = false; dp[1][akt] = true; } } } if (dp[0][root]) { cout << "YES" << endl; bejar(root); for (int d : v) { cout << d + 1 << endl; } return 0; } cout << "NO" << endl; return 0; }
#include <bits/stdc++.h> using namespace std; int read() { int xx = 0, ff = 1; char ch = getchar(); while (ch > '9' || ch < '0') { if (ch == '-') ff = -1; ch = getchar(); } while (ch >= '0' && ch <= '9') { xx = xx * 10 + ch - '0'; ch = getchar(); } return xx * ff; } const int maxn = 200010; int N, root; int lin[maxn], len, deg[maxn]; struct edge { int y, next; } e[maxn << 1]; inline void insert(int xx, int yy) { e[++len].next = lin[xx]; lin[xx] = len; e[len].y = yy; deg[xx]++; } bool v[maxn]; int cnt[maxn][2]; bool dfs(int x, int fa) { for (int i = lin[x]; i; i = e[i].next) if (e[i].y != fa) cnt[x][dfs(e[i].y, x)]++; if ((deg[x] - cnt[x][1]) % 2 == 0) v[x] = 1; else v[x] = 0; return v[x]; } void print(int x, int fa) { for (int i = lin[x]; i; i = e[i].next) if (e[i].y != fa) if (v[e[i].y]) print(e[i].y, x); printf("%d\n", x); for (int i = lin[x]; i; i = e[i].next) if (e[i].y != fa) if (!v[e[i].y]) print(e[i].y, x); } int main() { N = read(); for (int i = 1; i <= N; i++) { int temp = read(); if (!temp) root = i; else insert(i, temp), insert(temp, i); } if (dfs(root, 0)) { puts("YES"); print(root, 0); } else puts("NO"); return 0; }
#include <bits/stdc++.h> using namespace std; const int MX = 1147483646; const long long MX2 = 9223372036854775800; const int MOD = 1e9 + 9; int n; vector<int> tr[200011]; vector<int> destr[200011]; int sz[200011]; bool des[200011], visited[200011]; void dest(int& id) { cout << id << "\n"; des[id] = 1; for (int x : destr[id]) sz[x]--; return; } void dfs(int id) { bool rep = 1; if (visited[id] && !des[id] && sz[id] % 2 == 0) { rep = 0; dest(id); } visited[id] = 1; for (int x : tr[id]) { if (des[x]) continue; dfs(x); } if (!des[id] && sz[id] % 2 == 0) { dest(id); for (int x : tr[id]) { if (des[x]) continue; dfs(x); } } return; } int main() { cin.tie(NULL); ios::sync_with_stdio(false); int i, x; cin >> n; int rt; for (i = 1; i <= n; i++) { cin >> x; if (x) { tr[x].push_back(i); destr[x].push_back(i); destr[i].push_back(x); sz[i]++; sz[x]++; } else rt = i; } if (n & 1) { cout << "YES\n"; dfs(rt); } else { cout << "NO"; } return 0; }
#include <bits/stdc++.h> using namespace std; string itosm(long long x) { if (x == 0) return "0"; string ans = ""; while (x > 0) { ans += ((x % 10) + '0'); x /= 10; } reverse(ans.begin(), ans.end()); return ans; } long long stoim(string str) { long long ans = 0; long long k = 1; int p = 0; if (str[0] == '-') p++; for (int i = str.length() - 1; i >= p; i--) { ans += (str[i] - '0') * k; k *= 10; } return ans; } const long long infll = 1e18 + 3; const int inf = 1009000999; const long double eps = 1e-7; const int maxn = 1e6 + 1146; const int baseint = 1000200013; const long long basell = 1e18 + 3; const long double PI = acos(-1.0); const long long mod = 1e9 + 9; vector<int> g[maxn]; int d[maxn]; int lvl[maxn]; bool del[maxn]; void dfs(int v, int an) { for (int to : g[v]) { if (to == an) continue; lvl[to] = lvl[v] + 1; dfs(to, v); } } void solve() { int n; cin >> n; if (n % 2 == 0) { cout << "NO"; return; } int t; cout << "YES\n"; for (int i = 1; i <= n; i++) { int x; cin >> x; if (x == 0) { t = i; continue; } g[i].push_back(x); g[x].push_back(i); } dfs(t, -1); set<pair<int, int> > q; for (int v = 1; v <= n; v++) { d[v] = g[v].size(); if (g[v].size() % 2 == 0) q.insert({lvl[v], v}); } vector<int> ans; while (!q.empty()) { int v = (*q.rbegin()).second; q.erase({lvl[v], v}); ans.push_back(v); del[v] = 1; for (int to : g[v]) { d[to]--; if (d[to] % 2 == 0) { if (!del[to]) q.insert({lvl[to], to}); } else { q.erase({lvl[to], to}); } } } for (int v : ans) cout << v << "\n"; } int main() { ios_base::sync_with_stdio(0); ; cin.tie(0); cout.tie(0); solve(); return 0; }
#include <bits/stdc++.h> int B = 400; using namespace std; const long long inf = 1e12; int MOD = 1e9 + 9; const int mxn = 200010; int deg[mxn]; bool del[mxn]; vector<int> ans; vector<int> g[mxn]; void dell(int v, int p) { if (del[v] != 0) return; if (deg[v] % 2 != 0) return; del[v] = 1; ans.push_back(v); for (int u : g[v]) deg[u]--; for (int u : g[v]) { if (!del[u] && u != p) dell(u, v); } } void dfs(int v, int p) { for (int u : g[v]) { if (u != p) dfs(u, v); } if (deg[v] % 2 == 0) dell(v, p); } long long res = 0; int main() { ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0); int n; cin >> n; for (int i = 1; i <= n; i++) { int a; cin >> a; if (!a) continue; g[i].push_back(a); g[a].push_back(i); deg[a]++, deg[i]++; } dfs(1, -1); if (ans.size() == n) { cout << "YES" << endl; for (int u : ans) cout << u << endl; } else cout << "NO" << endl; }
#include <bits/stdc++.h> using namespace std; const int N = 2e5 + 10; vector<int> G[N]; stack<int> S; int in[N]; int pre[N]; int fa[N]; int dfss; void dfs(int u, int fas) { pre[u] = dfss++; fa[u] = fas; for (int i = 0; i < G[u].size(); i++) { int v = G[u][i]; if (v == fas) continue; dfs(v, u); } if (in[u] % 2 == 1) S.push(u); if (in[u] % 2 == 0) { printf("%d\n", u); in[fa[u]]--; while (!S.empty()) { int s = S.top(); if (pre[s] < pre[u]) break; S.pop(); printf("%d\n", s); in[fa[s]]--; } } } int main() { int n; scanf("%d", &n); int x; dfss = 0; memset(in, 0, sizeof(in)); for (int i = 1; i <= n; i++) { scanf("%d", &x); if (x == 0) continue; in[x]++; in[i]++; G[i].push_back(x); G[x].push_back(i); } if (n % 2 == 0) { puts("NO"); return 0; } printf("YES\n"); dfs(1, 0); return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 200000; int n, root; int sz[N + 5]; vector<int> v[N + 5]; void dfs1(int nod) { int ans = 0; for (auto nou : v[nod]) { dfs1(nou); ans += sz[nou]; } sz[nod] = ans + 1; } void dfs(int nod) { for (auto nou : v[nod]) if (sz[nou] % 2 == 0) dfs(nou); cout << nod << "\n"; for (auto nou : v[nod]) if (sz[nou] % 2 == 1) dfs(nou); } int main() { ios_base::sync_with_stdio(false); cin.tie(0); cin >> n; for (int nod = 1; nod <= n; nod++) { int t; cin >> t; if (t == 0) root = nod; else v[t].push_back(nod); } if (n % 2 == 0) { cout << "NO\n"; return 0; } cout << "YES\n"; dfs1(root); dfs(root); return 0; }
#include <bits/stdc++.h> using namespace std; vector<int> adj[200000 + 20]; bool mitParentKante[200000 + 20]; bool ohneParentKante[200000 + 20]; void dfs(int i, int parent) { if (adj[i].size() == 1 && parent != -1) { ohneParentKante[i] = true; mitParentKante[i] = false; return; } bool geradeAnzahlOhne = true; for (int child : adj[i]) { if (child != parent) { dfs(child, i); if (!mitParentKante[child] && !ohneParentKante[child]) { cout << "NO" << endl; exit(0); } if (ohneParentKante[child]) { geradeAnzahlOhne = !geradeAnzahlOhne; } if (mitParentKante[child]) { } } } if (geradeAnzahlOhne) { ohneParentKante[i] = true; mitParentKante[i] = false; } else { ohneParentKante[i] = false; mitParentKante[i] = true; }; } void deleteDFS(int i, int parent) { for (int child : adj[i]) { if (child != parent) { ; ; ; if (mitParentKante[child]) { deleteDFS(child, i); } } } cout << i + 1 << endl; for (int child : adj[i]) { if (child != parent) { if (ohneParentKante[child]) { deleteDFS(child, i); } } } } int32_t main() { int n; cin >> n; for (int i = 0; i < n; i++) { int v; cin >> v; v--; if (v != -1) { adj[v].push_back(i); adj[i].push_back(v); } } dfs(0, -1); if (!ohneParentKante[0]) { cout << "NO" << endl; exit(0); } cout << "YES" << endl; for (int i = 0; i < n; i++) { ; ; ; } deleteDFS(0, -1); }
#include <bits/stdc++.h> using namespace std; const int N = 2e5 + 5; int n, root; vector<int> adj[N]; int dp[N][2], deg[N]; bool mark[N]; void dfs(int u, int pre) { for (int v : adj[u]) { if (v == pre) continue; dfs(v, u); } for (int p = 0, _n = (2); p < _n; p++) { int d = (deg[u] + ((p == 0 && pre != -1) ? -1 : 0)); vector<int> ban; for (int v : adj[u]) if (v != pre) { if (!dp[v][0]) ban.push_back(v); } bool flag = false; for (int v : ban) { if (!dp[v][1]) { flag = true; break; } } if (flag) continue; if ((d - ban.size()) % 2 == 1) { flag = true; for (int v : adj[u]) if (v != pre && dp[v][0]) { if (dp[v][1]) flag = false; } if (flag) continue; } dp[u][p] = 1; } } void print_ans(int u, int pre, int p) { int d = (deg[u] + ((p == 0 && pre != -1) ? -1 : 0)), cnt = 0; for (int v : adj[u]) if (v != pre) { if (!dp[v][0]) { cnt++; print_ans(v, u, 1); mark[v] = 1; } } if ((d - cnt) % 2 == 1) { for (int v : adj[u]) if (v != pre && dp[v][0] && dp[v][1]) { print_ans(v, u, 1); mark[v] = 1; break; } } cout << u << '\n'; for (int v : adj[u]) if (v != pre && !mark[v]) print_ans(v, u, 0); } int main(int argc, char const *argv[]) { ios_base::sync_with_stdio(0); cin.tie(0); clock_t tStart = clock(); cin >> n; for (int i = (1), _b = (n); i <= _b; i++) { int j; cin >> j; if (j == 0) root = i; else { adj[i].push_back(j); adj[j].push_back(i); deg[i]++; deg[j]++; } } dfs(root, -1); if (!dp[root][0]) { cout << "NO" << '\n'; return 0; } else { cout << "YES" << '\n'; print_ans(root, -1, 0); } fprintf(stderr, "Time taken: %.2fs\n", (double)(clock() - tStart) / CLOCKS_PER_SEC); return 0; }
#include <bits/stdc++.h> using namespace std; const long long INF = 1e9 + 9; const int N = 2e5 + 10; vector<int> v[N]; vector<int> v2[N]; int sons[N]; int flag[N]; vector<int> ans; void dfs2(int x) { ans.push_back(x); for (auto &y : v2[x]) dfs2(y); } bool dfs(int x, int p = 0) { if (p) sons[x] = 1; for (auto &y : v[x]) { dfs(y, x); sons[x]++; } flag[x] = sons[x] & 1; if (flag[x] == 0) { ans.push_back(x); for (auto &y : v2[x]) { dfs2(y); } sons[p]--; } else { if (p == 0) return false; else v2[p].push_back(x); } return true; } int main() { int n; cin >> n; int rt = 0; for (int i = 1; i <= n; i++) { int x; cin >> x; v[x].push_back(i); } if (dfs(v[0].back())) { puts("YES"); for (auto &x : ans) printf("%d\n", x); } else puts("NO"); return 0; }
