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#include <bits/stdc++.h> using namespace std; long long gcd(long long a, long long b) { if (b > a) { return gcd(b, a); } if (b == 0) { return a; } return gcd(b, a % b); } long long expo(long long a, long long b, long long mod) { long long res = 1; while (b > 0) { if (b & 1) res = (res * a) % mod; a = (a * a) % mod; b = b >> 1; } return res; } vector<int> sieve(int n) { int *arr = new int[n + 1](); vector<int> vect; for (int i = 2; i <= n; i++) if (arr[i] == 0) { vect.push_back(i); for (int j = 2 * i; j <= n; j += i) arr[j] = 1; } return vect; } void extendgcd(long long a, long long b, long long *v) { if (b == 0) { v[0] = 1; v[1] = 0; v[2] = a; return; } extendgcd(b, a % b, v); long long x = v[1]; v[1] = v[0] - v[1] * (a / b); v[0] = x; return; } long long mminv(long long a, long long b) { long long arr[3]; extendgcd(a, b, arr); return arr[0]; } long long mminvprime(long long a, long long b) { return expo(a, b - 2, b); } bool revsort(long long a, long long b) { return a > b; } void swap(int &x, int &y) { int temp = x; x = y; y = temp; } long long combination(long long n, long long r, long long m, long long *fact) { long long val1 = fact[n]; long long val2 = mminvprime(fact[r], m); long long val3 = mminvprime(fact[n - r], m); return ((val1 * val2) % m * val3) % m; } int main() { ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL); long long x; cin >> x; long long val = x; for (long long i = 2; i <= sqrt(x); i++) if (x % i == 0) if (x / gcd(i, x / i) == x) val = min(val, max(i, x / i)); cout << x / val << " " << val << endl; return 0; }
#include <bits/stdc++.h> using namespace std; long long int gcd(long long int a, long long int b) { if (a % b == 0) return (b); return (gcd(b, a % b)); } int main() { long long int x, a = 1, b = 1, n1, n2; cin >> x; for (int i = 1; i <= (int)floor(sqrt(x)); i++) { if (x % i != 0) continue; n1 = i, n2 = x / i; if (((n1 * n2) / gcd(n2, n1)) == x) a = n1, b = n2; } cout << a << " " << b << endl; return (0); }
#include <bits/stdc++.h> using namespace std; long long gcd(long long a, long long b) { return b ? gcd(b, a % b) : a; } long long lcm(long long a, long long b) { return a / gcd(a, b) * b; } int main() { ios_base::sync_with_stdio(false); long long x; cin >> x; vector<long long> v; long long u = sqrt(x); for (long long i = 1; i * i <= x; i++) { if (x % i == 0) { v.push_back(i); long long y = x / i; if (y > u) v.push_back(y); } } sort(v.begin(), v.end()); for (int i = 0; i < v.size(); i++) { for (int j = i; j >= 0; j--) { if (lcm(v[i], v[j]) == x) { cout << v[i] << " " << v[j] << endl; return 0; } } } return 0; }
#include <bits/stdc++.h> using namespace std; long long gcd(long long a, long long b) { return (b == 0) ? a : gcd(b, a % b); } long long lcm(long long a, long long b) { return a * b / gcd(a, b); } void solve() { long long n, mn = (long long)1e7; cin >> n; for (long long i = 1; i < sqrt(n) + 1; ++i) if (n % i == 0 && lcm(i, n / i) == n) mn = min(i, n / i); cout << mn << " " << n / mn; } int32_t main() { ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL); long long t = 1; while (t--) { solve(); } return 0; }
#include <bits/stdc++.h> using namespace std; template <class T> int check_mod(T a, T b) { return (a % b) ? 1 : 0; } template <class T> void maxi(T &a, T b) { a = max(a, b); return; } template <class T> void mini(T &a, T b) { a = min(a, b); return; } bool is_prime(int a) { if (a == 2) return true; if (!(a & 1) || a == 1) return false; for (int i = 3; i * i <= a; i += 2) if (!(a % i)) return false; return true; } bool is_prime(long long a) { if (a == 2) return true; if (!(a & 1) || a == 1) return false; for (long long i = 3; i * i <= a; i += 2) if (!(a % i)) return false; return true; } bool is_palindrome(string s) { int len = (int)s.length(); int mid = len >> 1; for (int i = 0; i < mid; i++) if (s[i] != s[len - i - 1]) return false; return true; } int gcd(int a, int b) { while (b) { int mod = a % b; a = b; b = mod; } return a; } int lcm(int a, int b) { return a / gcd(a, b) * b; } int binpow(int a, int b) { int res = 1; while (b) { if (b & 1) res *= a; a *= a; b >>= 1; } return res; } int binpow(int a, int b, int MODULO) { int res = 1; while (b) { if (b & 1) { res *= a; res %= MODULO; } a *= a; a %= MODULO; b >>= 1; } return res; } long long gcd(long long a, long long b) { while (b) { long long mod = a % b; a = b; b = mod; } return a; } long long lcm(long long a, long long b) { return a / gcd(a, b) * b; } long long binpow(long long a, long long b) { long long res = 1; while (b) { if (b & 1) res *= a; a *= a; b >>= 1; } return res; } long long binpow(long long a, long long b, long long MODULO) { long long res = 1; while (b) { if (b & 1) { res *= a; res %= MODULO; } a *= a; a %= MODULO; b >>= 1; } return res; } string binary(int N) { if (!N) return "0"; string bin = ""; while (N) { bin += '0' + (N & 1); N >>= 1; } reverse((bin).begin(), (bin).end()); return bin; } string binary(long long N) { if (!N) return "0"; string bin = ""; while (N) { bin += '0' + (N & 1); N >>= 1; } reverse((bin).begin(), (bin).end()); return bin; } const int INF = 2147483547; const int MODULO = 1000000007; const int _MODULO = 998244353; const long long INF64 = 9223372036854775707; const long long MODULO64 = 1000000007; const long long _MODULO64 = 998244353; const double epsilon = 10e-6; const double PI = acos(-1); int main() { ios_base::sync_with_stdio(false); cin.tie(NULL); long long x; cin >> x; pair<long long, long long> ans = {INF64, INF64}; for (long long a = 1; a * a <= x; ++a) { long long b = x / a; if (a * b != x) continue; if (lcm(a, b) != x) continue; if (b < ans.second) ans = make_pair(a, b); } cout << ans.first << ' ' << ans.second << '\n'; return 0; }
#include <bits/stdc++.h> using namespace std; long long gcd(long long x, long long y) { return y == 0 ? x : gcd(y, x % y); } int main() { long long x, b; cin >> x; long long t = sqrt(x); for (long long a = t; a >= 1; a--) { if (x % a) continue; b = x / a; if (gcd(a, b) == 1) { cout << a << " " << b << endl; break; } } return 0; }
#include <bits/stdc++.h> using namespace std; long long gcd(long long a, long long b) { if (a % b == 0) return b; else return gcd(b, a % b); } long long lcm(long long a, long long b) { long long t = gcd(a, b); return (a * b) / t; } int main() { long long x, ma = 0, t; cin >> x; long long a, b, temp; for (long long i = 1; i * i <= x; i++) { if (x % i == 0) { a = i; b = x / i; temp = lcm(a, b); if (temp == x) { ma = max(a, ma); } } } printf("%lld %lld\n", ma, x / ma); }
#include <bits/stdc++.h> long long gcd(long long a, long long b) { if (!a) return b; return gcd(b % a, a); } int main() { long long n, a, b, c; scanf("%lld", &n); for (long long i = 1; i * i <= n; i++) if (n % i == 0 && gcd(i, n / i) == 1) { a = i; b = n / i; } printf("%lld %lld\n", a, b); }
#include <bits/stdc++.h> using namespace std; unsigned long long int gcd(unsigned long long int a, unsigned long long int b) { if (b == 0) { return a; } else { return gcd(b, a % b); } } unsigned long long int lcm(unsigned long long int a, unsigned long long int b) { unsigned long long int x; x = (a * b) / gcd(a, b); return x; } int main() { unsigned long long int n, x, y; cin >> n; unsigned long long int i, a = 9999999999999; for (i = 1; i <= sqrt(n); i++) { if (n % i == 0) { if (max(i, n / i) <= a && lcm(i, n / i) == n) { a = max(i, n / i); x = min(i, n / i); y = n / x; } } } cout << x << " " << y; return 0; }
#include <bits/stdc++.h> const double pi = 3.14159265358979323846; using namespace std; long long fastexp(long long a, long long b) { long long answer = 1; long long temp = a; while (b > 0) { if (b & 1) answer *= (temp); temp *= temp; b >>= 1; } return answer; } long long gcd(long long a, long long b) { if (a == 0) return b; return gcd(b % a, a); } int32_t main() { ios_base::sync_with_stdio(false); cin.tie(NULL); long long x; cin >> x; ; long long answer = x; long long a = 1, b = x; for (long long i = 2; i * i <= (x); i++) { if (x % i == 0) { long long q = (x / i); if (gcd(q, i) == 1) { answer = min(answer, max(q, i)); a = i; b = q; } } } cout << a << " " << b << endl; return 0; }
#include <bits/stdc++.h> using namespace std; long long int gcd(long long int a, long long int b) { if (b == 1) return 1; if (a % b) return gcd(b, a % b); return b; } int main() { ios_base::sync_with_stdio(false); cin.tie(NULL); long long int x, a; cin >> x; for (a = sqrt(x); a > 0; --a) { if (x % a) continue; if (gcd(a, (x / a)) == 1) { cout << a << " " << (x / a); break; } } }
#include <bits/stdc++.h> using namespace std; template <class T> inline void read(T &ret) { char c; int sgn; if (c = getchar(), c == EOF) return; while (c != '-' && (c < '0' || c > '9')) c = getchar(); sgn = (c == '-') ? -1 : 1; ret = (c == '-') ? 0 : (c - '0'); while (c = getchar(), c >= '0' && c <= '9') ret = ret * 10 + (c - '0'); ret *= sgn; return; } long long gcd(long long a, long long b) { if (b == 0) return a; else gcd(b, a % b); } int main() { long long n; read(n); long long x = sqrt(n); if (x * x == n) x -= 1; for (long long i = x; i >= 1; i--) { if (n % i == 0) { if (gcd(n / i, i) == 1) { printf("%lld %lld", i, n / i); return 0; } } } printf("1 %lld", n); return 0; }
#include <bits/stdc++.h> using namespace std; void ini() {} bool check(unsigned long long int n, unsigned long long int m, unsigned long long int x) { unsigned long long int res = n * m, temp; while (m != 0) { temp = m; m = n % m; n = temp; } if ((res / n) == x) { return true; } else { return false; } } int main() { ini(); unsigned long long int x, d; cin >> x; d = sqrt(x); unsigned long long int a = 2, temp, m = x; while (a <= d) { if (x % a == 0 && check(x / a, a, x)) { temp = max(x / a, a); m = min(m, temp); } a++; } cout << m << " " << x / m; }
#include <bits/stdc++.h> using namespace std; vector<bool> st(1000005); vector<int> prm; vector<long long> fct; vector<pair<long long, long long> > ans; void sieve() { int i, j; for (i = 3; i <= sqrt(1000005); i += 2) { if (!st[i]) { for (j = i * i; j <= 1000005; j += i) st[j] = true; } } prm.push_back(2); for (i = 3; i <= 1000005; i += 2) { if (!st[i]) prm.push_back(i); } } long long tot; void solve(int pos, long long mlt) { if (pos == fct.size() - 1) { ans.push_back({mlt, tot / mlt}); mlt *= fct[pos]; ans.push_back({mlt, tot / mlt}); } else { solve(pos + 1, mlt); solve(pos + 1, mlt * fct[pos]); } } bool cmp(pair<long long, long long> a, pair<long long, long long> b) { long long p = a.first, q = a.second, r = b.first, s = b.second; if (p < q) swap(p, q); if (r < s) swap(r, s); return p < r; } int main() { long long x; scanf("%lld", &x); if (x == 1) { cout << "1 1\n"; return 0; } tot = x; sieve(); int i, j; for (i = 0; i < prm.size() && prm[i] * prm[i] <= x; i++) { if (x % prm[i] == 0) { long long xx = 1; while (x % prm[i] == 0) { x /= prm[i]; xx *= prm[i]; } fct.push_back(xx); } if (x == 1) break; } if (x != 1) fct.push_back(x); solve(0, 1); sort(ans.begin(), ans.end(), cmp); cout << ans[0].first << " " << ans[0].second; printf("\n"); return 0; }
#include <bits/stdc++.h> using namespace std; int dx[] = {0, 0, 1, -1, 1, -1, 1, -1}; int dy[] = {1, -1, 0, 0, -1, 1, 1, -1}; long long gcd(long long a, long long b) { return !b ? a : gcd(b, a % b); } long long lcm(long long a, long long b) { return (a / gcd(a, b)) * b; } long long power(long long a, long long b, long long ret = 1LL) { while (b--) ret = (ret * a); return ret; } int main() { ios_base::sync_with_stdio(false); cin.tie(NULL); long long n, x; cin >> x; n = x; long long ans = 1; for (long long i = 2; i * i <= n; i++) if (n % i == 0) { if (lcm(i, x / i) == x) ans = i; } cout << ans << " " << x / ans; return 0; }
#include <bits/stdc++.h> using namespace std; long long int gcd(long long int a, long long int b) { if (b == 0) return a; return gcd(b, a % b); } int main() { ios_base::sync_with_stdio(false); cin.tie(NULL); long long int n; cin >> n; long long int x = LLONG_MAX, y = LLONG_MAX; for (long long int i = 1; i * i <= n; i++) { if (n % i == 0) { long long int lcm = ((i) * (n / i)) / (gcd(i, n / i)); if (max(x, y) > max(n / i, i) && lcm == n) x = i, y = n / i; } } cout << x << " " << y << endl; }
#include <bits/stdc++.h> using namespace std; long long x; long long gcd(long long a, long long b) { if (a == 0) return b; return gcd(b % a, a); } long long lcm(long long a, long long b) { return (a * b) / gcd(a, b); } int main() { cin >> x; long long m = sqrt(x); if (sqrt(x) == m && m != 1) --m; for (long long i = m; i >= 1; --i) { if (x % i == 0 && lcm(i, x / i) == x) { cout << i << " " << x / i; break; } } return 0; }
#include <bits/stdc++.h> using namespace std; long long gcd(long long a, long long b) { if (b == 0) return a; return gcd(b, a % b); } int main() { long long x; cin >> x; long long i = sqrt(x); if (i * i == x) i--; if (x == 1) cout << "1 1"; else for (; i > 0; i--) if (x % i == 0 && gcd(i, x / i) == 1) { cout << i << " " << x / i; break; } }
#include <bits/stdc++.h> using namespace std; long long a; int gcd(long long a, long long b) { if (b == 0LL) return a; a %= b; return gcd(b, a); } void solve(long long a) { long long x, y, mx, mn; for (long long i = 1; i * i <= a; i++) { if (a % i == 0LL) { x = i; y = a / i; if (a == ((x * y) / gcd(x, y))) { mx = i; mn = a / i; } } } cout << mx << " " << mn << "\n"; } int main() { scanf("%lld", &a); solve(a); return 0; }