#include <bits/stdc++.h> using namespace std; using ll = long long; const int maxn = 2e5 + 5; int n; vector<int> adj[maxn]; int deg[maxn]; bool used[maxn]; int sz[maxn]; void dfsSize(int i, int p) { sz[i] = 1; for (int j : adj[i]) { if (j == p) continue; dfsSize(j, i); sz[i] += sz[j]; } } vector<int> ans; void dfs(int i, int p) { for (int j : adj[i]) { if (j == p) continue; if (!(sz[j] & 1)) { dfs(j, i); } } ans.push_back(i); for (int j : adj[i]) { if (j == p) continue; if (sz[j] & 1) { dfs(j, i); } } } int main() { ios_base::sync_with_stdio(false); cin.tie(NULL); cin >> n; if (!(n & 1)) { cout << "NO\n"; return 0; } for (int i = 1; i <= n; i++) { int p; cin >> p; if (p != 0) { adj[i].push_back(p); adj[p].push_back(i); deg[i]++; deg[p]++; } } dfsSize(1, 1); dfs(1, 1); cout << "YES\n"; for (int i : ans) { cout << i << '\n'; } }
#include <bits/stdc++.h> #pragma GCC optimize(3, "Ofast", "inline") using namespace std; const int maxn = (long long)2e5 + 5; const int mod = 1000000007; const int inf = 0x3f3f3f3f; vector<int> v[maxn]; vector<int> ans; int in[maxn]; bool del[maxn]; int pre[maxn]; void dfs2(int x) { ans.push_back(x); del[x] = true; for (auto &i : v[x]) { --in[i]; if ((!del[i]) && (!(in[i] & 1))) dfs2(i); } } void dfs(int x) { for (auto &i : v[x]) if (!del[i]) dfs(i); if (!(in[x] & 1)) { --in[pre[x]]; dfs2(x); } } signed main() { ios::sync_with_stdio(false); cin.tie(0); cout.tie(0); ; int root; int n; cin >> n; for (int i = 1; i <= n; ++i) { int x; cin >> x; pre[i] = x; if (x == 0) root = i; else { v[x].push_back(i); ++in[x], ++in[i]; } } dfs(root); if (ans.size() == n) { cout << "YES" << '\n'; for (auto &i : ans) cout << i << '\n'; } else cout << "NO"; return 0; }
#include <bits/stdc++.h> using namespace std; const long long N = 1e6 + 5; long long n, tot, rt, du[N], vis[N], F[N], zhan[N]; vector<long long> g[N], xu; inline long long read() { long long ret = 0, f = 0; char c = getchar(); while (!isdigit(c)) { if (c == '-') f = 1; c = getchar(); } while (isdigit(c)) { ret = ret * 10 + c - 48; c = getchar(); } if (f) return -ret; return ret; } void dfs(long long u, long long fa) { F[u] = fa; for (long long i = 0; i < g[u].size(); i++) { long long v = g[u][i]; if (v == fa) continue; dfs(v, u); } if (du[u] % 2 == 0) { du[fa]--; xu.push_back(u); } if (u == rt && du[u] & 1) { puts("NO"); exit(0); } } void solve(long long u, long long fa) { zhan[++tot] = u; vis[u] = 1; for (long long i = 0; i < g[u].size(); i++) { long long v = g[u][i]; if (v == fa || vis[v]) continue; solve(v, u); } } signed main() { n = read(); for (long long i = 1; i <= n; i++) { long long x = read(); if (x > 0) { g[x].push_back(i); g[i].push_back(x); du[i]++; du[x]++; } else rt = i; } dfs(rt, 0); puts("YES"); for (long long i = 0; i < xu.size(); i++) { long long x = xu[i]; solve(x, F[x]); } for (long long i = 1; i <= n; i++) printf("%lld\n", zhan[i]); return 0; }
#include <bits/stdc++.h> using namespace std; const int maxn = 2e5 + 5; vector<int> G[maxn]; void insert(int u, int v) { G[u].push_back(v); G[v].push_back(u); } int sz[maxn]; void dfs(int u, int fa) { sz[u] = 1; for (int v : G[u]) { if (v == fa) continue; dfs(v, u); sz[u] += sz[v]; } } void del(int u, int fa) { for (int v : G[u]) { if (v == fa) continue; if (sz[v] % 2 == 0) del(v, u); } printf("%d\n", u); for (int v : G[u]) { if (v == fa) continue; if (sz[v] & 1) del(v, u); } } int n; int main() { scanf("%d", &n); int rt; for (int i = 1, x; i <= n; i++) { scanf("%d", &x); if (x == 0) rt = i; else insert(i, x); } if (n % 2 == 0) { puts("NO"); return 0; } puts("YES"); dfs(rt, 0); del(rt, 0); return 0; }
#include <bits/stdc++.h> using namespace std; const int MAXN = 2e5 + 5; int vecinos[MAXN]; int prof[MAXN]; int n; set<int> arbol[MAXN]; void dfs(int i, int p, int profund) { prof[i] = profund; for (int h : arbol[i]) { if (h == p) continue; dfs(h, i, profund + 1); } } int main() { ios::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL); cin >> n; int raiz; for (int i = (0); i < (n); i++) { int p; cin >> p; p--; if (p != -1) { arbol[p].insert(i); vecinos[p]++; arbol[i].insert(p); vecinos[i]++; } else { raiz = i; } } dfs(raiz, -1, 0); set<pair<int, int> > q; for (int i = (0); i < (n); i++) { if (vecinos[i] % 2 == 0) { q.insert({-prof[i], i}); } } vector<int> eliminados; while (!q.empty()) { auto actual = *q.begin(); q.erase(q.begin()); int act = actual.second; if (vecinos[act] % 2) continue; for (int h : arbol[act]) { vecinos[h]--; arbol[h].erase(arbol[h].find(act)); if (vecinos[h] % 2 == 0) { q.insert({-prof[h], h}); } } arbol[act].clear(); eliminados.push_back(act); } if ((int)(eliminados).size() != n) { cout << "NO\n"; } else { cout << "YES\n"; for (int e : eliminados) { cout << e + 1 << "\n"; } } }
#include <bits/stdc++.h> using namespace std; int N; vector<int> G[200000]; bool dpA[200000], dpB[200000]; void dfs(int x, int p) { for (int t : G[x]) if (t != p) dfs(t, x); int a_only = 0, both = 0; for (int t : G[x]) if (t != p) { bool a = dpA[t], b = dpB[t]; if (!a && !b) return; if (a && !b) a_only++; if (a && b) both++; } if ((a_only % 2 == 0) || (both > 0)) { dpA[x] = true; } if ((a_only % 2 == 1) || (both > 0)) { dpB[x] = true; } } vector<int> perm; void restore(int x, int p, bool par) { vector<int> a_only, both, b_only; for (int t : G[x]) if (t != p) { bool a = dpA[t], b = dpB[t]; assert(a || b); if (a && !b) a_only.push_back(t); if (a && b) both.push_back(t); if (!a && b) b_only.push_back(t); } for (int i = 0; i < (both.size()); i++) if (i != 0) restore(both[i], x, true); for (int v : b_only) restore(v, x, true); if ((a_only.size() + par) % 2 == 0) { if (both.size() > 0) restore(both[0], x, true); } perm.push_back(x); for (int v : a_only) restore(v, x, false); if ((a_only.size() + par) % 2 != 0) { assert(both.size() > 0); restore(both[0], x, false); } } signed main() { ios::sync_with_stdio(false); cin.tie(0); cin >> N; for (int i = 0; i < (N); i++) { int p; cin >> p; p--; if (p != -1) G[i].push_back(p), G[p].push_back(i); } dfs(0, -1); if (dpA[0]) { cout << "YES\n"; restore(0, -1, false); assert(perm.size() == N); for (int i = 0; i < (N); i++) cout << perm[i] + 1 << "\n"; } else { cout << "NO\n"; } return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 200010; int k, n, m, x, Rt; int h[N], nx[N << 1], t[N << 1], num; int A[N], B[N], C[N], l1, l2, l3; int a[N], cnt; bool f[N][2], fl; bool g[2][N], d[N]; set<int> S; void Add(int x, int y) { t[++num] = y; nx[num] = h[x]; h[x] = num; } void Dfs(int x) { for (int i = h[x]; i; i = nx[i]) Dfs(t[i]); l1 = l2 = l3 = 0; for (int i = h[x]; i; i = nx[i]) { if (f[t[i]][0] && f[t[i]][1]) A[++l1] = t[i]; else if (f[t[i]][0]) B[++l2] = t[i]; else if (f[t[i]][1]) C[++l3] = t[i]; } if (!l1) { bool t = d[x] ^ (l2 & 1); f[x][t] = 1; for (int i = 1; i <= l3; i++) g[t][C[i]] = 1; } else { f[x][0] = f[x][1] = 1; for (int t = 0; t < 2; t++) { if (!(t ^ (l2 & 1) ^ d[x])) g[t][A[1]] = 1; for (int i = 2; i <= l1; i++) g[t][A[i]] = 1; for (int i = 1; i <= l3; i++) g[t][C[i]] = 1; } } if (!f[x][0] && !f[x][1]) fl = 1; } void Get(int x, bool d) { for (int i = h[x]; i; i = nx[i]) if (!g[d][t[i]]) Get(t[i], 0); a[++cnt] = x; for (int i = h[x]; i; i = nx[i]) if (g[d][t[i]]) Get(t[i], 1); } int main() { scanf("%d", &n); for (int i = 1; i <= n; i++) { scanf("%d", &x); if (x) Add(x, i), d[x] ^= 1, d[i] ^= 1; else Rt = i; } Dfs(Rt); if (fl || !f[Rt][0]) puts("NO"); else { puts("YES"); Get(Rt, 0); for (int i = 1; i <= n; i++) printf("%d\n", a[i]); } return 0; }
#include <bits/stdc++.h> using namespace std; vector<int> son[200050]; bool deleted[200500]; int seq[200050]; int dcnt, root; void dfs2(int u) { if (deleted[u]) return; deleted[u] = 1; seq[++dcnt] = u; for (int i = 0; i < son[u].size(); ++i) dfs2(son[u][i]); } void dfs(int u) { int d = 0; if (u != root) d++; for (int i = 0; i < son[u].size(); ++i) { dfs(son[u][i]); if (!deleted[son[u][i]]) d++; } if (d % 2 == 0) dfs2(u); return; } int main() { int n, fa; scanf("%d", &n); for (int j = 1; j <= n; ++j) { scanf("%d", &fa); if (!fa) root = j; else son[fa].push_back(j); } dfs(root); if (dcnt != n) printf("NO\n"); else { printf("YES\n"); for (int i = 1; i <= dcnt; ++i) printf("%d\n", seq[i]); } }
#include <bits/stdc++.h> using namespace std; const int N = 2e5 + 5; int n, sumsub[N], deg[N], par[N]; vector<int> adj[N]; bool mark[N]; void des(int v) { if (!mark[v]) { cout << v + 1 << '\n'; mark[v] = true; } for (auto u : adj[v]) if (!mark[u] && u != par[v]) des(u); } void dfs(int v) { sumsub[v] = 1; for (auto u : adj[v]) { if (u != par[v]) { par[u] = v; dfs(u); sumsub[v] += sumsub[u]; } } if (sumsub[v] % 2 == 0) des(v); } void input() { cin >> n; for (int i = 0; i < n; i++) { int v; cin >> v; if (v) { v--; adj[i].push_back(v); adj[v].push_back(i); } } } void solve() { if (n % 2 == 0) cout << "NO", exit(0); cout << "YES" << '\n'; int st = -1; for (int i = 0; i < n; i++) if (adj[i].size() == 1) st = i; if (st == -1) cout << 1 << '\n', exit(0); par[st] = -1; dfs(st); cout << st + 1 << '\n'; } int main() { ios ::sync_with_stdio(0), cin.tie(0), cout.tie(0); input(), solve(); }