#include <bits/stdc++.h> int gcd(long long n, long long m) { long long temp; while (m && n) { temp = n % m; n = m; m = temp; } if (n == 1) return 1; else return 0; } int main() { long long n, ans = 0, d, i; int c = 0; scanf("%lld", &n); for (i = 2; 1LL * i * i <= n; i++) { if (n % i == 0) { d = n / i; if (i > ans && i != d && gcd(i, d)) ans = i; } if (c >= 2) break; } if (ans == 0) printf("1 %lld", n); else printf("%lld %lld", ans, n / ans); return 0; }
#include <bits/stdc++.h> using namespace std; int prime(long long x) { for (long long i = 2; i * i <= x; i++) { if (x % i == 0) { return 0; } } return 1; } int gcd(long long a, long long b) { if (b > a) { swap(a, b); } if (b == 0) { return a; } else { return gcd(b, a % b); } } int main() { ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0); long long test, l = 0, g = 0, a = 0, b = 0; cin >> test; long long mini = LONG_LONG_MAX; if (prime(test)) { cout << 1 << " " << test << endl; } else { for (long long i = 1; i * i <= test; i++) { if (test % i == 0) { if (gcd(i, test / i) == 1) { g = max(i, test / i); if (g <= mini) { mini = g; } else { break; } } } } cout << mini << " " << test / mini << endl; } return 0; }
#include <bits/stdc++.h> using namespace std; bool RELAXED = false; template <int, typename T> struct MINMAX { T val; MINMAX(T val) : val(val) {} }; template <typename T> MINMAX<1, T> MAX(T val) { return MINMAX<1, T>(val); }; template <typename T> MINMAX<2, T> MIN(T val) { return MINMAX<2, T>(val); }; template <typename T, typename U> inline T& operator|=(T& lhs, MINMAX<1, U> rhs) { return lhs = (rhs.val > lhs ? (RELAXED = true, rhs.val) : (RELAXED = false, lhs)); } template <typename T, typename U> inline T& operator|=(T& lhs, MINMAX<2, U> rhs) { return lhs = (rhs.val < lhs ? (RELAXED = true, rhs.val) : (RELAXED = false, lhs)); } template <typename T> inline vector<T> readVector(int n) { vector<T> vec(n); for (int i = 0; i < int(n); i++) cin >> vec[i]; return vec; } template <typename T> void EXIT(T answer) { cout << answer << endl; exit(0); } int main() { ios_base::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr); signed long long int x; cin >> x; vector<signed long long int> primes; for (int p = int(2); p <= int(1e6 + 5); p++) { if (x % p) continue; signed long long int pp = p; while (x % (pp * p) == 0) pp *= p; x /= pp; primes.push_back(pp); } if (x > 1) primes.push_back(x); signed long long int best = 1e18; pair<signed long long int, signed long long int> ans; for (int i = 0; i < int(1 << 20); i++) { signed long long int a = 1, b = 1; for (int j = 0; j < int(primes.size()); j++) if ((1 << j) & i) a *= primes[j]; else b *= primes[j]; best |= MIN(max(a, b)); if (RELAXED) ans = {a, b}; } cout << ans.first << " " << ans.second << endl; return 0; }
#include <bits/stdc++.h> using namespace std; long long gcd(long long a, long long b) { return b == 0 ? a : gcd(b, a % b); } int main() { long long x; cin >> x; long long ans = x; for (long long i = 1; i <= sqrt(x); i++) { if (x % i == 0 && gcd(i, x / i) == 1) { ans = min(ans, max(i, x / i)); } } cout << x / ans << " " << ans << endl; return 0; }
#include <bits/stdc++.h> using namespace std; const long long N = 1000005; const long long INF = 1e18; long long x, m, n, i, j, k; pair<long long, long long> a[N]; long long gcd(long long a, long long b) { if (b == 0) return a; return gcd(b, a % b); } long long lcd(long long a, long long b) { return a * b / gcd(a, b); } int main() { ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0); cin >> x; n = 1; a[1] = make_pair(1, x); for (i = 2; i * i <= x; i++) { if (x % i == 0) { long long j = x / i; if (lcd(i, j) == x) { n++; a[n] = make_pair(i, j); } } } sort(a + 1, a + 1 + n); cout << a[n].first << " " << a[n].second << endl; return 0; }
#include <bits/stdc++.h> using namespace std; vector<long long> v; int vn; vector<long long> vl; void put(int ind, long long val) { if (ind == vn) { vl.push_back(val); return; } put(ind + 1, val); put(ind + 1, val * v[ind]); } int main(void) { long long x; scanf("%lld", &x); if (x == 1) { printf("1 1"); return 0; } for (long long i = 2; i * i <= x; i++) { long long k = 1; while (x % i == 0) { k *= i; x /= i; } if (k != 1) { v.push_back(k); } } if (x != 1) { v.push_back(x); } vn = v.size(); put(0, 1); int vln = vl.size(); sort(vl.begin(), vl.end()); printf("%lld %lld", vl[vln / 2 - 1], vl[vln / 2]); return 0; }
#include <bits/stdc++.h> using namespace std; vector<long long> v, vc; int main() { ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0); long long n; cin >> n; long long sm = n; for (long long i = 2; i * i <= n; i++) { if (n % i == 0) { long long c = 0, d = 1; while (n % i == 0) { n /= i; c++; d *= i; } v.push_back(d); } } if (n > 1) { v.push_back(n); } long long l = v.size(); long long m = (1LL << l); for (long long i = 0; i < m; i++) { long long p = 1; for (long long j = 0; j < l; j++) { if (i & (1LL << j)) { p *= v[j]; } } vc.push_back(p); } long long x1, x2; long long mx = 1e18; for (long long u : vc) { long long p = sm / u; long long q = max(u, p); if (mx > q) { mx = q; x1 = u, x2 = p; } } if (x1 > x2) swap(x1, x2); cout << x1 << " " << x2 << "\n"; return 0; }
#include <bits/stdc++.h> using namespace std; const double eps = 1e-6; const int maxn = 2010; const int inf = 0x3f3f3f3f; long long gcd(long long a, long long b) { return b ? gcd(b, a % b) : a; } int main() { long long x; cin >> x; for (long long i = sqrt(x); i >= 1; i--) { if (x % i == 0) { long long tem = x / i; if (gcd(tem, i) == 1) { cout << min(tem, i) << ' ' << max(tem, i) << endl; break; } } } return 0; }
#include <bits/stdc++.h> #pragma GCC optimize("O3") constexpr auto INF = 9223372036854775807; using namespace std; inline int mex(unordered_set<int> st) { int m = 0; while (st.find(m) != st.end()) { m += 1; } return m; } inline int calculateGrundy(int n) { if (n == 1) return 0; unordered_set<int> mexi; for (int i = 1; i <= sqrt(n); i += 1) { if (n % i == 0) { if (n / i != n) mexi.insert(calculateGrundy(n / i)); mexi.insert(calculateGrundy(i)); } } return mex(mexi); } inline long long int gcd(long long int a, long long int b) { if (b == 0) return a; return gcd(b, a % b); } long long int power(long long int x, long long int y) { long long int res = 1; x = x % 1000000007; if (x == 0) return 0; while (y > 0) { if (y & 1) res = (res * x) % 1000000007; y = y >> 1; x = (x * x) % 1000000007; } return res; } bool check(long long int a) { long long int count = 0; while (a % 2 == 0) { a /= 2; count += 1; } if (count > 1) return false; bool flag = true; for (long long int i = 3; i <= sqrt(a); i += 2) { if (a % i == 0) { flag = false; break; } } return flag; } long long int sum(long long int n) { return (n * (n + 1)) / 2; } int main() { ios_base::sync_with_stdio(0), cin.tie(0); long long int n; cin >> n; long long int mini = INF, f = 0, s = 0; for (long long int i = 1; i <= sqrt(n); i += 1) { if (n % i == 0) { if (max(i, n / i) < mini && n == (i * (n / i)) / gcd(i, n / i)) { mini = max(i, n / i); f = i; s = n / i; } } } cout << f << " " << s; }
#include <bits/stdc++.h> using namespace std; using ll = long long; using ld = long double; using pii = pair<int, int>; using pll = pair<ll, ll>; using vi = vector<int>; const ll INF = 100000000000ll; const int N = 200005; const int prime = 31; const ll mod = 1000000007; const ld eps = 1e-5; mt19937_64 strong_random( chrono::system_clock::now().time_since_epoch().count()); ll n; void input() { scanf("%lld", &n); } void solve() { vector<ll> divisors; ll nval = n; ll dv = 2; while (dv * dv <= n) { if (n % dv == 0) { int cc = 0; divisors.push_back(1); while (n % dv == 0) { n /= dv; divisors.back() *= dv; } } else { dv++; } } if (n != 1) { divisors.push_back(n); } int bitcnt = (int)(divisors).size(); pll ans = {nval, 1}; for (int i = 0; i < (1 << bitcnt); i++) { ll a = 1, b = 1; for (int j = 0; j < bitcnt; j++) { if ((1 << j) & i) { a *= divisors[j]; } else { b *= divisors[j]; } } if (a < b) swap(a, b); ans = min(ans, {a, b}); } cout << ans.second << " " << ans.first << endl; } void precalc() {} int main() { precalc(); int testcases = 1; for (int testId = 1; testId <= testcases; testId++) { input(); solve(); } return 0; }
#include <bits/stdc++.h> using namespace std; const long long mod = 1e9 + 7; const long long modl = 998244353; const double pie = 3.1415926535; unsigned long long power(unsigned long long x, unsigned long long y) { if (y == 0) return 1; else { if (y % 2 == 0) return power(x * x, y / 2); else return x * power(x * x, (y - 1) / 2); } } long long mod_power(long long x, long long y, long long m) { long long r = 1; x = x % m; if (x == 0) return 0; while (y > 0) { if (y & 1) r = (r * x) % m; y = y / 2; x = (x * x) % m; } return r; } long long gcd(long long x, long long y) { if (y == 0) return x; return gcd(y, x % y); } int main() { ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL); int TESTS = 1; while (TESTS--) { long long x; scanf("%lld", &x); long long a = 0; for (long long i = 1; i * i <= x; i++) { if (x % i == 0 && gcd(i, x / i) == 1) { a = i; } } printf("%lld %lld", a, x / a); } }
#include <bits/stdc++.h> using namespace std; template <class T> bool chmax(T& a, const T& b) { if (a < b) { a = b; return 1; } return 0; } template <class T> bool chmin(T& a, const T& b) { if (b < a) { a = b; return 1; } return 0; } const long long int MOD = 1e9 + 7, INF = 1e18; long long int dx[8] = {0, -1, 1, 0, 1, -1, 1, -1}, dy[8] = {1, 0, 0, -1, -1, -1, 1, 1}; struct edge { long long int cost; long long int u, v; }; vector<int64_t> divisor(int64_t n) { vector<int64_t> ret; for (int64_t i = 1; i * i <= n; i++) { if (n % i == 0) { ret.push_back(i); if (i * i != n) ret.push_back(n / i); } } sort(begin(ret), end(ret)); return (ret); } long long int gcd(long long int a, long long int b) { if (b == 0) return a; else return gcd(b, a % b); } long long int N; int main() { cin >> N; auto vec = divisor(N); pair<long long int, long long int> p = {N, 1}; for (long long int i = (((long long int)(vec).size())) - 1, i_begin_ = (0); i >= i_begin_; i--) { if (vec[i] < N / vec[i]) break; if (gcd(vec[i], N / vec[i]) == 1) { if (max(p.first, p.second) > vec[i]) { p = {vec[i], N / vec[i]}; } } } cout << p.first << " " << p.second << '\n'; }
#include <bits/stdc++.h> using namespace std; int main() { ios::sync_with_stdio(false); cin.tie(0); long long n; cin >> n; vector<long long> a; for (long long i = 2; i * i <= n; i++) if (n % i == 0) { long long t = 1; while (n % i == 0) t *= i, n /= i; a.push_back(t); } if (n > 1) a.push_back(n); if (a.size() <= 1) a.push_back(1); if (a.size() <= 1) a.push_back(1); sort(a.begin(), a.end()); pair<long long, long long> ans = pair<long long, long long>(LLONG_MAX, LLONG_MAX); for (int c = 0; c < (1 << a.size()); c++) { long long u = 1, v = 1; for (int i = 0; i <= a.size() - 1; i++) if ((c >> i) & 1) u *= a[i]; else v *= a[i]; if (max(ans.first, ans.second) > max(u, v)) ans = pair<long long, long long>(u, v); } cout << ans.first << ' ' << ans.second; return 0; }
#include <bits/stdc++.h> using namespace std; struct primefactorisation { long long count, pf; }; void generate(long long curr_idx, long long curr_divisor, vector<primefactorisation> &arr, vector<long long> &final) { if (curr_idx == arr.size()) { final.push_back(curr_divisor); return; } for (long long i = 0; i <= arr[curr_idx].count; i++) { generate(curr_idx + 1, curr_divisor, arr, final); curr_divisor *= arr[curr_idx].pf; } } long long gcd(long long a, long long b) { if (a == 0) return b; return gcd(b % a, a); } void fun(long long n) { long long d = n; vector<primefactorisation> arr; for (long long i = 2; i * i <= n; ++i) { if (n % i == 0) { long long cnt = 0; while ((n % i) == 0) { n = n / i; cnt++; } arr.push_back({cnt, i}); } } if (n > 1) { arr.push_back({1, n}); } long long curr_idx = 0, curr_divisor = 1; vector<long long> final; generate(curr_idx, curr_divisor, arr, final); sort(final.begin(), final.end()); long long mini = LLONG_MAX, a = -1, b = -1; for (int i = 0; i < final.size(); i++) { long long x = final[i]; if (gcd(max(x, d / x), min(x, d / x)) == 1) { if (max(x, d / x) < mini) { a = min(x, d / x); b = max(x, d / x); mini = b; } } } cout << a << " " << b; return; } int main() { long long x; cin >> x; fun(x); return 0; }
#include <bits/stdc++.h> using namespace std; const long long int mxN = 1e12 + 1; const long long int MOD = 1e9 + 7; long long int gcd(long long int a, long long int b) { if (a == 0) return b; return gcd(b % a, a); } long long int lcm(long long int a, long long int b) { return (a * b) / gcd(a, b); } void solve() { set<pair<long long int, long long int>> s; long long int n; cin >> n; for (long long int i = 1; i <= sqrt(n); i++) { if (n % i == 0) { if (lcm(i, n / i) == n) s.insert(make_pair(i, n / i)); } } pair<long long int, long long int> mn(mxN, mxN); for (auto a : s) { long long int x = max(a.first, a.second); long long int y = max(mn.first, mn.second); if (x < y) { mn = a; } } cout << mn.first << " " << mn.second << "\n"; } signed main() { long long int t = 1; while (t--) { solve(); } return 0; }
#include <bits/stdc++.h> using namespace std; const long long MOD = 1000 * 1000 * 1000 + 7; const long long INF = 1ll * 1000 * 1000 * 1000 * 1000 * 1000 * 1000 + 7; const long long MOD2 = 998244353; const long long N = 1000 * 100 + 10; const long long N2 = 70; const long double PI = 3.141592653589793; long long gcd(long long a, long long b) { if (!b) return a; return gcd(b, a % b); } long long power(long long x, long long y, long long p = LLONG_MAX) { long long res = 1; x %= p; while (y > 0) { if (y & 1) res = (res * x) % p; y = y >> 1; x = (x * x) % p; } return res; } long long lcm(long long a, long long b) { return (a * b) / gcd(a, b); } void solve() {} signed main() { ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0); long long x; cin >> x; long long ans = 1; for (long long i = 1; (i * i) <= x; i++) { if (x % i == 0) { if (lcm(i, x / i) == x) { ans = i; } } } cout << ans << " " << (x / ans); return 0; }
#include <bits/stdc++.h> using namespace std; long long n, m; int prim[2000002], cnt; bool isp[2000002]; int js, ps[2000002], ci[2000002]; long long pr[2000002]; int main() { scanf("%lld", &n); m = n; if (n == 1) { puts("1 1"); return 0; } for (int i = 2; i <= 2000000; i++) isp[i] = 1; for (int i = 2; i <= 2000000; i++) { if (isp[i]) prim[++cnt] = i; for (int j = 1; j <= cnt && prim[j] * i <= 2000000; j++) { isp[prim[j] * i] = 0; if (i % prim[j] == 0) break; } } for (int i = 1; i <= cnt && prim[i] <= n; i++) { if (n % prim[i] == 0) { ps[++js] = prim[i]; pr[js] = 1; while (n % prim[i] == 0) { ci[js]++; n /= prim[i]; pr[js] *= prim[i]; } } } if (n > 1) ps[++js] = n, ci[js] = 1, pr[js] = n; long long mn = 1e18, as1, as2; for (int i = 1; i < (1 << js); i++) { long long tp = 1; for (int j = 1; j <= js; j++) { if (i & (1 << (j - 1))) tp *= pr[j]; } long long ano = m / tp; if (max(tp, ano) < mn) { mn = max(tp, ano); as1 = tp, as2 = ano; } } printf("%I64d %I64d\n", as1, as2); }
#include <bits/stdc++.h> using namespace std; long long gcd(long long a, long long b) { return b ? gcd(b, a % b) : a; } int main() { ios::sync_with_stdio(false); long long x; cin >> x; long long sq = sqrt(x); long long sol = x; long long a = 1; long long b = x; for (long long i = 1; i <= sq + 1; i++) { if (x % i == 0) { long long t = x / i; if (gcd(t, i) == 1) { if (sol > max(t, i)) { sol = max(t, i); a = t; b = i; } } } } cout << a << " " << b << endl; return 0; }
#include <bits/stdc++.h> #pragma GCC optimize("O3") #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx") #pragma GCC optimize("unroll-loops") using namespace std; using ll = long long; using ld = long double; using pi = pair<int, int>; using pl = pair<ll, ll>; using pd = pair<double, double>; using vi = vector<int>; using vb = vector<bool>; using vl = vector<ll>; using vd = vector<double>; using vs = vector<string>; using vpi = vector<pi>; using vpl = vector<pl>; using vpd = vector<pd>; const int di[4] = {-1, 0, 1, 0}, dj[4] = {0, 1, 0, -1}; const int di8[8] = {-1, -1, 0, 1, 1, 1, 0, -1}, dj8[8] = {0, 1, 1, 1, 0, -1, -1, -1}; const ld PI = acos((ld)-1); const ll INF = 1e18; mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count()); ll randint(ll a, ll b) { return uniform_int_distribution<ll>(a, b)(rng); } bool pow2(int i) { return i && (i & -i) == i; } constexpr int pct(int x) { return __builtin_popcount(x); } constexpr int bits(int x) { return 31 - __builtin_clz(x); } ll cdiv(ll a, ll b) { return a / b + ((a ^ b) > 0 && a % b); } ll fdiv(ll a, ll b) { return a / b - ((a ^ b) < 0 && a % b); } ll half(ll x) { return fdiv(x, 2); } template <class T> bool chmin(T& a, const T& b) { return b < a ? a = b, 1 : 0; } template <class T> bool chmax(T& a, const T& b) { return a < b ? a = b, 1 : 0; } template <class T> void remDup(vector<T>& v) { sort((v).begin(), (v).end()); v.erase(unique((v).begin(), (v).end()), end(v)); } template <class T, class U> void remAll(vector<T>& v, U a) { v.erase(remove((v).begin(), (v).end(), a), v.end()); } void HIGH(string& a) { transform((a).begin(), (a).end(), a.begin(), ::toupper); } void LOW(string& a) { transform((a).begin(), (a).end(), a.begin(), ::tolower); } template <class T, class U> T fstTrue(T lo, T hi, U f) { while (lo < hi) { T mid = half(lo + hi); f(mid) ? hi = mid : lo = mid + 1; } return lo; } template <class T, class U> T lstTrue(T lo, T hi, U f) { while (lo < hi) { T mid = half(lo + hi + 1); f(mid) ? lo = mid : hi = mid - 1; } return lo; } template <class T, class U, class C> string to_string(tuple<T, U, C> p); template <class T, class U, class C, class D> string to_string(tuple<T, U, C, D> p); string to_string(char c) { return string(1, c); } string to_string(bool b) { return to_string((int)b); } string to_string(const char* s) { return (string)s; } string to_string(string s) { return s; } template <class T> string to_string(complex<T> c) { stringstream ss; ss << c; return ss.str(); } string to_string(vb v) { string res = "{"; for (int i = (0); i < (((int)(v).size())); ++i) res += char('0' + v[i]); res += "}"; return res; } template <size_t SZ> string to_string(bitset<SZ> b) { string res = ""; for (int i = (0); i < (((int)(b).size())); ++i) res += char('0' + b[i]); return res; } template <class T, class U> string to_string(pair<T, U> p); template <class T> string to_string(T v) { bool fst = 1; string res = ""; for (const auto& x : v) { if (!fst) res += " "; fst = 0; res += to_string(x); } return res; } template <class T, class U> string to_string(pair<T, U> p) { return to_string(p.first) + " " + to_string(p.second); } template <class T, class U, class C> string to_string(tuple<T, U, C> p) { return to_string(get<0>(p)) + " " + to_string(get<1>(p)) + " " + to_string(get<2>(p)); } template <class T, class U, class C, class D> string to_string(tuple<T, U, C, D> p) { return to_string(get<0>(p)) + " " + to_string(get<1>(p)) + " " + to_string(get<2>(p)) + " " + to_string(get<3>(p)); } template <class T, class U, class C> void re(tuple<T, U, C>& p); template <class T, class U, class C, class D> void re(tuple<T, U, C, D>& p); template <class T> void re(complex<T>& c); template <class T, class U> void re(pair<T, U>& p); template <class T> void re(vector<T>& v); template <class T, size_t SZ> void re(array<T, SZ>& a); template <class T> void re(T& x) { cin >> x; } void re(double& d) { string t; re(t); d = stod(t); } void re(ld& d) { string t; re(t); d = stold(t); } template <class T, class... U> void re(T& t, U&... u) { re(t); re(u...); } template <class T> void re(complex<T>& c) { T a, b; re(a, b); c = {a, b}; } template <class T, class U> void re(pair<T, U>& p) { re(p.first, p.second); } template <class T> void re(vector<T>& x) { for (auto& a : x) re(a); } template <class T, size_t SZ> void re(array<T, SZ>& x) { for (auto& a : x) re(a); } template <class T, class U, class C> void re(tuple<T, U, C>& p) { re(get<0>(p), get<1>(p), get<2>(p)); } template <class T, class U, class C, class D> void re(tuple<T, U, C, D>& p) { re(get<0>(p), get<1>(p), get<2>(p), get<3>(p)); } template <class T> void pr(T x) { cout << to_string(x); } template <class T, class... U> void pr(const T& t, const U&... u) { pr(t); pr(u...); } void ps() { pr("\n"); } template <class T, class... U> void ps(const T& t, const U&... u) { pr(t); if (sizeof...(u)) pr(" "); ps(u...); } void DBG() { cerr << "]" << endl; } template <class T, class... U> void DBG(const T& t, const U&... u) { cerr << to_string(t); if (sizeof...(u)) cerr << ", "; DBG(u...); } struct chash { const uint64_t C = ll(2e18 * PI) + 71; const int RANDOM = rng(); ll operator()(ll x) const { return __builtin_bswap64((x ^ RANDOM) * C); } }; template <class T> using V = vector<T>; template <class T, size_t SZ> using AR = array<T, SZ>; template <class T> using mpq = priority_queue<T, vector<T>, greater<T>>; template <class T, class U> using um = unordered_map<T, U, chash>; template <class T> using us = unordered_set<T, chash>; const int MOD = 1e9 + 7; template <int MOD, int RT> struct mint { static const int mod = MOD; static constexpr mint rt() { return RT; } int v; explicit operator int() const { return v; } mint() { v = 0; } mint(ll _v) { v = (-MOD < _v && _v < MOD) ? _v : _v % MOD; if (v < 0) v += MOD; } friend bool operator==(const mint& a, const mint& b) { return a.v == b.v; } friend bool operator!=(const mint& a, const mint& b) { return !(a == b); } friend bool operator<(const mint& a, const mint& b) { return a.v < b.v; } friend void re(mint& a) { ll x; re(x); a = mint(x); } friend string to_string(mint a) { return to_string(a.v); } mint& operator+=(const mint& m) { if ((v += m.v) >= MOD) v -= MOD; return *this; } mint& operator-=(const mint& m) { if ((v -= m.v) < 0) v += MOD; return *this; } mint& operator*=(const mint& m) { v = (ll)v * m.v % MOD; return *this; } mint& operator/=(const mint& m) { return (*this) *= inv(m); } friend mint pow(mint a, ll p) { mint ans = 1; assert(p >= 0); for (; p; p /= 2, a *= a) if (p & 1) ans *= a; return ans; } friend mint inv(const mint& a) { assert(a.v != 0); return pow(a, MOD - 2); } mint operator-() const { return mint(-v); } mint& operator++() { return *this += 1; } mint& operator--() { return *this -= 1; } friend mint operator+(mint a, const mint& b) { return a += b; } friend mint operator-(mint a, const mint& b) { return a -= b; } friend mint operator*(mint a, const mint& b) { return a *= b; } friend mint operator/(mint a, const mint& b) { return a /= b; } }; typedef mint<MOD, 5> mi; vector<vector<mi>> scmb; void genComb(int SZ) { scmb.assign(SZ, vector<mi>(SZ)); scmb[0][0] = 1; for (int i = (1); i < (SZ); ++i) for (int j = (0); j < (i + 1); ++j) scmb[i][j] = scmb[i - 1][j] + (j ? scmb[i - 1][j - 1] : 0); } vi invs, fac, ifac; void genFac(int SZ) { invs.resize(SZ), fac.resize(SZ), ifac.resize(SZ); invs[1] = fac[0] = ifac[0] = 1; for (int i = (2); i < (SZ); ++i) invs[i] = MOD - (ll)MOD / i * invs[MOD % i] % MOD; for (int i = (1); i < (SZ); ++i) { fac[i] = (ll)fac[i - 1] * i % MOD; ifac[i] = (ll)ifac[i - 1] * invs[i] % MOD; } } mi comb(int a, int b) { if (a < b || b < 0) return 0; return (ll)fac[a] * ifac[b] % MOD * ifac[a - b] % MOD; } ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; } void setIn(string s) { freopen(s.c_str(), "r", stdin); } void setOut(string s) { freopen(s.c_str(), "w", stdout); } void IOS(int n = 10, string s = "") { ios::sync_with_stdio(0); cin.tie(0); cout.tie(0); cout.precision(n); cerr.precision(n); cerr << fixed; cout << fixed; if (((int)(s).size())) { setIn(s + ".in"), setOut(s + ".out"); } } const int mxN = 2e5; void solve() { ll x, a1, a2; re(x); for (ll i = 1; i * i <= x; ++i) { if (x % i) continue; ll b1 = i, b2 = x / i; if (gcd(b1, b2) == 1) a1 = b1, a2 = b2; } ps(a1, a2); } int main() { IOS(); int t = 1; for (int i = (0); i < (t); ++i) { solve(); } }
#include <bits/stdc++.h> using namespace std; long long gcd(long long x, long long y) { return y == 0 ? x : gcd(y, x % y); } int main() { long long x, b; cin >> x; long long t = sqrt(x); for (long long a = t; a >= 1; a--) { if (x % a) continue; b = x / a; if (gcd(a, b) == 1) { cout << a << " " << b << endl; break; } } return 0; }
#include <bits/stdc++.h> using namespace std; long long a; int gcd(long long a, long long b) { if (b == 0) return a; a %= b; return gcd(b, a); } void solve(long long a) { long long mn = 1e8; long long mx = 0LL; for (long long i = 1; i * i <= a; i++) { if (a % i == 0) { if (a == ((i * a / i) / (gcd(i, a / i)))) { mx = i; mn = a / i; } } } cout << mx << " " << mn << "\n"; } int main() { scanf("%lld", &a); solve(a); return 0; }
#include <bits/stdc++.h> using namespace std; long long res, a, b; void solve(vector<long long> v, long long i, long long x, long long cur) { long long j, k, n = v.size(); if (i == n) { long long x1 = max(cur, x / cur); if (res > x1) { res = x1; a = cur; b = x / cur; } return; } solve(v, i + 1, x, cur); solve(v, i + 1, x, cur * v[i]); } int main() { long long i, j, k, n; cin >> n; map<long long, long long> mp; long long x = n; while (x % 2 == 0) { mp[2]++; x /= 2; } for (i = 3; i * i <= x; i += 2) { while (x % i == 0) { mp[i]++; x /= i; } } if (x > 1) mp[x]++; vector<long long> v; for (auto it = mp.begin(); it != mp.end(); it++) { v.push_back(it->first); } for (i = 0; i < v.size(); i++) { v[i] = pow(v[i], mp[v[i]]); } res = n; a = n; b = 1; solve(v, 0LL, n, 1LL); cout << a << ' ' << b; }
#include <bits/stdc++.h> using namespace std; const double E = 2.718281828459; const double pi = acos(-1.0); const double eps = 1e-9; const int inf = 0x3f3f3f3f; const long long INF = 0x3f3f3f3f3f3f3f3f; const int mod = 1e9 + 7; const int maxn = 1e5 + 10; const int maxm = 1e2; void debug() { cout << "_____five___\n"; } long long a[1000], b[1000]; int tot; void factor(long long n, long long a[1000], long long b[1000], int &tot) { long long i, now; long long temp; temp = (long long)((double)sqrt(n) + 1); tot = 0; now = n; for (i = 2; i <= temp; ++i) if (now % i == 0) { a[++tot] = i; b[tot] = 0; while (now % i == 0) { ++b[tot]; now /= i; } } if (now != 1) { a[++tot] = now; b[tot] = 1; } } long long pu(int x, int y) { long long sum = 1; for (int i = 1; i <= y; ++i) { sum *= x; } return sum; } long long number[100], t; bool cmp(long long x, long long y) { return x > y; } long long gcd(long long x, long long y) { return y == 0 ? x : gcd(y, x % y); } long long putss; int main(int argc, const char *argv[]) { long long x; putss = INF; long long xx, yy; cin >> x; for (long long i = 1; i <= sqrt(x); ++i) { long long j = x / i; if (i * j == x && gcd(i, j) == 1) { if (putss > max(i, j)) { putss = max(i, j); xx = i, yy = j; } } } cout << xx << " " << yy << endl; return 0; }