#include <bits/stdc++.h> using namespace std; int A[300002]; vector<int> ans; vector<int> v[300002]; vector<int> lv[300002]; int papa[300002]; int done[300002]; int n; int last = 0; map<pair<int, int>, int> imap; void dfs(int root, int par, int p) { papa[root] = par; if (A[root] % 2 == 0) { lv[p].push_back(root); } last = max(last, p); for (int i = 0; i < v[root].size(); i++) { int num = v[root][i]; if (num != par) { dfs(num, root, p + 1); } } } bool checkis(int root, int par) { for (int i = 0; i < v[root].size(); i++) { int num = v[root][i]; if (imap[make_pair(root, num)] == 0) { return 1; } if (num != par) { checkis(num, root); } } return 0; } bool check(int root) { for (int i = last; i >= 0; i--) { for (int j = 0; j < lv[i].size(); j++) { int num = lv[i][j]; if (A[num] % 2 == 1 || done[num] == 1) { continue; } int pop = papa[num]; ans.push_back(num); done[num] = 1; for (int k = 0; k < v[num].size(); k++) { int y = v[num][k]; imap[make_pair(num, y)] = 1; imap[make_pair(y, num)] = 1; A[y] -= 1; if (A[y] % 2 == 0 && A[y] != 0) { if (y == pop) { lv[i - 1].push_back(y); } else { lv[i + 1].push_back(y); } } } } } for (int i = 0; i <= last; i++) { for (int j = 0; j < lv[i].size(); j++) { int num = lv[i][j]; if (A[num] % 2 == 1 || done[num] == 1) { continue; } ans.push_back(num); done[num] = 1; for (int k = 0; k < v[num].size(); k++) { int y = v[num][k]; A[y] -= 1; if (A[y] % 2 == 0 && A[y] != 0) { lv[i + 1].push_back(y); } imap[make_pair(num, y)] = 1; imap[make_pair(y, num)] = 1; } } } if (!checkis(root, 0)) { return 1; } return 0; } void solve(int root) { dfs(root, 0, 0); if (check(root)) { cout << "YES" << endl; for (int i = 0; i < ans.size(); i++) { cout << ans[i] << " "; } for (int i = 1; i <= n; i++) { if (done[i] == 0) { cout << i << " "; } } cout << endl; } else { cout << "NO" << endl; } } int main() { scanf("%d", &n); int root; for (int i = 1; i <= n; i++) { int p; scanf("%d", &p); if (p != 0) { A[p] += 1; A[i] += 1; v[i].push_back(p); v[p].push_back(i); } else { root = i; } } int cnt = 0; for (int i = 1; i <= n; i++) { if (A[i] != 0) { if (A[i] % 2 == 0) { cnt++; } } } solve(root); }
#include <bits/stdc++.h> using namespace std; const int N = 2e5 + 10; const long long INF = 1e12; const double PI = acos(-1.0); const double eps = 1e-10; const int M = 1e9 + 9; int de[N]; vector<int> G[N]; int num[N], vis[N]; void cot(int u, int p) { num[u] = 1; for (int v : G[u]) if (v != p) { cot(v, u); num[u] += num[v]; } } void dfs(int u, int p) { for (int v : G[u]) if (v != p && !(num[v] & 1)) dfs(v, u); printf("%d ", u); for (int v : G[u]) if (v != p && (num[v] & 1)) dfs(v, u); } int main() { int n; scanf("%d", &n); for (int i = 1, j; i <= n; i++) { scanf("%d", &j); if (j) { de[i] ^= 1; de[j] ^= 1; G[i].push_back(j); G[j].push_back(i); } } bool f = n & 1; printf("%s\n", f ? "YES" : "NO"); if (f) { cot(1, 0); dfs(1, 0); } return 0; }
#include <bits/stdc++.h> using namespace std; const int maxn = 200010; struct edge { int y, next; } e[maxn << 1]; int N, root; int lin[maxn], len, deg[maxn]; bool v[maxn]; int cnt[maxn][2]; int read() { int xx = 0, ff = 1; char ch = getchar(); while (ch > '9' || ch < '0') { if (ch == '-') ff = -1; ch = getchar(); } while (ch >= '0' && ch <= '9') { xx = xx * 10 + ch - '0'; ch = getchar(); } return xx * ff; } inline void inse(int xx, int yy) { e[++len].next = lin[xx]; lin[xx] = len; e[len].y = yy; deg[xx]++; } bool dfs(int x, int f) { for (int i = lin[x]; i; i = e[i].next) if (e[i].y != f) cnt[x][dfs(e[i].y, x)]++; if ((deg[x] - cnt[x][1]) % 2 == 0) v[x] = 1; else v[x] = 0; return v[x]; } void print(int x, int f) { for (int i = lin[x]; i; i = e[i].next) if (e[i].y != f) if (v[e[i].y]) print(e[i].y, x); printf("%d\n", x); for (int i = lin[x]; i; i = e[i].next) if (e[i].y != f) if (!v[e[i].y]) print(e[i].y, x); } int temp; int main() { N = read(); for (int i = 1; i <= N; i++) { temp = read(); if (!temp) root = i; else inse(i, temp), inse(temp, i); } if (dfs(root, 0)) { puts("YES"); print(root, 0); } else puts("NO"); }
#include <bits/stdc++.h> using namespace std; const int maxn = 1000010; const long long mod = 1e9 + 7; const long long INF = 100000000000000LL; const double PI = acos(-1.0); typedef struct EDGE { int v; int next; } Edge; Edge edge[maxn]; int head[maxn], cnt; int deg[maxn]; int dp[maxn][2]; vector<int> g[200020]; int indeg[maxn]; void add(int u, int v) { edge[cnt].v = v; edge[cnt].next = head[u]; head[u] = cnt++; } int dfs(int u, int fa) { int sum = 0; for (int i = head[u], v; i != -1; i = edge[i].next) { v = edge[i].v; if (v == fa) continue; dfs(v, u); sum += dp[v][0]; } if ((deg[u] - sum) % 2 == 0) { if (fa == 0) return 1; dp[u][0] = 1, indeg[fa]++, g[u].push_back(fa); } else { if (fa == 0) return 0; dp[u][1] = 1, indeg[u]++, g[fa].push_back(u); } return 1; } int solve() { memset(dp, 0, sizeof(dp)); memset(deg, 0, sizeof(deg)); memset(head, -1, sizeof(head)); memset(indeg, 0, sizeof(indeg)); cnt = 0; int n; cin >> n; for (int i = 1, u, v; i <= n; i++) { u = i; scanf("%d", &v); if (!v) continue; add(u, v); add(v, u); deg[u]++; deg[v]++; } if (!dfs(1, 0)) cout << "NO" << endl; else { queue<int> q; cout << "YES" << endl; for (int i = 1; i <= n; i++) { if (!indeg[i]) q.push(i); } while (!q.empty()) { int u = q.front(); q.pop(); cout << u << endl; for (int i = 0; i < g[u].size(); i++) { indeg[g[u][i]]--; if (indeg[g[u][i]] == 0) q.push(g[u][i]); } } } return 0; } int main() { long long t = 1e18; while (t--) { if (!solve()) break; } int mark_EOF; if (scanf("%d", &mark_EOF) == EOF) return 0; return 0; }
#include <bits/stdc++.h> using namespace std; using ll = long long; using ld = long double; const int N = 200100; vector<int> g[N]; int n, deg[N], tin[N]; int timer; void dfs(int u = 1, int par = 0) { tin[u] = ++timer; for (auto& v : g[u]) if (v != par) { dfs(v, u); } } int main() { ios::sync_with_stdio(false); cin.tie(0); cout.tie(0); srand(time(0)); int root; cin >> n; for (int i = 1; i <= n; i++) { int p; cin >> p; if (p != 0) { g[p].emplace_back(i); g[i].emplace_back(p); } else root = i; } timer = 0; dfs(root); set<pair<int, int>> x[2]; for (int i = 1; i <= n; i++) { deg[i] = g[i].size(); x[deg[i] % 2].emplace(-tin[i], i); } if (x[0].size() % 2 == 0) { cout << "NO" << endl; return 0; } cout << "YES" << '\n'; while (x[0].size() > 0) { int u = x[0].begin()->second; x[0].erase(x[0].begin()); cout << u << '\n'; for (auto& v : g[u]) { if (deg[v] == 0) continue; x[deg[v] % 2].erase({-tin[v], v}); deg[v]--; x[deg[v] % 2].emplace(-tin[v], v); } deg[u] = 0; } return 0; }
#include <bits/stdc++.h> using namespace std; int d[200003]; int dd[200003]; bool vis[200003]; int siz[200003]; int f[200003]; int ans[200003]; queue<int> q; int n, rt, sum; struct Edge { int to, next; } edge[400003]; int head[200003]; int cnt; void init() { memset(head, -1, sizeof(head)); cnt = 0; } void add(int u, int v) { edge[cnt].to = v; edge[cnt].next = head[u]; head[u] = cnt++; } void getrt(int u, int fa) { siz[u] = 1; f[u] = 0; bool flag = true; for (int i = head[u]; ~i; i = edge[i].next) { if (edge[i].to != fa && !vis[edge[i].to]) { getrt(edge[i].to, u); siz[u] += siz[edge[i].to]; f[u] = max(f[u], siz[edge[i].to]); if (siz[edge[i].to] % 2 == 0) { dd[u]++; flag = false; } } } f[u] = max(f[u], sum - siz[u]); if (sum - siz[u] != 0 && (sum - siz[u]) % 2 == 0) dd[u]++; if (d[u] % 2 == 0 && flag) q.push(u); } void solve(int u) { vis[u] = true; printf("%d\n", u); for (int i = head[u]; ~i; i = edge[i].next) { dd[edge[i].to]--; if (dd[edge[i].to] == 0) q.push(edge[i].to); } } int main() { init(); scanf("%d", &n); for (int i = 1; i <= n; i++) { int v; scanf("%d", &v); if (v) { add(v, i); add(i, v); d[v]++; d[i]++; } } if (n % 2 == 0) { printf("NO\n"); } else { f[0] = n + 1, sum = n; printf("YES\n"); getrt(1, 0); while (!q.empty()) { rt = q.front(); q.pop(); solve(rt); } } }
#include <bits/stdc++.h> using namespace std; const int MAXN = 2e5 + 5; const int INF = 1e9 + 5; int child[MAXN]; bitset<MAXN> done; vector<int> rta; vector<int> G[MAXN]; int dfs1(int st) { done[st] = true; int sum = 0; for (auto &i : G[st]) if (!done[i]) sum += dfs1(i); return child[st] = sum + 1; } void dfs2(int st) { done[st] = true; for (auto &i : G[st]) if (!done[i] && !(child[i] & 1)) dfs2(i); rta.push_back(st); for (auto &i : G[st]) if (!done[i] && (child[i] & 1)) dfs2(i); } int main() { ios::sync_with_stdio(false); cin.tie(nullptr); ; int n; cin >> n; for (int i = 0; i < int(n); i++) { int x; cin >> x; x--; if (x >= 0) G[i].push_back(x), G[x].push_back(i); } if (!(n & 1)) return cout << "NO", 0; dfs1(0); done.reset(); dfs2(0); cout << "YES\n"; for (auto &i : rta) cout << i + 1 << '\n'; return 0; }
#include <bits/stdc++.h> using namespace std; int a[200010]; int deg[200010]; vector<int> e[200010]; vector<int> ans; int d[200010], c[200010]; int dfs2(int v, int p) { if (deg[v] & 1) return 0; ans.push_back(v); d[v] = 1; for (int i = 0; i < e[v].size(); i++) { if (!d[e[v][i]]) { --deg[e[v][i]]; if (!dfs2(e[v][i], v)) return 0; } } return 1; } int dfs(int v, int p = -1) { for (int i = 0; i < e[v].size(); i++) { if (e[v][i] != p) { if (dfs(e[v][i], v) == -1) return -1; } } if (deg[v] & 1) return 0; ans.push_back(v); d[v] = 1; for (int i = 0; i < e[v].size(); i++) { if (e[v][i] == p) { deg[p]--; } else if (!d[e[v][i]]) { deg[e[v][i]]--; if (!dfs2(e[v][i], v)) return -1; } } return 1; } int main() { int n; scanf("%d", &n); for (int i = 1; i <= n; i++) { scanf("%d", &a[i]); if (!a[i]) continue; e[a[i]].push_back(i); e[i].push_back(a[i]); deg[i]++; deg[a[i]]++; } if (n % 2 == 0) { puts("NO"); return 0; } if (dfs(1) == 1) { puts("YES"); for (int i = 0; i < ans.size(); i++) { printf("%d\n", ans[i]); } } else { puts("NO"); } return 0; }
#include <bits/stdc++.h> using namespace std; const int MAXN = 220000; int vis[MAXN], ans[MAXN]; struct Edge { int u, v, nxt; } e[MAXN << 1]; int e_cnt; int head[MAXN]; void Add(int u, int v) { int id = ++e_cnt; e[id].u = u; e[id].v = v; e[id].nxt = head[u]; head[u] = id; } void DFS2(int u, int fa) { ans[++ans[0]] = u; vis[u] = true; for (int id = head[u]; ~id; id = e[id].nxt) { int v = e[id].v; if (v == fa) continue; if (!vis[v]) DFS2(v, u); } } void DFS1(int u, int fa) { int siz = (u != 1); for (int id = head[u]; ~id; id = e[id].nxt) { int v = e[id].v; if (v == fa) continue; DFS1(v, u); if (!vis[v]) siz++; } if (siz % 2 == 0) DFS2(u, fa); } int main() { memset(head, -1, sizeof(head)); int n; scanf("%d", &n); for (int i = 1; i <= n; ++i) { int j; scanf("%d", &j); if (j) Add(j, i), Add(i, j); } DFS1(1, 0); if (ans[0] == n) { printf("YES\n"); for (int i = 1; i <= ans[0]; ++i) printf("%d\n", ans[i]); } else printf("NO\n"); return 0; }
#include <bits/stdc++.h> using namespace std; long long inf = 2147483647; const long long ll = 9223372036854775807, ninf = 1000000000; const double eps = 1e-6; const long long nll = 1000000000000000000; vector<int> node[200005]; vector<int> num; int deg[200005] = {}; void dfs(int x) { for (int i = 0; i < node[x].size(); i++) { dfs(node[x][i]); } num.push_back(x); } int A[200005] = {}; int main() { int a; while (cin >> a) { int r = 1; for (int i = 1; i <= a; i++) { cin >> A[i]; deg[A[i]]++; if (A[i]) { deg[i]++; node[A[i]].push_back(i); } else { r = i; } } if (a % 2 == 0) { cout << "NO" << '\n'; continue; } dfs(r); vector<int> ans1, ans2; cout << "YES" << '\n'; for (int i = 0; i < num.size(); i++) { int now = num[i]; if (deg[now] % 2 == 0) { ans2.push_back(now); deg[A[now]]--; } else { ans1.push_back(now); } } for (int i = 0; i < ans2.size(); i++) { cout << ans2[i] << '\n'; } reverse(ans1.begin(), ans1.end()); for (int i = 0; i < ans1.size(); i++) { cout << ans1[i] << '\n'; } } return 0; }
#include <bits/stdc++.h> using namespace std; const int maxN = 2e5 + 9, MOD = 1e9 + 7; int n, dp[maxN]; vector<int> adj[maxN]; vector<int> ans; void dfs(int nd, int an) { dp[nd] = 1; for (int sn : adj[nd]) { if (sn == an) continue; dfs(sn, nd); dp[nd] ^= dp[sn]; } } void cons(int nd, int an) { for (int sn : adj[nd]) { if (sn != an && dp[sn] == 0) { cons(sn, nd); } } ans.push_back(nd + 1); for (int sn : adj[nd]) { if (sn != an && dp[sn] == 1) { cons(sn, nd); } } } int main() { ios::sync_with_stdio(false); cin.tie(0), cout.tie(0); cin >> n; for (int i = 0, inp; i < n; i++) { cin >> inp; inp--; if (inp != -1) { adj[i].push_back(inp); adj[inp].push_back(i); } } dfs(0, -1); if (dp[0] == 0) { cout << "NO\n"; return 0; } dp[0] = 0; cons(0, -1); cout << "YES\n"; for (int el : ans) cout << el << '\n'; }
#include <bits/stdc++.h> using namespace std; const long long int maxn = 5 * 100000 + 50, inf = 1e13, N = 3050; long long int par[maxn]; vector<long long int> v[maxn]; long long int dp[maxn]; vector<long long int> p; bool f[maxn]; void dfs(long long int x) { long long int y = 0; p.push_back(x); for (long long int i = 0; i < v[x].size(); i++) dfs(v[x][i]); for (long long int i = 0; i < v[x].size(); i++) { if (dp[v[x][i]] == 1) y++; } if (y % 2 == 1) { dp[x] = 2; f[x] = true; } else dp[x] = 1; } int main() { long long int n; cin >> n; long long int rishe = -1; for (long long int i = 1; i <= n; i++) { long long int c; cin >> c; if (c == 0) { rishe = i; continue; } v[c].push_back(i); par[i] = c; } for (long long int i = 1; i <= n; i++) if (v[i].size() == 0) dp[i] = 1; dfs(rishe); if (dp[rishe] == 2) { cout << "NO"; } else { cout << "YES" << endl; for (long long int i = p.size() - 1; i > -1; i--) { if (f[p[i]] == true) cout << p[i] << endl; } for (long long int i = 0; i < p.size(); i++) { if (f[p[i]] == true) continue; cout << p[i] << endl; } } return 0; }
#include <bits/stdc++.h> using namespace std; const int MAXN = 2e5 + 7; int n, tim, tmp, cnt[MAXN]; int f[MAXN], vis[MAXN], rem[MAXN]; struct node { int h, num; friend bool operator<(node xx, node yy) { return xx.h < yy.h; } } a[MAXN]; priority_queue<node> q; queue<int> prin; vector<int> v[MAXN]; void dfs(int x, int h) { rem[x] = 1; int k = v[x].size(); for (int i = 0; i < k; i++) { if (rem[v[x][i]]) continue; dfs(v[x][i], h + 1); } a[x].h = h; } int main() { scanf("%d", &n); for (int i = 1; i <= n; i++) { scanf("%d", &tmp); v[tmp].push_back(i); if (tmp) v[i].push_back(tmp), cnt[i]++; cnt[tmp]++; a[i].num = i; } if (!(n & 1)) { printf("NO"); return 0; } dfs(1, 1); for (int i = 1; i <= n; i++) { if (cnt[i] & 1) continue; q.push(a[i]); } while (!q.empty()) { node tem = q.top(); q.pop(); if ((cnt[tem.num] & 1) || vis[tem.num]) continue; vis[tem.num] = true; prin.push(tem.num); int k = v[tem.num].size(); for (int i = 0; i < k; i++) { if (vis[v[tem.num][i]]) continue; cnt[v[tem.num][i]]--; if (cnt[v[tem.num][i]] & 1) continue; q.push(a[v[tem.num][i]]); } } printf("YES\n"); while (!prin.empty()) { printf("%d\n", prin.front()); prin.pop(); } }
#include <bits/stdc++.h> using namespace std; const int N = 1e6 + 10, NX = 1e9 + 7; int n, m, r, t, a, b, A[N], D[N], M[N]; set<int> V[N]; set<pair<int, int> > S; void DFS(int v, int p) { int c = 0; for (auto X : V[v]) { if (X == p) continue; DFS(X, v); c += !M[X]; } if (c & 1) M[v] = 1, c++; D[v] -= c; } int main() { scanf("%d", &n); for (int i = 1; i <= n; i++) { scanf("%d", &r); if (r) V[i].insert(r), V[r].insert(i); } if (n % 2 == 0) return !printf("NO"); for (int i = 1; i <= n; i++) D[i] = V[i].size(); printf("YES\n"); DFS(1, 0); for (int i = 1; i <= n; i++) S.insert({D[i], i}); while (S.size()) { auto X = *S.begin(); S.erase(S.begin()); for (auto v : V[X.second]) { V[v].erase(X.second); S.erase({D[v], v}); D[v]--; S.insert({D[v], v}); } V[X.second].clear(); printf("%d\n", X.second); } return (0); }
#include <bits/stdc++.h> using namespace std; int F() { char ch; int x, a; while (ch = getchar(), (ch < '0' || ch > '9') && ch != '-') ; if (ch == '-') ch = getchar(), a = -1; else a = 1; x = ch - '0'; while (ch = getchar(), ch >= '0' && ch <= '9') x = (x << 1) + (x << 3) + ch - '0'; return a * x; } int n; int fa[200010], in[200010]; set<int> edge[200010]; int deg(int u) { return in[fa[u]] + ((int)(edge[u]).size()); } int stk[200010], cnt; int del[200010], tp; void clear(int u) { stk[++cnt] = u; in[u] = 0; if (fa[u]) del[++tp] = u; for (auto v : edge[u]) clear(v); } void dfs(int u) { while (tp) { int x = del[tp--]; if (fa[x]) edge[fa[x]].erase(x); } for (auto v : edge[u]) dfs(v); while (tp) { int x = del[tp--]; if (fa[x]) edge[fa[x]].erase(x); } if (!in[u]) return; if (deg(u) & 1) return; clear(u); } int main() { ((n) = F()); for (int i = 1; i <= n; ++i) { ((fa[i]) = F()); in[i] = 1; if (fa[i]) edge[fa[i]].insert(i); } for (int i = 1; i <= n; ++i) if (!fa[i]) dfs(i); if (cnt != n) return puts("NO"), 0; puts("YES"); for (int i = 1; i <= n; ++i) printf("%d\n", stk[i]); return 0; }
#include <bits/stdc++.h> using namespace std; vector<long long> tree[200009], ans; long long sz[200009]; void dfs(long long u, long long p) { for (long long i = 0; i < tree[u].size(); i++) { long long nd = tree[u][i]; if (nd == p) continue; dfs(nd, u); } if (sz[u] % 2 != 0 || sz[u] == 0) return; ans.push_back(u); sz[u] = 0; for (long long i = 0; i < tree[u].size(); i++) { long long nd = tree[u][i]; sz[nd]--; if (sz[nd] == 0) ans.push_back(nd); } } void dfs2(long long u, long long p) { if (sz[u] % 2 == 0 && sz[u] != 0) { ans.push_back(u); sz[u] = 0; for (long long i = 0; i < tree[u].size(); i++) { long long nd = tree[u][i]; sz[nd]--; if (sz[nd] == 0) ans.push_back(nd); } } for (long long i = 0; i < tree[u].size(); i++) { long long nd = tree[u][i]; if (nd == p) continue; dfs2(nd, u); } } int main() { long long n; cin >> n; for (long long i = 1; i <= n; i++) { long long u; scanf("%lld", &u); if (u == 0) continue; tree[u].push_back(i); tree[i].push_back(u); } if (n == 1) { cout << "YES" << endl << 1 << endl; return 0; } for (long long i = 1; i <= n; i++) sz[i] = tree[i].size(); dfs(1, 0); dfs2(1, 0); if (ans.size() != n) { cout << "NO" << endl; return 0; } cout << "YES" << endl; for (long long i = 0; i < ans.size(); i++) printf("%lld\n", ans[i]); return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 2e5 + 20; int n; struct edge { int y, nxt; } e[N << 1]; int lin[N], len = 1; int degree[N], ans[N], pos; bool mark[N]; inline int read() { int s = 0, f = 1; char ch; for (; ch < '0' || ch > '9'; ch = getchar()) if (ch == '-') f = -1; for (; ch >= '0' && ch <= '9'; ch = getchar()) s = (s << 1) + (s << 3) + ch - '0'; return s * f; } inline void add(int xx, int yy) { e[++len] = (edge){yy, lin[xx]}; lin[xx] = len; } inline void dfs(int x, int fa, bool flag) { if (!flag) { for (int i = lin[x]; i; i = e[i].nxt) { int y = e[i].y; if (y == fa) continue; if (!mark[y]) dfs(y, x, 0); } } if (!(degree[x] % 2)) { degree[x] = 0; ans[++pos] = x; mark[x] = 1; for (int i = lin[x]; i; i = e[i].nxt) { int y = e[i].y; --degree[y]; if (y == fa) continue; if (!mark[y]) dfs(y, x, 1); } } } int main() { n = read(); for (int i = 1; i <= n; ++i) { int x = read(); if (x) { add(i, x); add(x, i); degree[i]++; degree[x]++; } } dfs(1, 0, 0); if (pos == n) { puts("YES"); for (int i = 1; i <= n; ++i) printf("%d\n", ans[i]); } else puts("NO"); return 0; }
#include <bits/stdc++.h> using namespace std; using ll = long long; const ll MOD = 1e9 + 7; const int N = 2 * (int)1e5; vector<int> conns[N]; int siz[N]; int dfs(int i, int p) { siz[i] = 1; for (auto t : conns[i]) { if (t != p) siz[i] += dfs(t, i); } return siz[i]; } void solve(int i, int p, vector<int>& res) { for (auto t : conns[i]) { if (t != p && siz[t] % 2 == 0) solve(t, i, res); } res.push_back(i); for (auto t : conns[i]) { if (t != p && siz[t] % 2 == 1) solve(t, i, res); } } int main() { ios_base::sync_with_stdio(false); cin.tie(0); int n; cin >> n; for (int i = 0; i < n; ++i) { int p; cin >> p; --p; if (p != -1) { conns[i].push_back(p); conns[p].push_back(i); } } if (n % 2 == 0) { cout << "NO\n"; } else { cout << "YES\n"; vector<int> res; dfs(0, 0); solve(0, 0, res); for (auto i : res) cout << i + 1 << '\n'; } }
#include <bits/stdc++.h> using namespace std; class Tree { int n; public: int *deg, *p; bool *EvenDeg, *erased; vector<int> *adj; Tree(int n); void AddEdge(int u, int v); void compEvenDeg(int x); void Dfs(int x); }; int root; Tree::Tree(int n) { this->n = n; deg = new int[n]; p = new int[n]; EvenDeg = new bool[n]; erased = new bool[n]; adj = new vector<int>[n]; for (int i = 0; i < n; ++i) erased[i] = deg[i] = EvenDeg[i] = 0; } void Tree::AddEdge(int u, int v) { adj[u].push_back(v); ++deg[u]; ++deg[v]; p[v] = u; } void Tree::compEvenDeg(int u) { EvenDeg[u] = false; for (int v : adj[u]) { compEvenDeg(v); EvenDeg[u] |= (EvenDeg[v] | !(deg[v] % 2)); } } void Tree::Dfs(int u) { bool ok = false; if ((deg[u] % 2 == 0) && !EvenDeg[u]) { erased[u] = true; ok = true; printf("%d\n", u + 1); if (u != root) --deg[p[u]]; } for (int v : adj[u]) { if (erased[u]) --deg[v]; if (!erased[v] && ((deg[v] % 2 == 0) || EvenDeg[v])) Dfs(v); } if (!erased[u] && (deg[u] % 2 == 0)) { erased[u] = true; printf("%d\n", u + 1); if (u != root) --deg[p[u]]; } for (int v : adj[u]) { if (erased[u] && !ok) --deg[v]; if (!erased[v]) Dfs(v); } } int deg[200002]; int main() { int n; scanf("%d", &n); if (n % 2) { printf("YES\n"); Tree T(n); for (int u = 0, v; u < n; ++u) { scanf("%d", &v); --v; if (v == -1) root = u; else T.AddEdge(v, u); } T.compEvenDeg(root); T.Dfs(root); } else printf("NO\n"); return 0; }