#include <bits/stdc++.h> const double pi = acos(-1.0); using namespace std; inline long long MAX2(long long a, long long b) { return (a) > (b) ? (a) : (b); } inline long long MAX3(long long a, long long b, long long c) { return (a) > (b) ? ((a) > (c) ? (a) : (c)) : ((b) > (c) ? (b) : (c)); } inline long long MIN2(long long a, long long b) { return (a) < (b) ? (a) : (b); } inline long long MIN3(long long a, long long b, long long c) { return (a) < (b) ? ((a) < (c) ? (a) : (c)) : ((b) < (c) ? (b) : (c)); } int mod = 1e9 + 7; long long gcd(long long a, long long b) { return b == 0 ? a : gcd(b, a % b); } long long powmod(long long a, long long b) { long long res = 1; if (a >= mod) a %= mod; for (; b; b >>= 1) { if (b & 1) res = res * a; if (res >= mod) res %= mod; a = a * a; if (a >= mod) a %= mod; } return res; } unsigned long int setbits(long long n) { unsigned long int count = 0; while (n) { n &= (n - 1); count++; } return count; } int modInverse(int A, int M) { return powmod(A, M - 2); } bool is_prime(long long n) { if (n == 1) { return false; } long long i = 2; while (i * i <= n) { if (n % i == 0) { return false; } i += 1; } return true; } long long lcm(long long a, long long b) { return (a * b) / gcd(a, b); } int main() { ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0); long long n; cin >> n; if (is_prime(n)) { cout << 1 << " " << n << '\n'; return 0; } int end = sqrt(n); long long second = LLONG_MAX, en = LLONG_MAX; for (int i = 1; i <= end; i++) { if (n % i == 0) { long long res1 = i; long long res2 = n / i; if (lcm(res1, res2) == n) { second = res1; en = res2; } } } cout << second << " " << en << '\n'; return 0; }
#include <bits/stdc++.h> long long max(long long a, long long b) { return (a < b) ? b : a; } long long min(long long a, long long b) { return (a > b) ? b : a; } using namespace std; long long x[300], y[300]; long long ab(long long r) { return (r < 0) ? -r : r; } int main() { long long x, ans = LLONG_MAX / 2, bb, aa; cin >> x; map<long long, long long> pr; while (x > 1) { long long br = 1; for (long long i = 2; i * i <= x; i++) { if (x % i == 0) { pr[i]++; x /= i; br = 0; break; } } if (br) { pr[x]++; x = 1; } } for (long long i = 0; i < 1 << pr.size(); i++) { long long a = 1, b = 1; long long te = i; for (auto&& j : pr) { if (te % 2 == 1) { for (long long v = 0; v < j.second; v++) a *= j.first; } else { for (long long v = 0; v < j.second; v++) b *= j.first; } te /= 2; } if (ans > max(a, b)) ans = max(a, b), aa = a, bb = b; } cout << aa << " " << bb << endl; }
#include <bits/stdc++.h> using namespace std; using namespace std; long long int gcd(long long int a, long long int b) { if (a == 0) return b; return gcd(b % a, a); } long long int lcm(long long int a, long long int b) { return (a / gcd(a, b) * b); } int main() { ios_base::sync_with_stdio(false); cin.tie(NULL); ; long long int t; cin >> t; long long int sum = 0; if (t == 1) cout << "1" << " " << "1" << '\n'; else { for (long long int i = 1; i * i < t; ++i) { if (t % i == 0 && lcm(i, t / i) == t) { sum = i; } } cout << sum << " " << t / sum << '\n'; } }
#include <bits/stdc++.h> using namespace std; int prime[1000003], tot; bool vis[1000003]; void shai(long long X) { tot = 0; memset(vis, 0, sizeof(vis)); for (long long i = 2; i < X; i++) { if (!vis[i]) { prime[tot++] = i; } for (long long j = 0; j < tot && prime[j] * i < X; j++) { vis[i * prime[j]] = 1; if (i % prime[j] == 0) { break; } } } } int q[100003], t[100003], len; bool can[10000003]; int main() { long long n, m; cin >> n; if (n == 1) { cout << "1 1"; return 0; } shai((int)(sqrt(n)) + 10); int i = 0; m = n, len = 0; while (1) { if (i >= tot) break; if ((long long)prime[i] * (long long)prime[i] > n) break; if (m % (long long)prime[i] == 0) { m /= prime[i]; ++len; q[len] = i; t[len] = 1; while (m % prime[i] == 0) m /= prime[i], t[len]++; } if (m == 1) break; ++i; } int sqr = (int)sqrt(n) + 1; memset(can, 0, sizeof(can)); can[1] = true; for (register int i = 1; i <= len; i++) { bool f = 0; long long tmp = 1; for (int j = 1; j <= t[i]; j++) { tmp *= prime[q[i]]; if (tmp > sqr) { f = 1; break; } } int lens = sqr / tmp; if (f) continue; for (register int j = lens; j >= 1; --j) if (can[j]) can[j * tmp] = 1; } for (register int i = sqr - 1; i >= 1; i--) { if (can[i]) { printf("%d %I64d", i, n / i); return 0; } } return 1; }
#include <bits/stdc++.h> using namespace std; template <typename Arg1> void __f(const char* name, Arg1&& arg1) { cerr << name << " : " << arg1 << std::endl; } template <typename Arg1, typename... Args> void __f(const char* names, Arg1&& arg1, Args&&... args) { const char* comma = strchr(names + 1, ','); cerr.write(names, comma - names) << " : " << arg1 << " | "; __f(comma + 1, args...); } void __print(int x) { cerr << x; } void __print(long x) { cerr << x; } void __print(long long x) { cerr << x; } void __print(unsigned x) { cerr << x; } void __print(unsigned long x) { cerr << x; } void __print(unsigned long long x) { cerr << x; } void __print(float x) { cerr << x; } void __print(double x) { cerr << x; } void __print(long double x) { cerr << x; } void __print(char x) { cerr << '\'' << x << '\''; } void __print(const char* x) { cerr << '\"' << x << '\"'; } void __print(const string& x) { cerr << '\"' << x << '\"'; } void __print(bool x) { cerr << (x ? "true" : "false"); } template <typename T, typename V> void __print(const pair<T, V>& x) { cerr << '{'; __print(x.first); cerr << ','; __print(x.second); cerr << '}'; } template <typename T> void __print(const T& x) { int f = 0; cerr << '{'; for (auto& i : x) cerr << (f++ ? "," : ""), __print(i); cerr << "}"; } void _print() { cerr << "]\n"; } template <typename T, typename... V> void _print(T t, V... v) { __print(t); if (sizeof...(v)) cerr << ", "; _print(v...); } long long int gcd(long long int a, long long int b) { if (a == 0) return b; return gcd(b % a, a); } long long int lcm(long long int a, long long int b) { return (a * b) / gcd(a, b); } int main(int argc, char* argv[]) { ios::sync_with_stdio(false); cin.tie(0); cout.tie(0); long long int x; cin >> x; vector<long long int> fac; pair<long long int, long long int> ans; for (long long int i = 1; i * i < x; ++i) { if (x % i == 0) fac.push_back(i); } for (auto i = fac.rbegin(); i != fac.rend(); ++i) { long long int y = *i; if (lcm(y, x / y) == x) { ans = {y, x / y}; break; } } if (x == 1) ans = {1, 1}; cout << ans.first << " " << ans.second; return 0; }
#include <bits/stdc++.h> using namespace std; long long int gcd(long long int a, long long int b) { if (a == 0) return b; return gcd(b % a, a); } int main() { ios_base::sync_with_stdio(false); cin.tie(NULL); long long int n; cin >> n; if (n == 1) { cout << "1 1" << "\n"; } else { long long int minn = n; vector<long long int> v; vector<long long int> vv; long long int a = 1, b = n; for (long long int i = 1; i <= sqrt(n); i++) { if (n % i == 0) { long long int x = n / i; if (gcd(i, x) == 1) { long long int k = max(i, x); if (k < minn) { a = min(i, x); b = max(i, x); minn = k; } } } } cout << a << " " << b << "\n"; } return 0; }
#include <bits/stdc++.h> using namespace std; long long gcd(long long a, long long b) { if (b == 0) return a; return gcd(b, a % b); } long long lcm(long long a, long long b) { long long ans = (a * b) / gcd(a, b); return ans; } int main() { long long x; cin >> x; vector<long long> v; for (long long i = 1; i <= (long long)sqrt(x); i++) { if (x % i == 0) { v.push_back(i); } } long long minv = x; for (auto i = v.begin(); i != v.end(); i++) { if (lcm(*i, x / (*i)) == x) { long long temp = max(*i, x / (*i)); minv = min(temp, minv); } } cout << minv << " " << x / minv << endl; return 0; }
#include <bits/stdc++.h> using namespace std; long long GCD(long long a, long long b) { if (b) while ((a %= b) && (b %= a)) ; return a + b; } long long LCM(long long a, long long b) { return a * b / GCD(a, b); } int main() { long long X; cin >> X; long long res = X; long long r1 = 1, r2 = X; for (long long i = 1; i * i <= X; i++) { if (X % i == 0) { long long j = X / i; if (LCM(i, j) == X && res > max(i, j)) { res = max(i, j); r1 = i; r2 = j; } } } cout << r1 << " " << r2 << endl; return 0; }
#include <bits/stdc++.h> #pragma warning(disable : 6031) #pragma warning(disable : 4101) using namespace std; const int INF = 1e9; const long long LINF = 1e18; const double PI = acos(-1); long long x; vector<long long> factors(long long n) { vector<long long> fs; for (long long i = 2; i <= sqrt(n); i++) { if (n % i == 0) { long long f = 1; while (n % i == 0) { f = f * i; n = n / i; } fs.push_back(f); } } if (n > 1) { fs.push_back(n); } return fs; } pair<long long, long long> bruteforce(vector<long long> fs, long long capacity) { long long best = capacity; pair<long long, long long> ans; for (int i = 0; i < (1 << (((int)(fs).size()))); i++) { long long cur_l = 1; long long cur_r = 1; for (int k = 0; k < ((int)(fs).size()); k++) { if ((i >> k) & 1) { cur_l *= fs[k]; } else { cur_r *= fs[k]; } } if (max(cur_l, cur_r) <= best) { best = max(cur_l, cur_r); ans = {cur_l, cur_r}; } } return ans; } int main() { scanf("%lld", &x); pair<long long, long long> k = bruteforce(factors(x), x); printf("%lld %lld\n", k.first, k.second); return 0; }
#include <bits/stdc++.h> using namespace std; const int maxn = 2e5 + 10; void prework() { ios::sync_with_stdio(0); cin.tie(0); cout.tie(0); } struct pair { long long x, y; } arr[maxn]; long long gcd(long long a, long long b) { return b == 0 ? a : gcd(b, a % b); } long long lcm(long long a, long long b) { return a / gcd(a, b) * b; } int main() { prework(); long long x; cin >> x; long long len = 0; for (long long i = 1; i <= sqrt(x) + 1; i++) { if (x % i == 0) { arr[len].x = i; arr[len++].y = x / i; } } long long x1 = arr[0].x, x2 = arr[0].y; for (long long i = 1; i < len; i++) { if (arr[i].x == arr[i].y) continue; if (lcm(arr[i].x, arr[i].y) != x) continue; long long cur1 = max(arr[i].x, arr[i].y); long long cur2 = max(x1, x2); if (cur2 > cur1) { x1 = arr[i].x; x2 = arr[i].y; } } cout << x1 << " " << x2 << endl; return 0; }
#include <bits/stdc++.h> using namespace std; clock_t tp = clock(); const long long mod = 1e9 + 7; long long int power(long long int a, long long int b) { long long int ans = 1; a = a; while (b > 0) { if (b & 1) ans = (ans * a); b >>= 1; a = (a * a); } return ans; } long long int power1(long long int a, long long int b, long long int m = mod) { long long int ans = 1; a %= m; while (b > 0) { if (b & 1) ans = (ans * a) % m; b >>= 1; a = (a * a) % m; } return ans; } long long int gcd(long long int a, long long int b) { if (a == 0) return b; return gcd(b % a, a); } long long int ncr(long long int n, long long int r) { if (n < r) return 0; long long int p = 1, k = 1; if (n - r < r) r = n - r; if (r != 0) { while (r) { p *= n; k *= r; long long int g = gcd(p, k); p /= g; k /= g; n--; r--; } } else p = 1; return p % mod; } long long int lcm(long long int a, long long int b) { return (a / gcd(a, b) * b); } bool compare_increasing(pair<long long int, long long int> l1, pair<long long int, long long int> l2) { if (l1.first != l2.first) return (l1.first < l2.first); else return (l1.second < l2.second); } int main() { ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0); ; int tt = 1; while (tt--) { long long int n, x, y; cin >> n; for (long long int i = 1; i * i <= n; i++) { if (n % i == 0 && gcd(min(i, n / i), max(i, n / i)) == 1) x = i, y = n / i; } cout << x << ' ' << y << '\n'; } return 0; }
#include <bits/stdc++.h> using namespace std; long long int gcd(long long int x, long long int y) { if (x == 0) return y; else return gcd(y % x, x); } int main() { ios_base::sync_with_stdio(false); cin.tie(NULL); long long int x; cin >> x; long long int a1 = 1, a2 = x; for (long long int i = 2; i * i <= x; i++) { if (x % i == 0) { long long int d = x / i; if (gcd(i, d) == 1) { long long int k = max(i, d); if (k < a2) { a2 = max(i, d); a1 = min(i, d); } } } } cout << a1 << " " << a2; }
#include <bits/stdc++.h> using namespace std; long long gcd(long long a, long long b) { if (b == 0) { return a; } else { return gcd(b, a % b); } } int main() { long long X; cin >> X; long long a = 1, b = X; long long m = X; for (long long i = 2; i * i < X; i++) { if (X % i == 0) { long long ta = i; long long tb = X / i; if (X * gcd(ta, tb) == ta * tb) { if (max(ta, tb) < m) { m = max(ta, tb); a = ta; b = tb; } } } } cout << a << " " << b << endl; return 0; }
#include <bits/stdc++.h> using namespace std; long long int gcd(long long int a, long long int b) { if (b == 0) return a; else return gcd(b, a % b); } int main() { long long int n, x, ans, ans1, y; cin >> y; n = (long long int)sqrt((double)y); for (long long int i = n; i > 0; i--) { if (y % i == 0) { x = y / i; if (gcd(i, x) == 1) { ans = i; ans1 = x; break; } } } if (y != 1) cout << ans << ' ' << ans1 << endl; else cout << 1 << ' ' << 1 << endl; }
#include <bits/stdc++.h> using namespace std; long long n, a, b; long long gcd(long long x, long long y) { if (x < y) swap(x, y); if (y == 0) return x; return gcd(y, x % y); } int main() { ios::sync_with_stdio(0); cin.tie(0); cin >> n; for (long long i = 1; i <= sqrt(n); ++i) { if (n % i != 0 || gcd(i, n / i) != 1) continue; a = i; b = n / i; } cout << a << ' ' << b; return 0; }
#include <bits/stdc++.h> using namespace std; long long fun(long long a, long long b) { if (a == 0) return b; return fun(b % a, a); } int main() { long long x; cin >> x; long long ans = 1e18; long long pa, pb; for (long long i = 1; i * i <= x; i++) { long long a = i; long long b = x / i; if ((a * b) == x) { long long g = fun(a, b); long long lcm = x / g; if (lcm == x) { if (ans > b) { ans = b; pa = a; pb = b; } } } } cout << pa << " " << pb << endl; return 0; }
#include <bits/stdc++.h> using namespace std; long long gcd(long long a, long long b) { if (b == 0) return a; else return gcd(b, a % b); } void jabru() { long long n; cin >> n; long long ans = LLONG_MAX; for (long long j = 1; j * j <= n; j++) { if (n % j == 0) { long long here = max(j, n / j); if (gcd(j, n / j) == 1) ans = min(ans, here); } } cout << ans << " " << n / ans << "\n"; } int main() { ios::sync_with_stdio(0); cin.tie(0); int t; t = 1; while (t--) { jabru(); } return 0; }
#include <bits/stdc++.h> using namespace std; using ll = long long; const int MAXN = 1e5 + 9; ll gcd(ll a, ll b) { if (a == 0) return b; return gcd(b % a, a); } int main() { ios::sync_with_stdio(false); ll a; cin >> a; ll b, c, x; for (int i = 0; i < 5; i++) x = sqrt(a); for (ll i = sqrt(a); i > 0; i--) { for (int i = 0; i < 123; i++) a = a; for (int i = 0; i < 123; i++) a = a; for (int i = 0; i < 123; i++) a = a; if (a % i == 0) { if (a / gcd(i, a / i) == a) { b = i; c = a / i; break; } if (i == 1) { b = i; c = a / i; break; } } } cout << b << " " << c << endl; return 0; }
#include <bits/stdc++.h> const long long int N = 2e5 + 5; using namespace std; bool isPrime(long long int n) { if (n == 1) return false; for (long long int i = 2; i * i <= n; i++) { if (n % i == 0) return false; } return true; } long long int gcd(long long int a, long long int b) { if (b == 0) return a; return gcd(b, a % b); } long long int lcm(long long int a, long long int b) { return a / gcd(a, b) * b; } void CSK() { long long int x; cin >> x; long long int as1 = 0, as2 = 0; for (long long int i = 1; i * i <= x; i++) { if (x % i == 0) { if (lcm(i, x / i) == x) { as1 = i; as2 = x / i; } } } cout << as1 << " " << as2 << "\n"; } int32_t main() { ios_base::sync_with_stdio(0); cin.tie(NULL); cout.tie(NULL); cout << fixed; cout.precision(10); long long int __TESTCASES = 1; while (__TESTCASES--) { CSK(); } }
#include <bits/stdc++.h> using namespace std; long long x; int main() { cin >> x; vector<long long> f; for (long long i = 2; i * i <= x; ++i) { if (x % i == 0) { long long cur = 1; while (x % i == 0) { x /= i; cur *= i; } f.push_back(cur); } } if (x > 1) f.push_back(x); int n = f.size(); long long ansa = 1e18, ansb = 1e18; for (int i = 0; i < (1 << n); ++i) { long long a = 1, b = 1; for (int j = 0; j < n; ++j) { if ((i >> j) & 1) a *= f[j]; else b *= f[j]; } if (max(a, b) < max(ansa, ansb)) { ansa = a; ansb = b; } } cout << ansa << " " << ansb << endl; return 0; }
#include <bits/stdc++.h> using namespace std; vector<long long int> factors(long long int number) { vector<long long int> result; for (long long int f = 2; f * f <= number; f++) { if (number % f != 0) continue; long long int factor = 1; while (number % f == 0) { factor *= f; number /= f; } result.push_back(factor); } if (number != 1) result.push_back(number); return result; } int main() { long long int X; cin >> X; vector<long long int> facts = factors(X); int n = facts.size(); long long int minmax = X + 1; long long int bestProduct = -1; long long int bestNotProduct = -1; for (int bitset = 0; bitset < (1 << n); bitset++) { long long int product = 1; long long int notProduct = 1; for (int i = 0; i < n; i++) { if (bitset & (1 << i)) { product *= facts[i]; } else notProduct *= facts[i]; } if (minmax > max(product, notProduct)) { minmax = max(product, notProduct); bestProduct = product; bestNotProduct = notProduct; } } cout << bestProduct << " " << bestNotProduct << endl; return 0; }
#include <bits/stdc++.h> using namespace std; using namespace std; template <typename Arg1> void __f(const char *name, Arg1 &&arg1) { cerr << name << " : " << arg1 << '\n'; } template <typename Arg1, typename... Args> void __f(const char *names, Arg1 &&arg1, Args &&...args) { const char *comma = strchr(names + 1, ','); cerr.write(names, comma - names) << " : " << arg1 << " | "; __f(comma + 1, args...); } long long gcd(long long a, long long b) { if (a < b) return gcd(b, a); else if (b == 0) return a; else return gcd(b, a % b); } long long lcm(long long a, long long b) { return (a * b) / gcd(a, b); } long long isPrime(long long n) { long long p = (long long)sqrt(n); for (long long i = 2; 2 < p + 1 ? i < p + 1 : i > p + 1; 2 < p + 1 ? i += 1 : i -= 1) if (n % i == 0) return 0; return 1; } long long pow(long long b, long long e) { if (e == 0) return 1; else if (e % 2 == 0) { long long a = pow(b, e / 2); return a * a; } else { long long a = pow(b, e / 2); return b * a * a; } } long long pow_m(long long x, long long y, long long m = 1000000007) { x = x % m; long long res = 1; while (y) { if (y & 1) res = res * x; res %= m; y = y >> 1; x = x * x; x %= m; } return res; } long long modInverse(long long a, long long m) { return pow_m(a, m - 2, m); } long long max(long long a, long long b) { if (a >= b) return a; else return b; } long long min(long long a, long long b) { if (a <= b) return a; else return b; } long long sum(vector<long long> v) { long long sm = 0; for (long long i = 0; 0 < v.size() ? i < v.size() : i > v.size(); 0 < v.size() ? i += 1 : i -= 1) sm += v[i]; return sm; } long long bin_coff(long long n, long long k, long long m) { vector<vector<long long> > ans(n + 1, vector<long long>(k, 0)); for (long long i = 0; 0 < n + 1 ? i < n + 1 : i > n + 1; 0 < n + 1 ? i += 1 : i -= 1) { for (long long j = 0; 0 < min(i, k) + 1 ? j < min(i, k) + 1 : j > min(i, k) + 1; 0 < min(i, k) + 1 ? j += 1 : j -= 1) { if (j == 0 || j == i) ans[i][j] = 1; else ans[i][j] = ans[i - 1][j - 1] % m + ans[i - 1][j] % m; } } return ans[n][k] % m; } long long inverse(long long i) { if (i == 1) return 1; return (1000000007 - ((1000000007 / i) * inverse(1000000007 % i)) % 1000000007 + 1000000007) % 1000000007; } long long maxProduct(vector<long long> arr, long long n, long long k) { sort(arr.begin(), arr.end()); long long prod = 1; if (arr[n - 1] == 0 && (k & 1)) return 0; if (arr[n - 1] <= 0 && (k & 1)) { for (long long i = n - 1; i >= n - k; i--) prod *= arr[i]; return prod; } long long i = 0, j = n - 1; if (k & 1) { prod *= arr[j]; j--; k--; } k >>= 1; for (long long itr = 0; itr < k; itr++) { long long left_product = arr[i] * arr[i + 1]; long long right_product = arr[j] * arr[j - 1]; if (left_product > right_product) { prod *= left_product; i += 2; } else { prod *= right_product; j -= 2; } } return prod; } int32_t main() { ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL); ; long long x, ans; cin >> x; for (long long i = 1; 1 < sqrt(x) + 1 ? i < sqrt(x) + 1 : i > sqrt(x) + 1; 1 < sqrt(x) + 1 ? i += 1 : i -= 1) { if (x % i == 0 && lcm(i, x / i) == x) ans = i; } cout << ans << " " << x / ans << endl; return 0; }
#include <bits/stdc++.h> using namespace std; const int mod = 1e9 + 7; inline long long add(long long a, long long b) { a += b; if (a >= mod) a -= mod; return a; } inline long long sub(long long a, long long b) { a -= b; if (a < 0) a += mod; return a; } inline long long mul(long long a, long long b) { return (long long)((long long)a * b % mod); } vector<vector<long long> > adj, dp; vector<long long> cnt, lvl; void DFSUtil(long long u, long long p) { if (u != 0) { lvl[u] = lvl[p] + 1; } dp[u][0] = p; for (long long i = (1); i <= (20); i++) { dp[u][i] = dp[dp[u][i - 1]][i - 1]; } for (auto it : adj[u]) if (it != p) DFSUtil(it, u); } void DFS() { long long V = adj.size(); lvl.assign(V, 0); DFSUtil(0, 0); } long long lca(long long x, long long y) { if (x == y) return 0; if (lvl[x] < lvl[y]) swap(x, y); long long d = lvl[x] - lvl[y]; long long x1 = x; for (long long i = (0); i <= (20); i++) if ((1 << i) & d) x1 = dp[x1][i]; if (x1 == y) return d; long long xx = x1, yy = y; for (long long i = (20); i >= (0); i--) if (dp[xx][i] != dp[yy][i]) { d += 2 * (1 << i); xx = dp[xx][i]; yy = dp[yy][i]; } d += 2; return d; } bool query() { long long a, b, x, y, k; cin >> a >> b >> x >> y >> k; x--; y--; a--; b--; long long v1 = lca(x, y), v2 = lca(x, a), v3 = lca(x, b), v4 = lca(y, a), v5 = lca(y, b); if (v1 <= k && (k - v1) % 2 == 0) { return true; } if ((v2 + v5 + 1) <= k && (k - (v2 + v5 + 1)) % 2 == 0) { return true; } if ((v3 + v4 + 1) <= k && (k - (v3 + v4 + 1)) % 2 == 0) { return true; } return false; } int main() { ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL); ; long long t = 1; while (t--) { long long n; cin >> n; adj.resize(n + 1); for (long long i = (1); i <= (n - 1); i++) { long long p, q; cin >> p >> q; p--; q--; adj[p].push_back(q); adj[q].push_back(p); } dp.assign(n + 1, vector<long long>(21, 0)); DFS(); long long m; cin >> m; for (long long i = (1); i <= (m); i++) { if (query()) cout << "YES\n"; else cout << "NO\n"; } } return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 1e5 + 10; const int logN = 17; int n, q, h[N], par[logN][N]; vector<int> adj[N]; void Dfs(int u, int p) { for (int i = 1; i <= logN - 1; i++) par[i][u] = par[i - 1][par[i - 1][u]]; for (int v : adj[u]) if (v != p) { h[v] = h[u] + 1; par[0][v] = u; Dfs(v, u); } } int LCA(int u, int v) { if (h[u] > h[v]) swap(u, v); for (int i = logN - 1; i >= 0; i--) if (h[u] <= h[v] - (1 << i)) v = par[i][v]; if (v == u) return u; for (int i = logN - 1; i >= 0; i--) if (par[i][u] != par[i][v]) { u = par[i][u]; v = par[i][v]; } return par[0][u]; } int Dist(int u, int v) { int lca = LCA(u, v); return h[u] + h[v] - 2 * h[lca]; } int main() { scanf("%d", &n); for (int i = 1; i <= n - 1; i++) { int u, v; scanf("%d %d", &u, &v); adj[u].push_back(v); adj[v].push_back(u); } Dfs(1, 1); scanf("%d", &q); while (q--) { int x, y, a, b, k; scanf("%d %d %d %d %d", &x, &y, &a, &b, &k); int tmp = Dist(a, b); if (k >= tmp && (k - tmp) % 2 == 0) { printf("YES\n"); continue; } tmp = Dist(a, x) + 1 + Dist(y, b); if (k >= tmp && (k - tmp) % 2 == 0) { printf("YES\n"); continue; } tmp = Dist(a, y) + 1 + Dist(x, b); if (k >= tmp && (k - tmp) % 2 == 0) { printf("YES\n"); continue; } printf("NO\n"); } }
#include <bits/stdc++.h> using namespace std; vector<long long int> adj[100005]; long long int n; long long int p[100005][35]; long long int parent[100005]; long long int level[100005]; void dfs(long long int v, long long int prev) { for (auto i : adj[v]) { if (i == prev) continue; parent[i] = v; level[i] = level[v] + 1; dfs(i, v); } } void preprocess() { for (long long int i = 1; i < 100005; i++) { for (long long int j = 0; j < 35; j++) { p[i][j] = -1; } } for (long long int i = 1; i < n + 1; i++) { p[i][0] = parent[i]; } for (long long int j = 1; j < int(log2(n)) + 1; j++) { for (long long int i = 1; i < n + 1; i++) { if (p[i][j - 1] != -1) p[i][j] = p[p[i][j - 1]][j - 1]; } } } long long int findnparent(long long int u, long long int dist) { while (dist > 0) { int raise_by = log2(dist); u = p[u][raise_by]; dist -= (1 << raise_by); } return u; } long long int LCA(long long int u, long long int v) { if (level[u] < level[v]) swap(u, v); int dist = level[u] - level[v]; u = findnparent(u, dist); if (u == v) return u; for (long long int j = 35 - 1; j > -1; j--) { if (p[u][j] != -1 and (p[u][j] != p[v][j])) { u = p[u][j]; v = p[v][j]; } } return parent[u]; } long long dis(long long x, long long y) { long long l1 = LCA(x, y); return level[x] + level[y] - 2 * level[l1]; } int main() { ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0); cout.precision(15); long long int e, f, q; cin >> n; for (long long int i = 0; i < n - 1; i++) { cin >> e >> f; adj[e].push_back(f); adj[f].push_back(e); } level[1] = 0; parent[1] = 1; dfs(1, 0); preprocess(); cin >> q; while (q--) { long long int x, y, a, b, k; cin >> x >> y >> a >> b >> k; long long int lab = LCA(a, b); long long int dab = level[a] + level[b] - 2 * level[lab]; long long int lax = LCA(a, x); long long int dax = level[a] + level[x] - 2 * level[lax]; long long int lby = LCA(y, b); long long int dby = level[b] + level[y] - 2 * level[lby]; long long int lay = LCA(a, y); long long int day = level[a] + level[y] - 2 * level[lay]; long long int lbx = LCA(x, b); long long int dbx = level[x] + level[b] - 2 * level[lbx]; if (k >= (1 + dax + dby) && (k - 1 - dax - dby) % 2 == 0) cout << "YES\n"; else if (k >= (1 + day + dbx) && (k - 1 - day - dbx) % 2 == 0) cout << "YES\n"; else if (k >= dab && (k - dab) % 2 == 0) cout << "YES\n"; else cout << "NO\n"; } }