#include <bits/stdc++.h> using namespace std; bool vowel(char che) { if (che == 'A' || che == 'E' || che == 'I' || che == 'O' || che == 'U' || che == 'Y') return true; else return false; } const int N = 2e5 + 5; const int mod = 1e9 + 7; long long a[N], b[N], c[N], d, dis, dp[N], dg[N], pd[N]; pair<long long, long long> p; vector<long long> vt[N], vm[N], vs; stack<long long> st; string s, s1; char o; bool mark[N], mark1[N], h; long long n1 = 0; void dfs(long long v, long long k, long long f) { pd[v] = k; vm[f].push_back(v); n1 = max(n1, f); f += 1; for (int i = 0; i < vt[v].size(); i++) { if (vt[v][i] != k) dfs(vt[v][i], v, f); } } void dst(long long v, long long k) { mark1[v] = true; dg[k]--; vs.push_back(v); for (int i = 0; i < vt[v].size(); i++) { if (vt[v][i] != k && !mark1[vt[v][i]]) dst(vt[v][i], v); } } int main() { long long t = 0, n, m = 0, k = 0, f = 0, sum = 0, ans = 0; cin >> n; for (int i = 1; i <= n; i++) { cin >> m; if (m) { vt[i].push_back(m); vt[m].push_back(i); } } for (int i = 1; i <= n; i++) { dg[i] = vt[i].size(); } if (n % 2 == 0) cout << "NO\n"; else { cout << "YES\n"; dfs(1, 0, 0); for (int i = n1; i >= 0; i--) { for (int j = 0; j < vm[i].size(); j++) { m = vm[i][j]; if (dg[m] % 2 == 0) dst(m, pd[m]); } } for (auto x : vs) { cout << x << endl; } } }
#include <bits/stdc++.h> using namespace std; int myRnd() { return abs(((rand() << 15) ^ rand())); } int myRnd(int L, int R) { return abs(((rand() << 15) ^ rand())) % (R - L + 1) + L; } void Parr(int *arr, int L, int R) { for (int i = L; R >= i; i++) { printf("%d%c", arr[i], " \n"[i == R]); } } void Pvec(vector<int> v) { for (int i = 0; ((int)(v).size()) > i; i++) { printf("%d%c", v[i], " \n"[i == ((int)(v).size()) - 1]); } } void Sarr(int *arr, int L, int R) { for (int i = L; R >= i; i++) { scanf("%d", &(arr[i])); ; } } const int N = 2e5 + 6; const int INF = 0x3f3f3f3f; const int mod = 1000000000 + 7; int a[N]; vector<int> G[N]; bool dp[2][N]; void dfs(int now, int par) { vector<int> child; for (int i : G[now]) { if (i != par) { child.push_back(i); dfs(i, now); } } if (((int)(child).size()) == 0) { dp[1][now] = true; dp[0][now] = false; } else { int _1L = 0, _1R = 0; for (int i : child) { if (dp[0][i] && dp[1][i]) { _1R++; } else if (dp[1][i]) { _1L++; _1R++; } } if (_1R == _1L) { if (_1L % 2 == 0) { dp[1][now] = true; dp[0][now] = false; } else { dp[0][now] = true; dp[1][now] = false; } } else { dp[0][now] = dp[1][now] = true; } } } vector<int> ans[2][N]; int lc[N], rc[N]; int head[2][N], tail[2][N]; void dfs2(int now, int par) { vector<int> child; for (int i : G[now]) { if (i != par) { child.push_back(i); dfs2(i, now); } } if (((int)(child).size()) == 0) { head[1][now] = tail[1][now] = now; } else { int _1L = 0, _1R = 0; for (int i : child) { if (dp[0][i] && dp[1][i]) { _1R++; } else if (dp[1][i]) { _1L++; _1R++; } } if (_1R == _1L) { if (_1L % 2 == 0) { int last = -1; for (int i : child) { if (!dp[1][i]) { if (last == -1) { head[1][now] = head[0][i]; last = tail[0][i]; } else { int _ = head[0][i]; rc[last] = _; lc[_] = last; last = tail[0][i]; } } } if (last == -1) { head[1][now] = now; last = now; } else { int _ = now; rc[last] = now; lc[_] = last; last = now; } for (int i : child) { if (dp[1][i]) { int _ = head[1][i]; rc[last] = _; lc[_] = last; last = tail[1][i]; } } tail[1][now] = last; } else { int last = -1; for (int i : child) { if (!dp[1][i]) { if (last == -1) { head[0][now] = head[0][i]; last = tail[0][i]; } else { int _ = head[0][i]; rc[last] = _; lc[_] = last; last = tail[0][i]; } } } if (last == -1) { head[0][now] = now; last = now; } else { int _ = now; rc[last] = now; lc[_] = last; last = now; } for (int i : child) { if (dp[1][i]) { int _ = head[1][i]; rc[last] = _; lc[_] = last; last = tail[1][i]; } } tail[0][now] = last; } } else { vector<int> child1, child2; vector<int> choice; for (int i : child) { if (dp[0][i] && dp[1][i]) { choice.push_back(i); } else if (dp[1][i]) { child1.push_back(i); child2.push_back(i); } } if (((int)(child1).size()) % 2 == 1) { child1.push_back(choice[0]); } else if (((int)(child1).size()) % 2 == 0) { child2.push_back(choice[0]); } int last = -1; for (int i : child2) { if (!dp[1][i]) { if (last == -1) { head[1][now] = head[0][i]; last = tail[0][i]; } else { int _ = head[0][i]; rc[last] = _; lc[_] = last; last = tail[0][i]; } } } if (last == -1) { head[1][now] = now; last = now; } else { int _ = now; rc[last] = now; lc[_] = last; last = now; } for (int i : child2) { if (dp[1][i]) { int _ = head[1][i]; rc[last] = _; lc[_] = last; last = tail[1][i]; } } tail[1][now] = last; last = -1; for (int i : child1) { if (!dp[1][i]) { if (last == -1) { head[0][now] = head[0][i]; last = tail[0][i]; } else { int _ = head[0][i]; rc[last] = _; lc[_] = last; last = tail[0][i]; } } } if (last == -1) { head[0][now] = now; last = now; } else { int _ = now; rc[last] = now; lc[_] = last; last = now; } for (int i : child1) { if (dp[1][i]) { int _ = head[1][i]; rc[last] = _; lc[_] = last; last = tail[1][i]; } } tail[0][now] = last; } } } int main() { srand(time(NULL)); int n; scanf("%d", &(n)); ; for (int i = 1; (n) >= i; ++i) { int p; scanf("%d", &(p)); ; if (p) { G[i].push_back(p); G[p].push_back(i); } } dfs(1, 1); if (!dp[1][1]) { puts("NO"); return 0; } puts("YES"); for (int i = 1; n >= i; i++) { lc[i] = rc[i] = i; } dfs2(1, 1); int start = -1; for (int i = 1; n >= i; i++) { if (lc[i] == i) { start = i; break; } } assert(start != -1); for (int i = 1; n >= i; i++) { printf("%d\n", start); start = rc[start]; } }
#include <bits/stdc++.h> const int maxn = 2e5 + 10; const int maxm = 2e5 + 10; const int mod = 1e9 + 7; const int inf = 0x3f3f3f3f; const double eps = 1e-7; using namespace std; vector<int> G[maxn]; int rt = 1; int n, p, sz[maxn]; void dfs(int u, int fa) { sz[u]++; for (auto v : G[u]) { if (v == fa) continue; dfs(v, u); sz[u] += sz[v]; } } void dfs1(int u, int fa) { for (auto v : G[u]) { if (v == fa) continue; if (sz[v] % 2 == 0) dfs1(v, u); } cout << u << endl; for (auto v : G[u]) { if (v == fa) continue; if (sz[v] & 1) dfs1(v, u); } } int main() { ios::sync_with_stdio(false); cin.tie(0); cout.tie(0); cin >> n; for (int i = 1; i <= n; i++) { cin >> p; if (p == 0) rt = i; else { G[i].push_back(p); G[p].push_back(i); } } if (n & 1) { cout << "YES" << endl; dfs(rt, 0); dfs1(rt, 0); } else cout << "NO"; return ~~(0 - 0); }
#include <bits/stdc++.h> using namespace std; const int N = 200005; int n; int sz[N]; int par[N]; int cnt[N]; bool visit[N]; vector<pair<int, int> > G[N]; void dfs(int u) { sz[u] = 1; for (auto v : G[u]) if (par[u] != v.first) { par[v.first] = u, dfs(v.first), sz[u] += sz[v.first]; } } int main() { ios::sync_with_stdio(false); cin >> n; for (int i = 1; i <= n; ++i) { int p; cin >> p; if (p) G[p].push_back({i, 0}), G[i].push_back({p, 0}); } if (n % 2 == 0) { cout << "NO"; return 0; } dfs(1); for (int i = 1; i <= n; ++i) { sort(G[i].begin(), G[i].end()); for (auto &j : G[i]) { if (par[i] == j.first) { j.second = (n - sz[i]) & 1; } else { j.second = sz[j.first] & 1; } cnt[i] += !j.second; } } queue<int> qu; for (int i = 1; i <= n; ++i) { if (!cnt[i]) qu.push(i), visit[i] = 1; } cout << "YES\n"; while (qu.size()) { int u = qu.front(); qu.pop(); cout << u << '\n'; for (auto v : G[u]) { auto i = lower_bound(G[v.first].begin(), G[v.first].end(), make_pair(u, 0)); cnt[v.first] -= !(i->second); if (!cnt[v.first] && !visit[v.first]) { qu.push(v.first), visit[v.first] = 1; } } } }
#include <bits/stdc++.h> using namespace std; const int N = 2e5 + 7; vector<int> g[N]; int sz[N]; bool vis[N]; int lvl[N]; void dfs(int node, int par) { for (int nxt : g[node]) { if (nxt == par) continue; lvl[nxt] = lvl[node] + 1; dfs(nxt, node); } } int main() { ios_base::sync_with_stdio(false); cin.tie(NULL); int n; cin >> n; int root; for (int i = 1; i <= n; i++) { int x; cin >> x; if (!x) { root = i; continue; } g[x].push_back(i); g[i].push_back(x); } memset(sz, 0, sizeof(sz)); memset(vis, 0, sizeof(vis)); memset(lvl, 0, sizeof(lvl)); dfs(root, 0); set<pair<int, int> > ss; for (int i = 1; i <= n; i++) { sz[i] = g[i].size(); if (sz[i] % 2 == 0) { ss.insert(make_pair(lvl[i], i)); } } vector<int> vec; while (ss.size()) { pair<int, int> p = *ss.rbegin(); int node = p.second; vec.push_back(node); vis[node] = true; ss.erase(prev(ss.end())); for (int nxt : g[node]) { if (vis[nxt]) continue; sz[nxt]--; if (sz[nxt] & 1) { ss.erase(make_pair(lvl[nxt], nxt)); } else ss.insert(make_pair(lvl[nxt], nxt)); } } if (vec.size() != n) { cout << "NO\n"; return 0; } cout << "YES\n"; for (int x : vec) { cout << x << endl; } return 0; }
#include <bits/stdc++.h> using namespace std; const int maxn = 2e5 + 10; int root; int N, Fa[maxn], degree[maxn], vis[maxn] = {}; vector<int> v[maxn << 1], ans; stack<int> s; inline long long read() { long long s = 0, f = 1; char ch; for (; ch < '0' || ch > '9'; ch = getchar()) if (ch == '-') f = -1; for (; ch >= '0' && ch <= '9'; ch = getchar()) s = (s << 3) + (s << 1) + ch - '0'; return s * f; } void dfs(int x, int fa) { s.push(x); for (int i = 0; i < v[x].size(); ++i) { if (v[x][i] == fa) continue; dfs(v[x][i], x); } } void Dfs(int x) { ans.push_back(x); vis[x] = 1; for (int i = 0; i < v[x].size(); ++i) { --degree[v[x][i]]; if (v[x][i] == Fa[x] || vis[v[x][i]]) continue; if ((degree[v[x][i]] & 1) == 0) Dfs(v[x][i]); } } int main() { N = read(); for (int i = 1; i <= N; ++i) { Fa[i] = read(); if (Fa[i]) v[i].push_back(Fa[i]), v[Fa[i]].push_back(i), ++degree[Fa[i]], ++degree[i]; else root = i; } dfs(root, 0); while (!s.empty()) { int x = s.top(); s.pop(); if (!(degree[x] & 1)) Dfs(x); } if (ans.size() == N) { puts("YES"); for (int i = 0; i < ans.size(); ++i) printf("%d\n", ans[i]); } else puts("NO"); }