#include <bits/stdc++.h> using namespace std; typedef pair<int, int> PII; long long qpow(long long a, long long b, long long m) { long long ans = 1; while (b) { if (b & 1) ans = ans * a % m; a = a * a % m, b >>= 1; } return ans; } long long qpow(long long a, long long b) { long long ans = 1; while (b) { if (b & 1) ans = ans * a; a = a * a, b >>= 1; } return ans; } long long qmul(long long a, long long b, long long m) { long long res = 0; while (b > 0) { if (b & 1) res = (res + a) % m; a = (a + a) % m; b >>= 1; } return res; } long long gcd(long long a, long long b) { return b == 0 ? a : gcd(b, a % b); } long long lcm(long long a, long long b) { return a / gcd(a, b) * b; } long long inv(long long t, long long p) { return t == 1 ? 1 : (p - p / t) * inv(p % t, p) % p; } long long exgcd(long long a, long long b, long long &x, long long &y) { if (b == 0) { x = 1; y = 0; return a; } long long r = exgcd(b, a % b, y, x); y -= (a / b) * x; return r; } long long inv1(long long a, long long p) { long long d, x, y; d = exgcd(a, p, x, y); return d == 1 ? (x % p + p) % p : -1; } template <typename T, typename B> T Add(T a, B b, long long m) { return a + b >= m ? (a + b) % m : a + b; } template <typename T, typename B> T Sub(T a, B b, long long m) { return a - b < 0 ? (a - b + m) % m : a - b; } template <class T> void _sf(T &x) { cin >> x; } void _sf(int &x) { scanf("%d", &x); } void _sf(long long &x) { scanf("%lld", &x); } void _sf(double &x) { scanf("%lf", &x); } void _sf(char &x) { scanf(" %c", &x); } void _sf(char *x) { scanf("%s", x); } void sf() {} template <class T, class... U> void sf(T &head, U &...tail) { _sf(head); sf(tail...); } template <class T> void _pf(const T &x) { cout << x; } void _pf(const int &x) { printf("%d", x); } void _pf(const long long &x) { printf("%lld", x); } void _pf(const double &x) { printf("%.16f", x); } void _pf(const char &x) { putchar(x); } void _pf(const char *x) { printf("%s", x); } template <class T, class U> void _pf(const pair<T, U> &x) { pf(x.first); putchar(' '); pf(x.second); } template <class T> void _pf(const vector<T> &x) { for (auto i = x.begin(); i != x.end(); _pf(*i++)) if (i != x.cbegin()) putchar(' '); } void pf() {} template <class T, class... U> void pf(const T &head, const U &...tail) { _pf(head); putchar(sizeof...(tail) ? ' ' : '\n'); pf(tail...); } template <typename T> inline void read(T &x) { x = 0; static int p; p = 1; static char c; c = getchar(); while (!isdigit(c)) { if (c == '-') p = -1; c = getchar(); } while (isdigit(c)) { x = (x << 1) + (x << 3) + (c - 48); c = getchar(); } x *= p; } const bool IOS = false; const double PI = acos(-1); const double eps = 1e-8; const long long linf = 0x3f3f3f3f3f3f3f3f; const long long INV2 = 500000004; const long long mod = 1e9 + 7; const int inf = 0x3f3f3f3f; const int maxn = 200000 + 10; int n, m, s, num = 0, head[1000001], dep[1000001], f[1000001][23]; int a1, a2; struct edg { int next, to; } edge[1000001]; void edge_add(int u, int v) { num++; edge[num].next = head[u]; edge[num].to = v; head[u] = num; edge[++num].next = head[v]; edge[num].to = u; head[v] = num; } void dfs(int u, int father) { dep[u] = dep[father] + 1; for (int i = 1; (1 << i) <= dep[u]; i++) { f[u][i] = f[f[u][i - 1]][i - 1]; } for (int i = head[u]; i; i = edge[i].next) { int v = edge[i].to; if (v == father) continue; f[v][0] = u; dfs(v, u); } } int lca(int x, int y) { if (dep[x] < dep[y]) swap(x, y); for (int i = 20; i >= 0; i--) { if (dep[f[x][i]] >= dep[y]) x = f[x][i]; if (x == y) return x; } for (int i = 20; i >= 0; i--) { if (f[x][i] != f[y][i]) { x = f[x][i]; y = f[y][i]; } } return f[x][0]; } int dis[maxn]; void bfs(int s) { queue<int> q; q.push(s); dis[s] = 1; while (!q.empty()) { int nx = q.front(); q.pop(); for (int i = head[nx]; i; i = edge[i].next) { int v = edge[i].to; if (dis[v]) continue; dis[v] = dis[nx] + 1; q.push(v); } } } void Main(); int main() { if (IOS) std::ios::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL); Main(); 0; return 0; } void Main() { sf(n); for (int i = 1; i <= n - 1; ++i) { int u, v; sf(u, v); edge_add(u, v); } dfs(1, 0); bfs(1); sf(m); while (m--) { int a, b, x, y, k; sf(x, y, a, b, k); int f = lca(a, b); int len = dis[a] + dis[b] - 2 * dis[f]; if (k >= len && (k - len) % 2 == 0) { pf("Yes"); continue; } else { int f1 = lca(a, x), f2 = lca(b, y); len = dis[a] + dis[x] - 2 * dis[f1] + dis[b] + dis[y] - 2 * dis[f2] + 1; if (k >= len && (k - len) % 2 == 0) { pf("Yes"); continue; } f1 = lca(a, y), f2 = lca(b, x); len = dis[a] + dis[y] - 2 * dis[f1] + dis[b] + dis[x] - 2 * dis[f2] + 1; if (k >= len && (k - len) % 2 == 0) { pf("Yes"); continue; } } pf("No"); } }
#include <bits/stdc++.h> using namespace std; using ll = long long; using ld = long double; template <typename T> using V = vector<T>; template <typename T> using VV = vector<vector<T>>; const ll mod = 1000000007; const ll INF = 1000000099; const ll LINF = (ll)(1e18 + 99); const vector<ll> dx = {-1, 1, 0, 0}, dy = {0, 0, -1, 1}; template <typename T, typename U> inline bool chmin(T& t, const U& u) { if (t > u) { t = u; return 1; } return 0; } template <typename T, typename U> inline bool chmax(T& t, const U& u) { if (t < u) { t = u; return 1; } return 0; } template <typename T> inline T gcd(T a, T b) { return b ? gcd(b, a % b) : a; } template <typename T, typename Y> inline T mpow(T a, Y n) { T res = 1; for (; n; n >>= 1) { if (n & 1) res = res * a; a = a * a; } return res; } template <typename T> struct LCA { int root, lg; vector<vector<T>> e; vector<T> dps; vector<vector<T>> anc; LCA(int _root, vector<vector<T>>& _e) : root(_root), lg(32 - __builtin_clz(_e.size())), e(_e), dps(_e.size()) { int numV = _e.size(); anc.assign(lg, vector<T>(numV, -1)); dfs(root, -1, 0); for (int i = 0; i < lg - 1; i++) { for (int j = 0; j < numV; j++) { if (anc[i][j] < 0) anc[i + 1][j] = -1; else anc[i + 1][j] = anc[i][anc[i][j]]; } } } void dfs(int now, int par, int d) { anc[0][now] = par; dps[now] = d; for (int i = 0; i < (int)e[now].size(); i++) { if (e[now][i] != par) dfs(e[now][i], now, d + 1); } } int get_lca(int a, int b) { if (dps[a] < dps[b]) swap(a, b); int dif = dps[a] - dps[b]; for (int i = lg - 1; 0 <= i; i--) { if (dif < (1 << i)) continue; dif -= (1 << i); a = anc[i][a]; } if (a == b) return a; for (int i = lg - 1; 0 <= i; i--) { if (anc[i][a] != anc[i][b]) { a = anc[i][a]; b = anc[i][b]; } } return anc[0][a]; } }; V<int> dis; signed main() { cin.tie(0); ios::sync_with_stdio(false); cout << fixed << setprecision(20); ll n; cin >> n; VV<int> e(n, V<int>(0)); int x, y, a, b, k; for (ll i = 0; i < (ll)(n - 1); ++i) { cin >> a >> b; a--; b--; e[a].push_back(b); e[b].push_back(a); } dis.assign(n, INF); queue<int> q; q.push(0); q.push(0); dis[0] = 0; while (q.size()) { int now = q.front(); q.pop(); int d = q.front(); q.pop(); for (ll i = 0; i < (ll)((ll)(e[now]).size()); ++i) { if (dis[e[now][i]] == INF) { dis[e[now][i]] = d + 1; q.push(e[now][i]); q.push(d + 1); } } } LCA<int> lca(0, e); int qq; cin >> qq; bool can = false; ll da, db, loop; while (qq--) { cin >> x >> y >> a >> b >> k; x--; y--; a--; b--; can = false; int l = lca.get_lca(a, b); if ((dis[a] + dis[b] - 2 * dis[l]) % 2 == k % 2 && (dis[a] + dis[b] - 2 * dis[l]) <= k) can = true; da = dis[a] + dis[x] - 2 * dis[lca.get_lca(a, x)]; db = dis[y] + dis[b] - 2 * dis[lca.get_lca(y, b)]; if ((da + db + 1) % 2 == k % 2 && (da + db + 1) <= k) can = true; da = dis[a] + dis[y] - 2 * dis[lca.get_lca(a, y)]; db = dis[x] + dis[b] - 2 * dis[lca.get_lca(x, b)]; if ((da + db + 1) % 2 == k % 2 && (da + db + 1) <= k) can = true; if (can) cout << "YES" << '\n'; else cout << "NO" << '\n'; } }
#include <bits/stdc++.h> using namespace std; const int INF = 0x3f3f3f3f; const int N = 1e5; vector<int> v[N + 5]; int vis[N + 5]; int d[N + 5], f[N + 5][50]; int n; int t; queue<int> q; void bfs() { q.push(1); d[1] = 1; while (q.size()) { int x = q.front(); q.pop(); for (auto y : v[x]) { if (d[y]) continue; d[y] = d[x] + 1; f[y][0] = x; for (int j = 1; j <= t; j++) f[y][j] = f[f[y][j - 1]][j - 1]; q.push(y); } } } int lca(int x, int y) { if (d[x] > d[y]) swap(x, y); for (int i = t; i >= 0; i--) if (d[f[y][i]] >= d[x]) y = f[y][i]; if (x == y) return x; for (int i = t; i >= 0; i--) { if (f[x][i] != f[y][i]) { x = f[x][i]; y = f[y][i]; } } return f[x][0]; } int main() { scanf("%d", &n); t = (int)(log(n) / log(2.0)) + 1; for (int i = 1; i < n; i++) { int uu, vv; scanf("%d%d", &uu, &vv); v[uu].push_back(vv); v[vv].push_back(uu); } bfs(); int q; scanf("%d", &q); while (q--) { int x, y, a, b, k; scanf("%d%d%d%d%d", &x, &y, &a, &b, &k); int dis1 = d[a] + d[b] - 2 * d[lca(a, b)]; int dis2 = d[a] + d[x] - 2 * d[lca(x, a)] + d[b] + d[y] - 2 * d[lca(y, b)] + 1; int dis3 = d[a] + d[y] - 2 * d[lca(y, a)] + d[b] + d[x] - 2 * d[lca(x, b)] + 1; bool f = false; if (k >= dis1) { if ((k - dis1) % 2 == 0) f = true; } if (k >= dis2) { if ((k - dis2) % 2 == 0) f = true; } if (k >= dis3) { if ((k - dis3) % 2 == 0) f = true; } if (f) printf("YES\n"); else printf("NO\n"); } return 0; }
#include <bits/stdc++.h> using namespace std; struct edge { int t, next; } e[100010 * 2]; int fa[100010][30], head[100010], p, n, m, s = 1, depth[100010]; void add_edge(int s, int t) { p++; e[p].t = t; e[p].next = head[s]; head[s] = p; } void dfs(int p, int fr) { depth[p] = depth[fr] + 1; fa[p][0] = fr; for (int i = 1; (1 << i) <= depth[p]; i++) { fa[p][i] = fa[fa[p][i - 1]][i - 1]; } for (int i = head[p]; i; i = e[i].next) { if (!depth[e[i].t]) { dfs(e[i].t, p); } } } int LCA(int x, int y) { if (depth[x] > depth[y]) swap(x, y); for (int i = 20; i >= 0; i--) { if (depth[x] <= depth[y] - (1 << i)) { y = fa[y][i]; } } if (x == y) return x; for (int i = 20; i >= 0; i--) { if (fa[x][i] == fa[y][i]) continue; x = fa[x][i]; y = fa[y][i]; } return fa[x][0]; } int main() { scanf("%d", &n); for (int i = 1; i < n; i++) { int x, y; scanf("%d%d", &x, &y); add_edge(x, y); add_edge(y, x); } dfs(s, 0); scanf("%d", &m); while (m--) { int x, y, a, b, k; scanf("%d%d%d%d%d", &x, &y, &a, &b, &k); int lca_ab = LCA(a, b); int lca_ax = LCA(a, x); int lca_ay = LCA(a, y); int lca_bx = LCA(b, x); int lca_by = LCA(b, y); int lca_xy = LCA(x, y); int dis1 = depth[a] + depth[b] - 2 * depth[lca_ab]; int dis2 = (depth[a] + depth[x] - 2 * depth[lca_ax]) + 1 + (depth[y] + depth[b] - 2 * depth[lca_by]); int dis3 = (depth[a] + depth[y] - 2 * depth[lca_ay]) + 1 + (depth[x] + depth[b] - 2 * depth[lca_bx]); int od = 0x7fffffff, ev = 0x7ffffffe; if (dis1 & 1) od = min(od, dis1); else ev = min(ev, dis1); if (dis2 & 1) od = min(od, dis2); else ev = min(ev, dis2); if (dis3 & 1) od = min(od, dis3); else ev = min(ev, dis3); if (k & 1) { if (k < od) { puts("NO"); } else { puts("YES"); } } else { if (k < ev) { puts("NO"); } else { puts("YES"); } } } return 0; }
#include <bits/stdc++.h> using namespace std; const int maxn = 1e5 + 5; int fi[maxn], ne[maxn * 2], dui[maxn * 2], qc[maxn]; int cc[17]; int f[maxn][17]; int dep[maxn]; int i, j, k, l, m, n, x, y, a, b, now, tmp; int q; bool bz; void add(int x, int y) { if (fi[x] == 0) fi[x] = ++now; else ne[qc[x]] = ++now; dui[now] = y; qc[x] = now; } void dfs(int x, int y) { int i = fi[x]; f[x][0] = y; dep[x] = dep[y] + 1; while (i) { if (dui[i] == y) { i = ne[i]; continue; } dfs(dui[i], x); i = ne[i]; } } int fd_dis(int x, int y) { int i, z, ans = 0; if (dep[x] < dep[y]) { z = x; x = y; y = z; } for (i = 16; i >= 0; i--) if (dep[x] - cc[i] >= dep[y]) { ans = ans + cc[i]; x = f[x][i]; } for (i = 16; i >= 0; i--) if (f[x][i] != f[y][i]) { ans = ans + cc[i] + cc[i]; x = f[x][i]; y = f[y][i]; } if (x != y) ans = ans + 2; return ans; } bool check(int x) { if (x <= k && (k - x) % 2 == 0) return true; else return false; } int main() { scanf("%d", &n); for (i = 1; i <= n - 1; i++) { scanf("%d%d", &x, &y); add(x, y); add(y, x); } cc[0] = 1; for (i = 1; i <= 16; i++) cc[i] = cc[i - 1] * 2; dfs(1, 0); for (j = 1; j <= 16; j++) for (i = 1; i <= n; i++) f[i][j] = f[f[i][j - 1]][j - 1]; scanf("%d", &q); while (q--) { scanf("%d%d%d%d%d", &x, &y, &a, &b, &k); bz = false; tmp = fd_dis(a, b); if (check(tmp)) { printf("YES\n"); continue; } tmp = fd_dis(a, x) + fd_dis(y, b) + 1; if (check(tmp)) { printf("YES\n"); continue; } tmp = fd_dis(a, y) + fd_dis(x, b) + 1; if (check(tmp)) { printf("YES\n"); continue; } tmp = fd_dis(a, x) + 2 + fd_dis(x, y) + fd_dis(y, b); if (check(tmp)) { printf("YES\n"); continue; } tmp = fd_dis(a, y) + 2 + fd_dis(x, y) + fd_dis(x, b); if (check(tmp)) { printf("YES\n"); continue; } tmp = fd_dis(a, x) + 1 + fd_dis(x, y) + fd_dis(x, b); if (check(tmp)) { printf("YES\n"); continue; } tmp = fd_dis(a, y) + 1 + fd_dis(x, y) + fd_dis(y, b); if (check(tmp)) { printf("YES\n"); continue; } tmp = fd_dis(a, x) + 1 + fd_dis(x, y) + fd_dis(x, b); if (check(tmp)) { printf("YES\n"); continue; } tmp = fd_dis(a, y) + 1 + fd_dis(x, y) + fd_dis(y, b); if (check(tmp)) { printf("YES\n"); continue; } printf("NO\n"); } return 0; }
#include <bits/stdc++.h> using namespace std; int n, u, v, q, xx, yy, aa, bb, kk, pp, b[100005], c[100005][20], d[100005], e[100005]; vector<int> a[100005]; void dfs(int x) { d[x] = ++pp; for (int i = 0; i < a[x].size(); ++i) { if (b[a[x][i]] == -1) { b[a[x][i]] = b[x] + 1; c[a[x][i]][0] = x; dfs(a[x][i]); } } e[x] = ++pp; } int anc(int x, int y) { if (d[x] <= d[y] && e[y] <= e[x]) return 1; else return 0; } int lca(int x, int y) { if (anc(x, y)) return x; if (anc(y, x)) return y; for (int i = 17; i >= 0; --i) { if (!anc(c[x][i], y)) x = c[x][i]; } return c[x][0]; } int dist(int x, int y) { return b[x] + b[y] - b[lca(x, y)] * 2; } int check(int kk, int xx) { return kk >= xx && (kk - xx) % 2 == 0; } int main() { scanf("%d", &n); memset(b, -1, sizeof(b)); for (int i = 1; i < n; ++i) { scanf("%d %d", &u, &v); a[u].push_back(v); a[v].push_back(u); } b[1] = 0; c[1][0] = 1; dfs(1); for (int i = 1; i <= 17; ++i) { for (int j = 1; j <= n; ++j) c[j][i] = c[c[j][i - 1]][i - 1]; } scanf("%d", &q); for (int i = 1; i <= q; ++i) { scanf("%d %d %d %d %d", &xx, &yy, &aa, &bb, &kk); if (check(kk, dist(aa, bb)) || check(kk, dist(aa, xx) + dist(bb, yy) + 1) || check(kk, dist(aa, xx) + dist(bb, yy) + dist(xx, yy) + 2) || check(kk, dist(aa, yy) + dist(bb, xx) + 1) || check(kk, dist(aa, yy) + dist(bb, xx) + dist(xx, yy) + 2)) puts("YES"); else puts("NO"); } return 0; }