#include <bits/stdc++.h> using namespace std; const int ms = 1e6; vector<int> adj[ms]; int root, n, sz[ms]; int precalc(int i) { sz[i] = 1; for (auto v : adj[i]) { sz[i] += precalc(v); } return sz[i]; } void dfs(int i) { for (auto v : adj[i]) if (!(sz[v] & 1)) dfs(v); cout << i << " "; for (auto v : adj[i]) if (sz[v] & 1) dfs(v); } int main() { ios::sync_with_stdio(0), cin.tie(0); int n, x; cin >> n; if (!(n & 1)) { cout << "NO"; return 0; } cout << "YES" << endl; for (int i = 1; i <= n; i++) { cin >> x; if (x) adj[x].push_back(i); else root = i; } precalc(root); dfs(root); return 0; }
#include <bits/stdc++.h> using namespace std; vector<int> G[200100]; int n, dp[200100], anses[200100], tp; void dfs(int u, int f) { for (auto p : G[u]) if (p != f) dfs(p, u); if (G[u].size() == 1) return (void)(dp[u] = 0); int cnt = 0; for (auto p : G[u]) if (p != f && dp[p] == 0) cnt++; dp[u] = cnt & 1; if (dp[u]) anses[++tp] = u; if (f == 0 && dp[u] == 1) { printf("NO\n"); exit(0); } } void dfs2(int u, int f) { if (!dp[u]) anses[++tp] = u; for (auto p : G[u]) if (p != f) dfs2(p, u); } int main() { scanf("%d", &n); if (n == 1) return printf("YES\n1"), 0; if (n == 2) return printf("NO"), 0; for (int i = 1, u; i <= n; ++i) { scanf("%d", &u); if (u) G[u].push_back(i), G[i].push_back(u); } int rt = 0; for (int i = 1; i <= n; ++i) if (G[i].size() > 1) rt = i; dfs(rt, 0), dfs2(rt, 0); puts("YES"); for (int i = 1; i <= n; ++i) printf("%d\n", anses[i]); }
#include <bits/stdc++.h> using namespace std; vector<vector<int>> vt; vector<int> dap; int degree[200010]; int visited[200010]; int n; void solve(int here) { visited[here] = 1; dap.push_back(here); for (int i = 0; i < vt[here].size(); i++) { int next = vt[here][i]; if (!visited[next]) solve(next); } } void dfs(int here, int par) { for (int i = 0; i < vt[here].size(); i++) { dfs(vt[here][i], here); } if (degree[here] % 2 == 0) { degree[par]--; solve(here); } } int main() { scanf("%d", &n); vt.resize(n + 1); int ch = 0; for (int i = 1; i <= n; i++) { int q; scanf("%d", &q); if (q == 0) { ch = i; continue; } vt[q].push_back(i); degree[q]++; degree[i]++; } if (n % 2 == 0) { puts("NO"); } else { puts("YES"); dfs(ch, 0); for (int i = 0; i < dap.size(); i++) printf("%d\n", dap[i]); } }
#include <bits/stdc++.h> using namespace std; vector<long long int> v[200005]; long long int degree[200005], vis2[200005]; deque<long long int> dq2; void DFS2(long long int x) { if (vis2[x]) { return; } vis2[x] = 1; long long int i; dq2.push_back(x); for (i = 0; i < v[x].size(); i++) { DFS2(v[x][i]); } } void DFS1(long long int x, long long int par) { long long int i; for (i = 0; i < v[x].size(); i++) { DFS1(v[x][i], x); } if (!(degree[x] % 2)) { DFS2(x); degree[par]--; } } int main(void) { long long int i, n, x, size = 0, lol; cin >> n; for (i = 1; i <= n; i++) { cin >> x; if (x != 0) { v[x].push_back(i); degree[i]++; degree[x]++; } else { lol = i; } } if (!(n % 2)) { cout << "NO\n"; return 0; } DFS1(lol, 200002); cout << "YES\n"; while (!dq2.empty()) { cout << dq2.front() << "\n"; dq2.pop_front(); } return 0; }
#include <bits/stdc++.h> using namespace std; struct X { int id; int sz; int dep; X() {} X(int id, int sz, int dep) : id(id), sz(sz), dep(dep) {} bool operator<(const X x) const { if (sz % 2 == 0 && x.sz % 2 != 0) return 1; if (sz % 2 != 0 && x.sz % 2 == 0) return 0; if (dep > x.dep) return 1; if (dep < x.dep) return 0; return id < x.id; } }; set<X> st; unordered_set<int> v[200005]; vector<int> ans; int dep[200005]; void dfs(int now, int fa) { dep[now] = dep[fa] + 1; for (auto x : v[now]) { if (x == fa) continue; dfs(x, now); } } int main(void) { int n; scanf("%d", &n); int i; for (i = 1; i <= n; i++) { int p; scanf("%d", &p); if (p != 0) { v[i].insert(p); v[p].insert(i); } } dfs(1, 1); for (i = 1; i <= n; i++) { st.insert(X(i, v[i].size(), dep[i])); } while (st.size()) { X b = *st.begin(); if (b.sz % 2 != 0) break; ans.push_back(b.id); st.erase(st.begin()); for (auto nxt : v[b.id]) { st.erase(X(nxt, v[nxt].size(), dep[nxt])); v[nxt].erase(b.id); st.insert(X(nxt, v[nxt].size(), dep[nxt])); } v[b.id].clear(); } if (st.size() == 0) { printf("YES\n"); for (auto g : ans) printf("%d\n", g); } else printf("NO\n"); return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 2e5, M = 4e5; int head[N + 10], ver[M + 10], nxt[M + 10], tot, sz[N + 10]; void add(int x, int y) { ver[++tot] = y; nxt[tot] = head[x]; head[x] = tot; ver[++tot] = x; nxt[tot] = head[y]; head[y] = tot; } void dfs1(int x, int fa) { sz[x] = 1; for (int i = head[x]; i; i = nxt[i]) { int y = ver[i]; if (y == fa) continue; dfs1(y, x); sz[x] += sz[y]; } } int ans[N + 10], cnt = 0; void dfs2(int x, int fa) { vector<int> odd, even; for (int i = head[x]; i; i = nxt[i]) { int y = ver[i]; if (y == fa) continue; if (sz[y] & 1) odd.push_back(y); else even.push_back(y); } for (int i = 0; i < even.size(); i++) { int y = even[i]; dfs2(y, x); } ans[++cnt] = x; for (int i = 0; i < odd.size(); i++) { int y = odd[i]; dfs2(y, x); } } int main() { int n; scanf("%d", &n); for (int i = 1; i <= n; i++) { int x; scanf("%d", &x); if (!x) continue; add(i, x); } dfs1(1, -1); if (!(sz[1] & 1)) printf("NO"); else { printf("YES\n"); dfs2(1, -1); for (int i = 1; i <= cnt; i++) printf("%d\n", ans[i]); } return 0; }
#include <bits/stdc++.h> using namespace std; int n; int p[200002]; vector<int> ke[200002]; bool mark[200002]; bool dfs(int u, int p) { int cnt = 0; for (int v : ke[u]) { if (v == p) continue; if (dfs(v, u)) cnt++; } if (cnt % 2 == 0) { return mark[u] = true; } return mark[u] = false; } void dfs2(int u, int p) { for (int v : ke[u]) { if (v == p) continue; if (!mark[v]) { dfs2(v, u); } } cout << u << "\n"; for (int v : ke[u]) { if (v == p) continue; if (mark[v]) { dfs2(v, u); } } } int main() { ios_base::sync_with_stdio(0); cin.tie(NULL); cout.tie(NULL); cin >> n; for (long long i = 1; i <= n; i++) { cin >> p[i]; if (p[i]) { ke[i].push_back(p[i]); ke[p[i]].push_back(i); } } if (dfs(1, 1)) { cout << "YES\n"; dfs2(1, 1); } else { cout << "NO"; } }
#include <bits/stdc++.h> using namespace std; const int maxn = 200005; int u[maxn], par[maxn]; bool vis[maxn]; vector<int> rode[maxn]; stack<int> P; queue<int> Q; void dfs(int v, int pre) { P.push(v); par[v] = pre; for (int i = 0; i < rode[v].size(); i++) { if (rode[v][i] == pre) continue; dfs(rode[v][i], v); } } void dfs2(int x) { Q.push(x); vis[x] = 1; for (int i = 0; i < rode[x].size(); i++) { int to = rode[x][i]; u[to]--; if (to == par[x] || vis[to]) continue; if (u[to] % 2 == 0) dfs2(to); } } int main() { int n; scanf("%d", &n); for (int i = 1; i <= n; i++) { int x; scanf("%d", &x); if (x) { rode[i].push_back(x), rode[x].push_back(i); u[i]++, u[x]++; } } dfs(1, 0); while (!P.empty()) { int x = P.top(); P.pop(); if (u[x] % 2 == 0) dfs2(x); } if (Q.size() == n) { printf("YES\n"); while (!Q.empty()) { printf("%d\n", Q.front()); Q.pop(); } } else printf("NO\n"); return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 5e5 + 50; int E, V[N], Next[N], Head[N]; bool vis[N]; void add(int a, int b) { V[E] = b; Next[E] = Head[a]; Head[a] = E++; } bool dfs(int u, int fa) { bool ans = 0; for (int i = Head[u]; i != -1; i = Next[i]) { int v = V[i]; if (v == fa) continue; vis[v] = dfs(v, u); if (!vis[v]) ans = !ans; } return ans; } void print(int u, int fa) { for (int i = Head[u]; i != -1; i = Next[i]) { int v = V[i]; if (v == fa) continue; if (vis[v]) print(v, u); } printf("%d\n", u); for (int i = Head[u]; i != -1; i = Next[i]) { int v = V[i]; if (v == fa) continue; if (!vis[v]) print(v, u); } } int main() { int n, rt; memset(Head, -1, sizeof(Head)); scanf("%d", &n); for (int i = 1; i <= n; i++) { int p; scanf("%d", &p); if (p == 0) { rt = i; continue; } add(i, p), add(p, i); } if (!dfs(rt, -1)) { puts("YES"); print(rt, -1); } else puts("NO"); }
#include <bits/stdc++.h> #pragma warning(disable : 4996) using namespace std; vector<set<int>> graph; vector<bool> seen; vector<bool> removed; vector<int> removedOrder; void dfs(int from) { seen[from] = true; set<int> edges = graph[from]; for (auto to : edges) { if (!seen[to] && !removed[from]) dfs(to); } const int deg = graph[from].size(); if (deg % 2 == 0) { removed[from] = true; removedOrder.push_back(from); for (auto to : graph[from]) graph[to].erase(from); graph[from].clear(); } } int main() { ios_base::sync_with_stdio(false); cin.tie(0); int n; cin >> n; graph.assign(n, set<int>()); for (int i = 0; i < n; ++i) { int p; cin >> p; if (p) { --p; graph[i].insert(p); graph[p].insert(i); } } removed.assign(n, false); for (int i = 0; i < n; ++i) { if (!removed[i]) { seen.assign(n, false); dfs(i); } } if (removedOrder.size() == n) { cout << "YES\n"; for (auto v : removedOrder) cout << v + 1 << '\n'; } else { cout << "NO\n"; } return 0; }