#include <bits/stdc++.h> using namespace std; template <typename Arg1> void __f(const char* name, Arg1&& arg1) { std::cerr << name << " : " << arg1 << '\n'; } template <typename Arg1, typename... Args> void __f(const char* names, Arg1&& arg1, Args&&... args) { const char* comma = strchr(names + 1, ','); std::cerr.write(names, comma - names) << " : " << arg1 << " | "; __f(comma + 1, args...); } template <typename T, typename U> static inline void amin(T& x, U y) { if (y < x) x = y; } template <typename T, typename U> static inline void amax(T& x, U y) { if (x < y) x = y; } long long max(long long a, long long b) { return (a > b) ? a : b; } long long min(long long a, long long b) { return (a < b) ? a : b; } const long long N = 1e5 + 10; long long n, l; std::vector<vector<long long> > adj(N); long long timer; vector<long long> tin(10000), tout(10000); vector<vector<long long> > up; vector<long long> lvl(N, 0); void dfs(long long v, long long p, long long level) { tin[v] = ++timer; lvl[v] = level; up[v][0] = p; for (long long i = 1; i < l + 1; i++) { up[v][i] = up[up[v][i - 1]][i - 1]; } for (auto i : adj[v]) if (i != p) dfs(i, v, level + 1); tout[v] = ++timer; } bool is_ancestor(long long u, long long v) { return tin[u] <= tin[v] && tout[u] >= tout[v]; } long long lca(long long u, long long v) { if (is_ancestor(u, v)) return u; if (is_ancestor(v, u)) return v; for (long long i = l; i >= 0; --i) { if (!is_ancestor(up[u][i], v)) u = up[u][i]; } return up[u][0]; } void preprocess(long long root) { tin.resize(n + 1); tout.resize(n + 1); timer = 0; l = ceil(log2(n + 1)); up.assign(n + 100, vector<long long>(l + 1)); dfs(root, root, 1); } long long dist(long long x, long long y) { long long a = lca(x, y); return abs(lvl[a] - lvl[x]) + abs(lvl[a] - lvl[y]); } long long solve() { cin >> n; for (long long i = 0; i < n - 1; i++) { long long u, v; cin >> u >> v; adj[u].push_back(v); adj[v].push_back(u); } preprocess(1); long long a = lca(3, 5); long long q; cin >> q; while (q--) { long long x, y, a, b, k; cin >> x >> y >> a >> b >> k; long long p = dist(a, b); if ((p - k) % 2 == 0 && p <= k) { cout << "YES" << '\n'; continue; } p = dist(a, x) + dist(y, b) + 1; if ((p - k) % 2 == 0 && p <= k) { cout << "YES" << '\n'; continue; } p = dist(a, y) + dist(x, b) + 1; if ((p - k) % 2 == 0 && p <= k) { cout << "YES" << '\n'; continue; } cout << "NO" << '\n'; } return 0; } signed main() { ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0); long long t = 1; while (t--) { solve(); } return 0; }
#include <bits/stdc++.h> using namespace std; const int MAXN = 5e5 + 5; struct edge { int next, v; } e[MAXN << 1]; int n, q, root, cnt, head[MAXN], dep[MAXN], anc[MAXN][30]; void addEdge(int x, int y) { e[++cnt].v = y; e[cnt].next = head[x]; head[x] = cnt; } void dfs(int x) { for (int i = head[x]; i != -1; i = e[i].next) { int y = e[i].v; if (y == anc[x][0]) continue; dep[y] = dep[x] + 1; anc[y][0] = x; dfs(y); } } void init() { cnt = 0; root = 1; memset(head, -1, sizeof(head)); } int lca(int a, int b) { if (dep[a] > dep[b]) swap(a, b); int h = dep[b] - dep[a]; for (int i = 0; (1 << i) <= h; i++) if ((1 << i) & h) b = anc[b][i]; if (a != b) { for (int i = (int)log2(dep[a]); i >= 0; i--) { if (anc[a][i] != anc[b][i]) { a = anc[a][i]; b = anc[b][i]; } } a = anc[a][0]; } return a; } int dist(int x, int y) { return dep[x] + dep[y] - 2 * dep[lca(x, y)]; } int main() { init(); scanf("%d", &n); for (int i = 1; i < n; i++) { int x, y; scanf("%d %d", &x, &y); addEdge(x, y); addEdge(y, x); } dep[root] = 0; dfs(root); for (int j = 1; (1 << j) <= n; j++) { for (int i = 1; i <= n; i++) { anc[i][j] = anc[anc[i][j - 1]][j - 1]; } } scanf("%d", &q); for (int kk = 1; kk < 10; kk++) int jj = kk + 1; for (int i = 1; i <= q; i++) { int x, y, a, b, k; scanf("%d %d %d %d %d", &x, &y, &a, &b, &k); int temp1 = dist(a, b); int temp2 = min(dist(a, x) + dist(y, b), dist(a, y) + dist(x, b)) + 1; int ans = k + 1; if (k % 2 == temp1 % 2) ans = min(ans, temp1); if (k % 2 == temp2 % 2) ans = min(ans, temp2); if (ans <= k) puts("YES"); else puts("NO"); } }
#include <bits/stdc++.h> #pragma comment(linker, "/STACK:1024000000,1024000000") using namespace std; const int maxn = 100007; struct node { int to, w; node(int a = 0, int b = 0) { to = a; w = b; } }; vector<node> e[maxn]; int f[maxn], dis[maxn], deep[maxn], p[maxn][20], n; void dfs(int u, int pre, int t) { int i, num; deep[u] = t; f[u] = pre; num = e[u].size(); for (i = 0; i < num; i++) { int v = e[u][i].to; if (v != pre) { dis[v] = dis[u] + e[u][i].w; dfs(v, u, t + 1); } } } void init() { int i, j; for (j = 1; (1 << j) <= n; j++) for (i = 1; i <= n; i++) p[i][j] = -1; for (i = 1; i <= n; i++) p[i][0] = f[i]; for (j = 1; (1 << j) <= n; j++) { for (i = 1; i <= n; i++) { if (p[i][j - 1] != -1) p[i][j] = p[p[i][j - 1]][j - 1]; } } } int lca(int a, int b) { int i, j; if (deep[a] < deep[b]) swap(a, b); for (i = 0; (1 << i) <= deep[a]; i++) ; i--; for (j = i; j >= 0; j--) { if (deep[a] - (1 << j) >= deep[b]) { a = p[a][j]; } } if (a == b) return a; for (j = i; j >= 0; j--) { if (p[a][j] != -1 && p[a][j] != p[b][j]) { a = p[a][j]; b = p[b][j]; } } return f[a]; } int flca(int x, int y) { int l = lca(x, y); if (l == x) { return deep[y] - deep[l]; } else if (l == y) { return deep[x] - deep[l]; } return deep[x] + deep[y] - 2 * deep[l]; } int main() { int m, i, a, b, c, ans; scanf("%d", &n); for (i = 1; i <= n; i++) e[i].clear(); for (i = 1; i < n; i++) { scanf("%d%d", &a, &b); e[a].push_back(node(b, 1)); e[b].push_back(node(a, 1)); } dis[1] = 0; dfs(1, -1, 0); init(); scanf("%d", &m); for (i = 0; i < m; i++) { int x, y, k; scanf("%d %d %d %d %d", &x, &y, &a, &b, &k); int t1 = flca(a, b); int t2 = flca(x, a) + flca(y, b) + 1; int t3 = flca(x, b) + flca(y, a) + 1; if ((t1 % 2 == k % 2 && t1 <= k) || (t2 % 2 == k % 2 && t2 <= k) || (t3 % 2 == k % 2 && t3 <= k)) { printf("YES\n"); } else { printf("NO\n"); } } return 0; }
#include <bits/stdc++.h> #pragma GCC optimize("Ofast") #pragma GCC optimization("unroll-loops") const int N = 2e5 + 5; const long long int mod = 1e9 + 7; const long long int Mod = 998244353; const long double Pi = acos(-1); const long long int Inf = 4e18; using namespace std; struct LCA { vector<int> euler, d, f, t, g[100001]; vector<bool> vis; int n; void Initialize(int s) { n = s; d.assign(n + 1, INT_MAX); f.assign(n + 1, INT_MAX); vis.assign(n + 1, false); d[1] = 0; t.assign(3 * N, 0); } void Dfs(int t) { vis[t] = true; euler.push_back(t); for (auto u : g[t]) { if (!vis[u]) { d[u] = d[t] + 1; Dfs(u); euler.push_back(t); } } } void Update(int idx, int node, int v, int tl, int tr) { if (tl == tr) t[v] = node; else { int tm = (tl + tr) / 2; if (idx <= tm) Update(idx, node, 2 * v + 1, tl, tm); else Update(idx, node, 2 * v + 2, tm + 1, tr); t[v] = (d[t[2 * v + 1]] > d[t[2 * v + 2]] ? t[2 * v + 2] : t[2 * v + 1]); } } int Query(int l, int r, int v, int tl, int tr) { if (tl == l && tr == r) return t[v]; else { int tm = (tl + tr) / 2; if (r <= tm) return Query(l, r, 2 * v + 1, tl, tm); else if (l > tm) return Query(l, r, 2 * v + 2, tm + 1, tr); else { int L = Query(l, tm, 2 * v + 1, tl, tm); int R = Query(tm + 1, r, 2 * v + 2, tm + 1, tr); if (d[L] < d[R]) return L; else return R; } } } int AncestOR(int x, int y, int k) { x = f[x], y = f[y]; if (x <= y) return Query(x, y, 0, 0, k - 1); else return Query(y, x, 0, 0, k - 1); } } lca; int Dist(int x, int y, int k) { return lca.d[x] + lca.d[y] - 2 * lca.d[lca.AncestOR(x, y, k)]; } bool Check(int x, int y) { return (x <= y && (x % 2 == y % 2)); } void TestCase() { int n, q; cin >> n; lca.Initialize(n); for (int i = 1, u, v; i < n; i++) { cin >> u >> v; lca.g[u].push_back(v); lca.g[v].push_back(u); } lca.Dfs(1); for (int i = 0; i < (int)lca.euler.size(); i++) lca.f[lca.euler[i]] = min(lca.f[lca.euler[i]], i); int m = (int)lca.euler.size(), msb = -1; for (int i = 31; i >= 0; i--) { if (m & (1 << i)) msb = max(msb, i); } m = (1 << (msb + 1)); while ((int)lca.euler.size() < m) lca.euler.push_back(0); for (int i = 0; i < (int)lca.euler.size(); i++) lca.Update(i, lca.euler[i], 0, 0, m - 1); cin >> q; while (q--) { int x, y, a, b, k; cin >> x >> y >> a >> b >> k; bool ok = false; int ab = Dist(a, b, m), ax = Dist(a, x, m), ay = Dist(a, y, m); int xy = Dist(x, y, m), bx = Dist(b, x, m), by = Dist(b, y, m); ok |= Check(ab, k); ok |= Check(ax + xy + by, k); ok |= Check(ax + 1 + by, k); ok |= Check(ay + xy + bx, k); ok |= Check(ay + 1 + bx, k); ok |= Check(ax + (xy + 1) + xy + by, k); ok |= Check(ax + (xy + 1) + 1 + by, k); ok |= Check(ay + (xy + 1) + xy + bx, k); ok |= Check(ay + (xy + 1) + 1 + bx, k); ok ? cout << "YES\n" : cout << "NO\n"; } } int main() { ios_base::sync_with_stdio(0); cin.tie(0); ; int T = 1; while (T--) { TestCase(); cout << "\n"; } return 0; }
#include <bits/stdc++.h> using namespace std; std::unordered_map<int, int> lookup; struct Node { int depth; int id; std::vector<Node*> parent; Node* KStepParent(int k) { if (k > depth) { return nullptr; } if (k == 0) { return this; } int lsb = k & (-k); return this->parent[lookup[lsb]]->KStepParent(k - lsb); } }; Node* LCA(Node* lhs, Node* rhs) { if (lhs->depth != rhs->depth) { if (lhs->depth > rhs->depth) { lhs = lhs->KStepParent(lhs->depth - rhs->depth); } else { rhs = rhs->KStepParent(rhs->depth - lhs->depth); } } if (lhs->depth == 0 || lhs == rhs) { return lhs; } int l = 1, r = lhs->depth; while (l != r) { int mid = (l + r) / 2; if (lhs->KStepParent(mid) != rhs->KStepParent(mid)) { l = mid + 1; } else { r = mid; } } return lhs->KStepParent(l); } class LCAKaryTree { public: LCAKaryTree(vector<pair<int, int>>& edges) { for (int i = 0; i < 30; ++i) { lookup[1 << i] = i; } n = edges.size() + 1; connect.resize(n); for (auto& pa : edges) { connect[pa.first - 1].push_back(pa.second - 1); connect[pa.second - 1].push_back(pa.first - 1); } for (int i = 0; i < n; ++i) { auto ptr = new Node(); ptr->id = i; nodes[i] = ptr; } nodes[0]->depth = 0; for (int nxt : connect[0]) { dfs(nodes[nxt], nodes[0]); } } ~LCAKaryTree() { for (auto& pa : nodes) { delete pa.second; } } int Distance(int x, int y) { auto lhs = nodes[x]; auto rhs = nodes[y]; auto lca = LCA(lhs, rhs); return lhs->depth + rhs->depth - 2 * lca->depth; } private: void dfs(Node* cur, Node* par) { cur->depth = par->depth + 1; cur->parent.push_back(par); int steplog = 0; Node* trace = par; while (trace->parent.size() > steplog) { cur->parent.push_back(trace->parent[steplog]); trace = trace->parent[steplog]; steplog++; } for (int nxt : connect[cur->id]) { if (nxt == par->id) { continue; } dfs(nodes[nxt], cur); } } int n; std::vector<std::vector<int>> connect; std::map<int, Node*> nodes; }; bool ok(int distance, int k) { return distance <= k && !((k - distance) & 1); } class Solver { public: void solve() { ios_base::sync_with_stdio(false); cin.tie(NULL); int n; vector<pair<int, int>> edg; cin >> n; int l, r; for (int i = 1; i < n; ++i) { cin >> l >> r; edg.emplace_back(l, r); } LCAKaryTree lca(edg); int q; cin >> q; while (q--) { int x, y, a, b, k; cin >> x >> y >> a >> b >> k; x--; y--; a--; b--; int d1 = lca.Distance(a, b); int d2 = lca.Distance(x, a) + lca.Distance(y, b) + 1; int d3 = lca.Distance(y, a) + lca.Distance(x, b) + 1; if (ok(d1, k) || ok(d2, k) || ok(d3, k)) { cout << "YES" << endl; } else { cout << "NO" << endl; } } } }; int main() { Solver sol; sol.solve(); return 0; }
#include <bits/stdc++.h> using namespace std; const int MOD = 1e9 + 7; const long long INF = 1e18; const double EPS = 1e-6; const int MAX_N = 3e5 + 5; const int MAX_LOG = 25; int N; vector<int> adjList[MAX_N]; int depth[MAX_N], parent[MAX_N][MAX_LOG]; void DFS(int u, int p, int d) { depth[u] = d; parent[u][0] = p; for (int v : adjList[u]) { if (v != p) DFS(v, u, d + 1); } } void LCA_precompute() { DFS(1, 0, 0); for (int k = 1; k < MAX_LOG; ++k) { for (int i = 1; i <= N; ++i) { parent[i][k] = parent[parent[i][k - 1]][k - 1]; } } } int lift(int u, int h) { for (int i = 0; (1 << i) <= h; ++i) { if ((h & (1 << i)) != 0) { u = parent[u][i]; } } return u; } int LCA(int a, int b) { if (depth[a] < depth[b]) { b = lift(b, depth[b] - depth[a]); } else if (depth[b] < depth[a]) { a = lift(a, depth[a] - depth[b]); } if (a == b) return a; for (int k = MAX_LOG - 1; k >= 0; --k) { if (parent[a][k] != parent[b][k]) { a = parent[a][k], b = parent[b][k]; } } return parent[a][0]; } int dist(int a, int b) { int lca = LCA(a, b); return depth[a] + depth[b] - 2 * depth[lca]; } int main() { ios_base::sync_with_stdio(0); cin.tie(0); cin >> N; for (int i = 0; i < N - 1; ++i) { int u, v; cin >> u >> v; adjList[u].push_back(v); adjList[v].push_back(u); } LCA_precompute(); int q; cin >> q; while (q-- > 0) { int x, y, a, b, k; cin >> x >> y >> a >> b >> k; bool ans = false; if (dist(a, b) <= k && (k - dist(a, b)) % 2 == 0) ans = true; int d = dist(a, x) + dist(b, y) + 1; if (d <= k && (k - d) % 2 == 0) ans = true; d = dist(b, x) + dist(a, y) + 1; if (d <= k && (k - d) % 2 == 0) ans = true; if (ans) cout << "YES\n"; else cout << "NO\n"; } return 0; }