#include <bits/stdc++.h> using namespace std; const int P = 1e9 + 9; const int MAXN = 200200; vector<int> g[MAXN]; int del[MAXN]; int deg[MAXN]; void dfs1(int v, int p = -1) { del[v] = 1; cout << v + 1 << endl; for (int u : g[v]) { if (u == p) { continue; } if (!del[u]) { dfs1(u, v); } } } void dfs(int v, int p = -1) { for (int u : g[v]) { if (u == p) { continue; } dfs(u, v); } int deg = (int)(g[v]).size(); for (int u : g[v]) { if (u == p) { continue; } if (del[u]) { --deg; } } if (deg % 2 == 0) { dfs1(v, p); } } int main() { ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0); int n; cin >> n; vector<int> p(n); for (int i = 0; i < n; ++i) { cin >> p[i]; --p[i]; if (p[i] != -1) { g[p[i]].push_back(i); g[i].push_back(p[i]); } } if (n == 1) { cout << "YES" << endl; cout << 1 << endl; return 0; } int e = 0; for (int i = 0; i < n; ++i) { if ((int)(g[i]).size() % 2 == 0) { ++e; } } if (e % 2 == 0) { cout << "NO" << endl; return 0; } cout << "YES" << endl; dfs(0); return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 200005; struct Gragh { int cnt, y[N * 2], nxt[N * 2], fst[N]; void clear() { cnt = 0; memset(fst, 0, sizeof fst); } void add(int a, int b) { y[++cnt] = b, nxt[cnt] = fst[a], fst[a] = cnt; } } g; int n, dp[N]; vector<int> sted[N]; bool spec_cmp(int a, int b) { return dp[a] < dp[b]; } void solve(int x, int pre) { int cnt = 1; sted[x].clear(); for (int i = g.fst[x]; i; i = g.nxt[i]) if (g.y[i] != pre) { solve(g.y[i], x); cnt++; sted[x].push_back(g.y[i]); } sort(sted[x].begin(), sted[x].end(), spec_cmp); if (sted[x].size() == 0) { dp[x] = 1; return; } for (int i = 0; i < sted[x].size(); i++) { if (dp[sted[x][i]]) break; cnt--; } dp[x] = cnt & 1; } void dfs2(int x) { int i = 0; while (i < sted[x].size() && dp[sted[x][i]] == 0) dfs2(sted[x][i]), i++; printf("%d\n", x); while (i < sted[x].size()) dfs2(sted[x][i]), i++; } int main() { g.clear(); scanf("%d", &n); for (int i = 1, p; i <= n; i++) { scanf("%d", &p); if (p != 0) g.add(i, p), g.add(p, i); } solve(1, 0); if (dp[1] == 1) { puts("YES"); dfs2(1); } else puts("NO"); return 0; }
#include <bits/stdc++.h> using namespace std; const int Nmax = 1000005; int n, v[Nmax], degree[Nmax], solved[Nmax]; vector<int> L[Nmax], Depend[Nmax], Sol; void deleteNode(int node) { solved[node] = 1; Sol.push_back(node); for (auto it : L[node]) --degree[it]; } void clearNode(int node) { deleteNode(node); for (auto it : Depend[node]) clearNode(it); } void dfs(int node, int tata) { vector<int> Bad, Good; for (auto it : L[node]) { if (it == tata) continue; dfs(it, node); if (solved[it]) continue; Depend[node].push_back(it); } if (degree[node] % 2 == 0) clearNode(node); } int main() { scanf("%d", &n); int rad; for (int i = 1; i <= n; i++) { int x; scanf("%d", &x); if (x == 0) rad = i; else { L[x].push_back(i); L[i].push_back(x); degree[i]++; degree[x]++; } } dfs(rad, 0); if (Sol.size() < n) { cout << "NO\n"; return 0; } cout << "YES\n"; for (auto it : Sol) cout << it << "\n"; return 0; }
#include <bits/stdc++.h> using namespace std; vector<int> node[200005], ans; int cnt; int n, p, rt; bool vis[200005]; void dfshelper(int x) { if (vis[x]) return; vis[x] = true; ans.push_back(x); for (int i = 0; i < node[x].size(); i++) dfshelper(node[x][i]); } void dfs(int x) { int deg = 0; if (x != rt) deg++; for (int i = 0; i < node[x].size(); i++) { dfs(node[x][i]); if (!vis[node[x][i]]) deg++; } if (deg % 2 == 0) dfshelper(x); } int main() { scanf("%d", &n); memset(vis, 0, sizeof(vis)); cnt = 0; for (int i = 1; i <= n; i++) { scanf("%d", &p); if (p != 0) cnt++; node[p].push_back(i); if (p == 0) rt = i; } if (cnt % 2) { printf("NO\n"); return 0; } dfs(rt); puts("YES"); for (int i = 0; i < ans.size(); i++) printf("%d\n", ans[i]); return 0; }
#include <bits/stdc++.h> using namespace std; vector<int> edge[200000 + 5]; vector<int> sol; bool dp[200000 + 5]; bool dfs(int idx, int p = -1) { vector<int> D, ND; for (auto x : edge[idx]) if (x != p) { if (dfs(x, idx)) ND.push_back(x); else D.push_back(x); } if (ND.empty() && D.empty()) return dp[idx] = true; if (ND.size() & 1) return dp[idx] = false; return dp[idx] = true; } void backT(int idx, int p = -1) { for (auto x : edge[idx]) if (x != p) { if (!dp[x]) { backT(x, idx); } } sol.push_back(idx); for (auto x : edge[idx]) if (x != p) { if (dp[x]) { backT(x, idx); } } } int main() { int i, n, p; scanf("%d", &n); for (i = 1; i <= n; i++) { scanf("%d", &p); if (p) { edge[p].push_back(i); edge[i].push_back(p); } } if (dfs(1)) { puts("YES"); backT(1); for (auto x : sol) printf("%d\n", x); } else puts("NO"); return 0; }
#include <bits/stdc++.h> using namespace std; vector<int> g[200100]; int sz[200100], root; bool vist[200100]; void delSubtree(int u) { vist[u] = true; printf("%d\n", u); for (auto v : g[u]) if (!vist[v]) delSubtree(v); } void DFS(int u, int p) { int degree = 0; for (auto v : g[u]) { if (v == p) continue; DFS(v, u); if (!vist[v]) degree++; } if (u != root) degree++; if (!(degree & 1)) delSubtree(u); } int main() { int n, u; scanf("%d", &n); for (int v = 1; v <= n; v++) { scanf("%d", &u); if (u) g[u].push_back(v); else root = v; } if (n & 1) printf("YES\n"), DFS(root, 0); else printf("NO"); return 0; }
#include <bits/stdc++.h> using namespace std; template <class T> inline bool read(T &num) { char in; bool IsN = false; while (in = getchar(), in != '-' && (in < '0' || in > '9')) if (in == EOF) return false; in == '-' ? (IsN = true, num = 0) : num = in - '0'; while (in = getchar(), in >= '0' && in <= '9') num = num * 10 + in - '0'; return IsN ? num = -num : num, true; } const int maxn = 2e5 + 7; const int inf = 2e9 + 7; const int mod = 1e9 + 7; stack<int> tree; vector<int> edge[maxn]; int deg[maxn]; vector<int> ans; int fa[maxn], vis[maxn]; void dfs(int u, int p) { tree.push(u); fa[u] = p; for (int i = (0); i < (edge[u].size()); i++) { if (edge[u][i] != p) dfs(edge[u][i], u); } } void gao(int u) { ans.push_back(u); vis[u] = 1; for (int i = (0); i < (edge[u].size()); i++) { int v = edge[u][i]; deg[v]--; if (v == fa[u]) continue; if (vis[v]) continue; if (deg[v] % 2 == 0) gao(v); } } int main() { ios::sync_with_stdio(false); int n; cin >> n; int root; for (int i = (1); i < (n + 1); i++) { int k; cin >> k; if (k) { edge[i].push_back(k); edge[k].push_back(i); deg[k]++; deg[i]++; } else root = i; } dfs(root, -1); while (!tree.empty()) { int u = tree.top(); tree.pop(); if (deg[u] % 2 == 0) { gao(u); } } if (ans.size() == n) { cout << "YES" << endl; for (int i = (0); i < (ans.size()); i++) cout << ans[i] << endl; } else cout << "NO" << endl; return 0; }
#include <bits/stdc++.h> using namespace std; vector<int> v[200005], sol; queue<int> q; int deg[200005], t[200005]; bool viz[200005]; void dfs(int i); void afiseaza(int i); int main() { int n, i, a, wait, root; cin >> n; for (i = 1; i <= n; ++i) { cin >> a; t[i] = a; if (a) { v[i].push_back(a); v[a].push_back(i); ++deg[a]; ++deg[i]; } else { root = i; } } dfs(root); if (sol.size() < n) { cout << "NO\n"; return 0; } cout << "YES\n"; for (auto it = sol.begin(); it != sol.end(); ++it) { cout << *it << '\n'; } } void dfs(int i) { for (auto it = v[i].begin(); it != v[i].end(); ++it) { if (*it != t[i]) { dfs(*it); } } if (deg[i] % 2 == 0) { afiseaza(i); --deg[t[i]]; } } void afiseaza(int i) { viz[i] = 1; sol.push_back(i); for (auto it = v[i].begin(); it != v[i].end(); ++it) { if (*it != t[i] && !viz[*it]) { afiseaza(*it); } } }
#include <bits/stdc++.h> using namespace std; long long sqr(long long x) { return x * x; } int mysqrt(long long x) { int l = 0, r = 1e9 + 1; while (r - l > 1) { int m = (l + r) / 2; if (m * (long long)m <= x) l = m; else r = m; } return l; } mt19937 rnd(1227); mt19937_64 rndll(12365); long long AR = 19, BR = 13, CR = 23, XR = 228, YR = 322, MODR = 1e9 + 993; long long myrand() { long long ZR = (XR * AR + YR * BR + CR) % MODR; XR = YR; YR = ZR; return ZR; } const int Mod = 1e9 + 9; int bpow(int x, int y) { if (y == 0) return 1; if (y == 1) return x; int ret = bpow(x, y >> 1); ret = (ret * (long long)ret) % Mod; if (y & 1) ret = (ret * (long long)x) % Mod; return ret; } int bdiv(int x, int y) { return (x * (long long)bpow(y, Mod - 2)) % Mod; } void setmin(int &x, int y) { x = min(x, y); } void setmax(int &x, int y) { x = max(x, y); } void setmin(long long &x, long long y) { x = min(x, y); } void setmax(long long &x, long long y) { x = max(x, y); } int gcd(int a, int b) { return a ? gcd(b % a, a) : b; } const long long llinf = 2e18 + 100; const double eps = 1e-9; const int maxn = 2e5 + 100, maxw = 1e7 + 100, inf = 2e9 + 100, sq = 300, mod = 1e9 + 9, LG = 17; int n; vector<int> e[maxn]; int a[maxn]; vector<int> ans; bool vis[maxn]; void go(int v, int par) { ans.push_back(v); vis[v] = 1; for (int i : e[v]) if (i != par && !vis[i]) go(i, v); } void dfs(int v, int par) { for (int i : e[v]) if (i != par) { dfs(i, v); if (vis[i]) a[v] ^= 1; } if (a[v] == 0) go(v, par); } int main() { ios::sync_with_stdio(0); cin.tie(0); cout.tie(0); cin >> n; for (int i = 0; i < n; i++) { int v = i, u; cin >> u; u--; if (u >= 0) { e[v].push_back(u); e[u].push_back(v); a[v] ^= 1; a[u] ^= 1; } } dfs(0, -1); if (ans.size() < n) cout << "NO"; else { cout << "YES\n"; for (int i : ans) cout << i + 1 << '\n'; } }
#include <bits/stdc++.h> using namespace std; void boost() { ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0); } const int N = 1e6; const long long inf = 1e9 + 9; const long double PI = acos(-1); long long bin_pow(long long x, long long y) { long long res = 1, base = x; while (y) { if (y & 1) { res *= base; res %= inf; } base *= base; base %= inf; y /= 2; } return res; } int n; vector<int> g[N]; int sz[N], cnt[N]; bool used[N]; queue<int> q; void dfs(int v, int pr = -1) { sz[v] = 1; for (int i = 0; i < g[v].size(); i++) { int to = g[v][i]; if (to == pr) { continue; } dfs(to, v); sz[v] += sz[to]; if (sz[to] % 2 == 0) { cnt[v]++; } } if (v != 1 && (sz[v] & 1)) { cnt[v]++; } } int main() { boost(); cin >> n; if (n % 2 == 0) { cout << "NO"; return 0; } for (int i = 1; i <= n; i++) { int x; cin >> x; if (x != 0) { g[x].push_back(i); g[i].push_back(x); } } dfs(1); vector<int> ans; for (int i = 1; i <= n; i++) { if (cnt[i] == 0) { q.push(i); } } while (!q.empty()) { int v = q.front(); q.pop(); ans.push_back(v); used[v] = 1; for (int i = 0; i < g[v].size(); i++) { int to = g[v][i]; if (used[to]) { continue; } cnt[to]--; if (cnt[to] == 0) { q.push(to); } } } cout << "YES\n"; for (int i = 0; i < ans.size(); i++) { cout << ans[i] << "\n"; } }
#include <bits/stdc++.h> using namespace std; int n, d[200005], a[200005], id[200005], t; vector<int> g[200005]; void dfs(int v, int p) { t++; id[t] = v; for (int i = 0; i < g[v].size(); i++) { int to = g[v][i]; if (to == p) continue; dfs(to, v); } if (d[v] % 2 == 0) { cout << v << endl; d[p]--; a[v] = 1; } } int main() { cin >> n; for (int i = 1; i <= n; i++) { int p; cin >> p; if (p) { g[i].push_back(p); g[p].push_back(i); d[i]++; d[p]++; } } if (n % 2 == 0) { cout << "NO" << endl; return 0; } cout << "YES" << endl; dfs(1, 0); for (int i = 1; i <= n; i++) if (!a[id[i]]) cout << id[i] << endl; return 0; }
#include <bits/stdc++.h> using namespace std; template <typename T> inline void gmax(T &x, T y) { x = x > y ? x : y; } template <typename T> inline void gmin(T &x, T y) { x = x < y ? x : y; } const int MAXN = 200010; int n, rt; int f[MAXN]; int dp[MAXN]; vector<int> G[MAXN]; void dfs(int x) { int sz = G[x].size(); for (register unsigned i = 0; i < G[x].size(); i++) { int y = G[x][i]; dfs(y); if (dp[y]) sz--; } dp[x] = sz & 1; } void dfs2(int x) { for (register unsigned i = 0; i < G[x].size(); i++) { int y = G[x][i]; if (dp[y]) dfs2(y); } printf("%d\n", x); for (register unsigned i = 0; i < G[x].size(); i++) { int y = G[x][i]; if (!dp[y]) dfs2(y); } } int main() { scanf("%d", &n); for (int i = 1; i <= n; i++) scanf("%d", &f[i]), G[f[i]].push_back(i); for (int i = 1; i <= n; i++) if (!f[i]) { rt = i; break; } dfs(rt); if (!dp[rt]) { puts("YES"); dfs2(rt); } else puts("NO"); return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 2e5 + 5; int n, p[N], la[N], ne[N], rt, d[N]; int an[N], ans, f[N][3], ct[N][3], b[N]; void dfs(int x) { for (int i = la[x]; i; i = ne[i]) dfs(i); int cnt = 0, cnt2 = 0, cnt3 = 0, cnt4 = 0; for (int i = la[x]; i; i = ne[i]) { cnt += f[i][2]; if (f[i][2]) cnt2 += f[i][1]; else cnt3 += f[i][1]; } ct[x][1] = cnt; ct[x][2] = cnt2; ct[x][3] = cnt3; if ((!((d[x] - cnt) & 1) || cnt2 > 0) && (cnt3 + cnt == d[x])) f[x][1] = 1; if ((((d[x] - cnt) & 1) || cnt2 > 0) && (cnt3 + cnt == d[x])) f[x][2] = 1; } void fi(int x, int st) { int ne1; b[x] = st; if (st == 1) ne1 = !((d[x] - ct[x][1]) & 1) && ct[x][2] > 0; else ne1 = ((d[x] - ct[x][1]) & 1) && ct[x][2] > 0; for (int i = la[x]; i; i = ne[i]) { if (f[i][2]) { fi(i, 2); if (ne1 && f[i][1]) ne1--, fi(i, 1); } } an[++ans] = x; for (int i = la[x]; i; i = ne[i]) if (!b[i]) fi(i, 1); } int main() { scanf("%d", &n); for (int i = 1, E = n; i <= E; i++) scanf("%d", &p[i]), (p[i] ? ne[i] = la[p[i]], la[p[i]] = i, d[p[i]]++ : rt = i); dfs(rt); if (f[rt][1]) { printf("YES\n"); fi(rt, 1); for (int i = 1, E = n; i <= E; i++) printf("%d ", an[i]); } else printf("NO\n"); }
#include <bits/stdc++.h> using namespace std; const int mod = 1e9 + 7; int vis[200005], sum[200005], pre[200005], n, start; vector<int> v[200005]; queue<int> q; void del(int x) { printf("%d\n", x); vis[x] = 1; for (int i = 0; i < v[x].size(); i++) { int y = v[x][i]; sum[y]--; if (!vis[y] && y != pre[x] && sum[y] % 2 == 0) { del(y); } } } void dfs(int p, int x) { for (int i = 0; i < v[x].size(); i++) { int y = v[x][i]; if (y != p) dfs(x, y); } q.push(x); pre[x] = p; } int main() { scanf("%d", &n); memset(sum, 0, sizeof(sum)); memset(vis, 0, sizeof(vis)); for (int i = 1; i <= n; i++) { int x; scanf("%d", &x); if (x) { v[i].push_back(x); v[x].push_back(i); sum[i]++; sum[x]++; } } if (n & 1) { printf("YES\n"); dfs(0, 1); while (!q.empty()) { int x = q.front(); q.pop(); if (sum[x] % 2 == 0) { del(x); } } } else { printf("NO\n"); } return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 2e5 + 10; const int MOD = 1e9 + 9; int n; vector<int> v[N]; int pa[N]; int f[N][2]; vector<int> t[N][2]; int q[N]; void BFS() { int top = 1, bot = 1; q[1] = 1; while (top <= bot) { int x = q[top++]; for (auto y : v[x]) if (y != pa[x]) { pa[y] = x; q[++bot] = y; } } } void trace(int x, int label) { int n1 = v[x].size(); for (int i = n1 - 1; i >= 0; i--) { int y = v[x][i]; if (y == pa[x]) continue; int use = t[x][label][i]; if (use == 0) trace(y, use); } cout << x << " "; for (int i = n1 - 1; i >= 0; i--) { int y = v[x][i]; if (y == pa[x]) continue; int use = t[x][label][i]; if (use == 1) trace(y, use); } } int tr[2][2][N]; int cf[2][2], tf[2][2]; void solve() { BFS(); for (int j = n; j >= 1; j--) { int cur = q[j]; memset(cf, 0, sizeof(cf)); cf[1][0] = cf[0][1] = 1; int n1 = v[cur].size(); for (int i = 0; i < n1; i++) { int y = v[cur][i]; if (y == pa[cur]) continue; for (int k0 = 0; k0 <= 1; k0++) for (int k1 = 0; k1 <= 1; k1++) tf[k0][k1] = cf[k0][k1]; memset(cf, 0, sizeof(cf)); for (int k0 = 0; k0 <= 1; k0++) for (int k1 = 0; k1 <= 1; k1++) if (tf[k0][k1]) { for (int last = 0; last <= 1; last++) if (f[y][last]) { cf[k0 ^ last][k1] = 1; tr[k0 ^ last][k1][i] = last; } } } for (int i = 0; i <= 1; i++) { f[cur][i] = cf[0][i]; int st = 0; t[cur][i].resize(n1); for (int j = n1 - 1; j >= 0; j--) { int y = v[cur][j]; if (y == pa[cur]) continue; t[cur][i][j] = tr[st][i][j]; st ^= tr[st][i][j]; } } } if (f[1][1]) { cout << "YES\n"; v[1].push_back(0); t[1][0].push_back(0); t[1][1].push_back(0); trace(1, 1); return; } cout << "NO"; } int main() { cin >> n; if (n % 2 == 0) { cout << "NO"; return 0; } for (int i = 1; i <= n; i++) { int x; cin >> x; if (x != 0) { v[x].push_back(i); v[i].push_back(x); } } for (int i = 1; i <= n; i++) for (int j = 0; j <= 1; j++) t[i][j].resize(v[i].size()); solve(); }
#include <bits/stdc++.h> using namespace std; const int N = 222222; int n, p[N], f[N]; vector<int> v[N]; void dfs0(int u) { int i = v[u].size(); while (i--) { dfs0(v[u][i]); f[u] ^= f[v[u][i]]; } f[u] ^= 1; } void dfs(int u) { int i = v[u].size(), x; while (i--) { x = v[u][i]; if (!f[x]) dfs(x); } cout << u << endl; i = v[u].size(); while (i--) { x = v[u][i]; if (f[x]) dfs(x); } } int main() { int i, rt; scanf("%d", &n); for (i = 1; i <= n; i = i + 1) { scanf("%d", p + i); if (p[i]) v[p[i]].push_back(i); else rt = i; } dfs0(rt); if (!f[rt]) cout << "NO\n"; else { cout << "YES\n"; dfs(rt); } return 0; }
#include <bits/stdc++.h> using namespace std; int n, bb, first[200100], size[200100], ds[200100], ans[200100], aa; struct Bn { int to, next; } bn[200100 << 1]; vector<int> vec[200100]; queue<int> que; inline void add(int u, int v) { bb++; bn[bb].to = v; bn[bb].next = first[u]; first[u] = bb; } void gs(int now, int last) { int p, q; size[now] = 1; for (p = first[now]; p != -1; p = bn[p].next) { if (bn[p].to == last) continue; gs(bn[p].to, now); size[now] += size[bn[p].to]; } } void dfs(int now, int last) { int p; for (p = first[now]; p != -1; p = bn[p].next) { if (bn[p].to == last) continue; if (size[bn[p].to] % 2) { vec[now].push_back(bn[p].to); ds[bn[p].to]++; } else { vec[bn[p].to].push_back(now); ds[now]++; } dfs(bn[p].to, now); } } int main() { memset(first, -1, sizeof(first)); int i, j, p, q; cin >> n; for (i = 1; i <= n; i++) { scanf("%d", &p); if (p) add(p, i), add(i, p); } if (n % 2 == 0) { puts("NO"); return 0; } puts("YES"); gs(1, -1); dfs(1, -1); for (i = 1; i <= n; i++) { if (!ds[i]) que.push(i); } for (; !que.empty();) { p = que.front(); que.pop(); printf("%d\n", p); for (i = 0; i < vec[p].size(); i++) { ds[vec[p][i]]--; if (!ds[vec[p][i]]) { que.push(vec[p][i]); } } } }
#include <bits/stdc++.h> using namespace std; const int mod = 1000000007; const int N = 212345; int par[N]; vector<int> g[N]; int num[N], adj[N], ct, vis[N]; void dfs(int u) { num[u] = ct++; for (auto v : g[u]) dfs(v); } int main(void) { int n; scanf("%d", &n); int root = -1; for (int i = 1; i <= n; i++) { int p; scanf("%d", &p); g[p].push_back(i); par[i] = p; if (!p) root = i; else { adj[i]++; adj[p]++; } } dfs(root); set<pair<int, int> > s; for (int i = 1; i <= n; i++) { if (par[i]) g[i].push_back(par[i]); if (adj[i] % 2 == 0) { s.emplace(-num[i], i); } } vector<int> ans; while (!s.empty()) { int u = s.begin()->second; s.erase(s.begin()); vis[u] = 1; for (auto v : g[u]) { if (vis[v]) continue; if (adj[v] % 2) { s.emplace(-num[v], v); } else { s.erase(make_pair(-num[v], v)); } adj[v]--; } ans.push_back(u); } if (ans.size() == n) { printf("YES\n"); for (int i = 0; i < n; i++) printf("%d\n", ans[i]); } else printf("NO\n"); return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 300100; int n, x, l[N], deg[N]; bool mark[N]; set<pair<int, int> > v[N]; vector<int> g[N]; vector<int> q; vector<int> res; int main() { scanf("%d", &n); for (int i = 0; i < n; i++) { scanf("%d", &x); x--; if (x != -1) { g[x].push_back(i); g[i].push_back(x); } } for (int i = 0; i < n; i++) { l[i] = -1; } l[0] = 0; q.push_back(0); for (int i = 0; i < q.size(); i++) { int now = q[i]; for (int j = 0; j < g[now].size(); j++) { int tmp = g[now][j]; if (l[tmp] == -1) { q.push_back(tmp); l[tmp] = l[now] + 1; } } } for (int i = 0; i < n; i++) { mark[i] = false; deg[i] = g[i].size(); v[g[i].size() % 2].insert(make_pair(-l[i], i)); } for (int i = 0; i < n; i++) { if (v[0].size() == 0) { puts("NO"); exit(0); } int now = (*v[0].begin()).second; mark[now] = true; v[0].erase(v[0].begin()); res.push_back(now + 1); for (int j = 0; j < g[now].size(); j++) { int tmp = g[now][j]; if (mark[tmp]) { continue; } v[deg[tmp] & 1].erase(make_pair(-l[tmp], tmp)); deg[tmp]--; v[deg[tmp] & 1].insert(make_pair(-l[tmp], tmp)); } } puts("YES"); for (int i = 0; i < res.size(); i++) { printf("%d\n", res[i]); } return 0; }
#include <bits/stdc++.h> using namespace std; int sz[200010]; int vis[200010]; int p[200010]; vector<int> son[200010]; void del(int x) { vis[x] = 1; cout << x << endl; for (int i = 0; i < son[x].size(); i++) if (!vis[son[x][i]]) del(son[x][i]); } void dfs(int x) { sz[x] = 1; for (int i = 0; i < son[x].size(); i++) dfs(son[x][i]), sz[x] += sz[son[x][i]]; if (!(sz[x] & 1)) del(x); } int main() { int n; int root; cin >> n; if (n & 1) cout << "YES" << endl; else return cout << "NO" << endl, 0; for (int i = 1; i <= n; i++) { cin >> p[i]; if (p[i]) son[p[i]].push_back(i); else root = i; } dfs(root); del(root); return 0; }