#include <bits/stdc++.h> using namespace std; int t, n, a, b, q, x, y, k, anc; int std_dis, spc_dis, xy_dis, real_dis; vector<int> V[101000]; vector<int> T[101000]; int LCAtab[101000][18]; void rearange(int node, int father, int depth) { T[node].push_back(depth); T[node].push_back(father); for (int i = 0; i < V[node].size(); i++) { if (V[node][i] != father) { T[node].push_back(V[node][i]); rearange(V[node][i], node, depth + 1); } } } void generateLCAtab() { for (int i = 0; i < 18; i++) { LCAtab[1][i] = 1; } for (int i = 2; i <= n; i++) { LCAtab[i][0] = T[i][1]; } for (int i = 1; i < 18; i++) { for (int ii = 2; ii <= n; ii++) { LCAtab[ii][i] = LCAtab[LCAtab[ii][i - 1]][i - 1]; } } } int findLCA(int node1, int node2) { if (node1 == node2) { return node1; } if (T[node1][0] < T[node2][0]) { swap(node1, node2); } while (T[node1][0] > T[node2][0]) { int wsk = 0; while (T[LCAtab[node1][wsk + 1]][0] > T[node2][0]) { wsk++; } node1 = LCAtab[node1][wsk]; } while (node1 != node2) { int wsk = 0; while (LCAtab[node1][wsk + 1] != LCAtab[node2][wsk + 1]) { wsk++; } node1 = LCAtab[node1][wsk]; node2 = LCAtab[node2][wsk]; } return node1; } int dis(int node1, int node2) { anc = findLCA(node1, node2); return (T[node1][0] + T[node2][0] - (2 * T[anc][0])); } void testCase() { cin >> n; for (int i = 0; i < n - 1; i++) { cin >> a >> b; V[a].push_back(b); V[b].push_back(a); } rearange(1, 1, 1); generateLCAtab(); cin >> q; for (int i = 0; i < q; i++) { cin >> x >> y >> a >> b >> k; std_dis = dis(a, b); spc_dis = min(dis(a, x) + dis(b, y) + 1, dis(a, y) + dis(b, x) + 1); real_dis = min(std_dis, spc_dis); xy_dis = dis(x, y); if (xy_dis % 2 == 1) { if (k >= real_dis && k % 2 == real_dis % 2) { cout << "YES" << endl; } else { cout << "NO" << endl; } } else { if (k % 2 == std_dis % 2) { if (k >= std_dis) { cout << "YES" << endl; } else { cout << "NO" << endl; } } else { if (k >= spc_dis) { cout << "YES" << endl; } else { cout << "NO" << endl; } } } } } int main() { cin.tie(0); ios_base::sync_with_stdio(0); t = 1; for (int i = 0; i < t; i++) { testCase(); } }
#include <bits/stdc++.h> using namespace std; vector<int> g; class segment_tree_max { private: vector<int> m; vector<int> delta; int n; bool is_bulk; int get_val(int i) { if (!is_bulk) { return m[i]; } int ans = m[i] + delta[i]; i /= 2; while (i >= 1) { ans += delta[i]; i /= 2; } return ans; } void inc(int i, int val) { delta[i] += val; i /= 2; while (i >= 1) { m[i] = max(m[2 * i] + delta[2 * i], m[2 * i + 1] + delta[2 * i + 1]); i /= 2; } } public: segment_tree_max() {} segment_tree_max(int nn, int def, bool bulk = false) { is_bulk = bulk; n = 1; while (n < nn) { n *= 2; } m.assign(2 * n, def); if (is_bulk) { delta.assign(2 * n, 0); } } segment_tree_max(const vector<int>& d, int def = 0, bool bulk = false, int mult = 1) { is_bulk = bulk; n = 1; while (n < d.size()) { n *= 2; } m.assign(2 * n, def); if (is_bulk) { delta.assign(2 * n, 0); } for (int i = 0; i < d.size(); i++) { m[i + n] = d[i] * mult; } for (int i = n - 1; i >= 1; i--) { m[i] = max(m[2 * i], m[2 * i + 1]); } } int get_max(int l, int r) { if (l > r) { swap(l, r); } l += n; r += n; int ans = -1e9; while (l <= r) { if (l % 2 == 1) { ans = max(ans, get_val(l)); l++; } if (r % 2 == 0) { ans = max(ans, get_val(r)); r--; } l /= 2; r /= 2; } return ans; } void inc_bulk(int l, int r, int val) { if (!is_bulk) { cout << "cant inc_bulk in not bulk mode" << endl; exit(1); } if (l > r) { swap(l, r); } l += n; r += n; while (l <= r) { if (l % 2 == 1) { inc(l, val); l++; } if (r % 2 == 0) { inc(r, val); r--; } l /= 2; r /= 2; } } void update(int i, int val) { i += n; m[i] = val; i /= 2; while (i >= 1) { if (is_bulk) { m[i] = max(m[2 * i] + delta[2 * i], m[2 * i + 1] + delta[2 * i + 1]); } else { m[i] = max(m[2 * i], m[2 * i + 1]); } i /= 2; } } }; class segment_tree_min { private: segment_tree_max max_tree; public: segment_tree_min() {} segment_tree_min(int nn, int def, bool bulk = false) { max_tree = segment_tree_max(nn, def, bulk); } segment_tree_min(const vector<int>& d, int def = -1e9, bool bulk = false) { max_tree = segment_tree_max(d, def, bulk, -1); } int get_min(int l, int r) { return -max_tree.get_max(l, r); } void inc_bulk(int l, int r, int val) { max_tree.inc_bulk(l, r, -val); } void update(int i, int val) { max_tree.update(i, -val); } }; class lca { private: segment_tree_min min_tree; vector<int> h; vector<int> d; vector<int> di; int n; void dfs(const vector<vector<int> >& g, int x, int l, int p) { di[x] = d.size(); h[x] = l; d.push_back(l); for (int y : g[x]) { if (y != p) { dfs(g, y, l + 1, x); d.push_back(l); } } } public: lca(const vector<vector<int> >& g) { int n = g.size(); h.assign(n, 0); di.assign(n, 0); dfs(g, 0, 0, -1); min_tree = segment_tree_min(d); } int get_dist(int x, int y) { int parent_h = min_tree.get_min(di[x], di[y]); return h[x] - parent_h + h[y] - parent_h; } }; bool check(int l, int k) { if (l <= k && ((k - l) % 2 == 0)) { return true; } else { return false; } } void solve() { int n; cin >> n; vector<vector<int> > g(n); for (int i = 0; i < n - 1; i++) { int x, y; cin >> x >> y; g[x - 1].push_back(y - 1); g[y - 1].push_back(x - 1); } lca r(g); int m; cin >> m; for (int i = 0; i < m; i++) { int x, y, a, b, k; cin >> x >> y >> a >> b >> k; int ab = r.get_dist(a - 1, b - 1); int ax = r.get_dist(a - 1, x - 1); int ay = r.get_dist(a - 1, y - 1); int bx = r.get_dist(b - 1, x - 1); int by = r.get_dist(b - 1, y - 1); int xy = 1; if (check(ab, k) || check(ax + xy + by, k) || check(ay + xy + bx, k) || check(ax + xy + ay + ab, k)) { cout << "YES"; } else { cout << "NO"; } cout << endl; } } int main() { ios::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr); solve(); cout << endl; return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 1e5 + 10; const int mo = 1e9 + 7; const int inf = 1e9; int f[18][N], h[N]; vector<int> p[N]; void dfs(int x) { for (auto& i : p[x]) if (i != f[0][x]) { f[0][i] = x; h[i] = h[x] + 1; dfs(i); } } int lca(int x, int y) { if (h[x] < h[y]) swap(x, y); for (auto i = (17); i >= (0); --i) if (((h[x] - h[y]) >> i) & 1) x = f[i][x]; if (x == y) return x; for (auto i = (17); i >= (0); --i) if (f[i][x] != f[i][y]) x = f[i][x], y = f[i][y]; return f[0][x]; } int dis(int x, int y) { return h[x] + h[y] - h[lca(x, y)] * 2; } bool ok(int x, int y) { return y >= x && x % 2 == y % 2; } int main() { int n, q; scanf("%d", &n); for (auto i = (2); i <= (n); ++i) { int x, y; scanf("%d%d", &x, &y); p[x].push_back(y); p[y].push_back(x); } dfs(1); for (auto i = (1); i <= (17); ++i) for (auto j = (1); j <= (n); ++j) f[i][j] = f[i - 1][f[i - 1][j]]; scanf("%d", &q); for (auto i = (1); i <= (q); ++i) { int x, y, a, b, k; scanf("%d%d%d%d%d", &x, &y, &a, &b, &k); printf("%s\n", (ok(dis(a, b), k) || ok(dis(a, x) + dis(b, y) + 1, k) || ok(dis(a, y) + dis(b, x) + 1, k)) ? "YES" : "NO"); } }
#include <bits/stdc++.h> using namespace std; struct LCA { vector<int> height, euler, first, segtree, parent; vector<bool> visited; int n; LCA(vector<vector<int> > &adj, int root = 0) { n = adj.size(); height.resize(n); first.resize(n); parent.resize(n); euler.reserve(n * 2); visited.assign(n, false); parent[root] = -1; dfs(adj, root); int m = euler.size(); segtree.resize(m * 4); build(1, 0, m - 1); } void dfs(vector<vector<int> > &adj, int node, int h = 0) { visited[node] = true; height[node] = h; first[node] = euler.size(); euler.push_back(node); for (auto to : adj[node]) { if (!visited[to]) { parent[to] = node; dfs(adj, to, h + 1); euler.push_back(node); } } } void build(int node, int b, int e) { if (b == e) { segtree[node] = euler[b]; } else { int mid = (b + e) / 2; build(node << 1, b, mid); build(node << 1 | 1, mid + 1, e); int l = segtree[node << 1], r = segtree[node << 1 | 1]; segtree[node] = (height[l] < height[r]) ? l : r; } } int query(int node, int b, int e, int L, int R) { if (b > R || e < L) return -1; if (b >= L && e <= R) return segtree[node]; int mid = (b + e) >> 1; int left = query(node << 1, b, mid, L, R); int right = query(node << 1 | 1, mid + 1, e, L, R); if (left == -1) return right; if (right == -1) return left; return height[left] < height[right] ? left : right; } int lca(int u, int v) { int left = first[u], right = first[v]; if (left > right) swap(left, right); return query(1, 0, euler.size() - 1, left, right); } }; void solve() { int n; cin >> n; vector<vector<int> > adj(n); for (int i = 0; i < n - 1; i++) { int x, y; cin >> x >> y; x--, y--; adj[x].push_back(y); adj[y].push_back(x); } LCA Tree(adj, 0); auto dis = [&](int u, int v) { int lc = Tree.lca(u, v); return Tree.height[u] + Tree.height[v] - 2 * Tree.height[lc]; }; int q; cin >> q; while (q--) { int x, y, a, b, k; cin >> x >> y >> a >> b >> k; x--, y--, a--, b--; bool ok = false; vector<int> pos; int ab = dis(a, b); int ax = dis(a, x); int ay = dis(a, y); int bx = dis(b, x); int by = dis(b, y); pos.push_back(ab); pos.push_back(ax + 1 + by); pos.push_back(ax + 1 + ay + ab); pos.push_back(ay + 1 + bx); ; for (auto &d : pos) { if (d <= k) { ok |= ((d & 1) == (k & 1)); } } if (ok) { cout << "YES\n"; } else { cout << "NO\n"; } } } int main() { ios_base::sync_with_stdio(false); cin.tie(NULL); int t = 1; while (t--) { solve(); } }
#include <bits/stdc++.h> using namespace std; using namespace chrono; int setBit(int n, int x) { return n | (1 << x); } int clearBit(int n, int x) { return n & ~(1 << x); } int toggleBit(int n, int x) { return n ^ (1 << x); } bool checkBit(int n, int x) { return (bool)(n & (1 << x)); } int dx8[] = {1, 1, 0, -1, -1, -1, 0, 1}; int dy8[] = {0, 1, 1, 1, 0, -1, -1, -1}; int dx4[] = {1, 0, -1, 0}; int dy4[] = {0, 1, 0, -1}; void yes() { cout << "YES" << endl; } void no() { cout << "NO" << endl; } template <typename T> void amax(T& t1, T t2) { t1 = max(t1, t2); } template <typename T> void amin(T& t1, T t2) { t1 = min(t1, t2); } void _print(long long t) { cerr << t; } void _print(int t) { cerr << t; } void _print(string t) { cerr << t; } void _print(char t) { cerr << t; } void _print(long double t) { cerr << t; } void _print(double t) { cerr << t; } void _print(unsigned long long t) { cerr << t; } template <class T, class V> void _print(pair<T, V> p); template <class T> void _print(vector<T> v); template <class T> void _print(set<T> v); template <class T, class V> void _print(map<T, V> v); template <class T> void _print(multiset<T> v); template <class T, class V> void _print(pair<T, V> p) { cerr << "{"; _print(p.first); cerr << ","; _print(p.second); cerr << "}"; } template <class T> void _print(vector<T> v) { cerr << "[ "; for (T i : v) { _print(i); cerr << " "; } cerr << "]"; } template <class T> void _print(set<T> v) { cerr << "[ "; for (T i : v) { _print(i); cerr << " "; } cerr << "]"; } template <class T> void _print(multiset<T> v) { cerr << "[ "; for (T i : v) { _print(i); cerr << " "; } cerr << "]"; } template <class T, class V> void _print(map<T, V> v) { cerr << "[ "; for (auto i : v) { _print(i); cerr << " "; } cerr << "]"; } long long binpow(long long a, long long b, long long m) { long long ans = 1; a %= m; while (b) { if (b & 1) ans = (ans * a); b /= 2; a = (a * a); ans %= m; a %= m; } return ans; } struct cmp { bool operator()(pair<long long, long long> a, pair<long long, long long> b) { return ((a.first - a.first / 2) * a.second) > ((b.first - b.first / 2) * b.second); } }; const int N = 1e5 + 5; vector<int> g[N]; int up[N][24]; int lvl[N]; int n, q; int T; void fill_lvl(int src, int p) { if (src != p) lvl[src] = lvl[p] + 1; for (auto e : g[src]) { if (e == p) continue; fill_lvl(e, src); } return; } void binary_lifting(int src, int p) { up[src][0] = p; for (int i = 1; i < 20; i++) { up[src][i] = -1; if (up[src][i - 1] != -1) { up[src][i] = up[up[src][i - 1]][i - 1]; } } for (auto e : g[src]) { if (e == p) continue; binary_lifting(e, src); } return; } int lift_node(int src, int jump) { int node = src; for (int i = 19; i >= 0; i--) { int mask = (1 << i); if (mask & jump) { node = up[node][i]; } if (node == -1) break; } return node; } int LCA(int u, int v) { if (lvl[u] < lvl[v]) swap(u, v); u = lift_node(u, lvl[u] - lvl[v]); if (u == v) return u; for (int i = 19; i >= 0; i--) { if (up[u][i] != up[v][i]) { u = up[u][i]; v = up[v][i]; } } return lift_node(u, 1); } int dist(int a, int b) { int lca = LCA(a, b); return lvl[a] + lvl[b] - 2 * lvl[lca]; } void JAI_MAHAKAL() { cin >> n; int x, y, a, b, k; for (int i = 1; i < n; i++) { cin >> x >> y; g[x].push_back(y); g[y].push_back(x); } cin >> q; fill_lvl(1, 1); binary_lifting(1, -1); while (q--) { cin >> x >> y >> a >> b >> k; int op1 = dist(a, b); int op2 = dist(a, x) + dist(y, b) + 1; int op3 = dist(a, y) + dist(x, b) + 1; int ok = 0; if (op1 % 2 == k % 2 and op1 <= k) ok = 1; if (op2 % 2 == k % 2 and op2 <= k) ok = 1; if (op3 % 2 == k % 2 and op3 <= k) ok = 1; if (ok) yes(); else no(); } return; } int32_t main() { ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL); int t = 1; while (t--) JAI_MAHAKAL(); cerr << "Time elapsed: " << 1000 * clock() / CLOCKS_PER_SEC << "ms\n"; return 0; }
#include <bits/stdc++.h> using namespace std; std::unordered_map<int, int> lookup; struct Node { int depth; int id; std::vector<Node*> parent; Node* KStepParent(int k) { if (k > depth) { return nullptr; } if (k == 0) { return this; } int lsb = k & (-k); return this->parent[lookup[lsb]]->KStepParent(k - lsb); } }; Node* LCA(Node* lhs, Node* rhs) { if (lhs->depth != rhs->depth) { if (lhs->depth > rhs->depth) { lhs = lhs->KStepParent(lhs->depth - rhs->depth); } else { rhs = rhs->KStepParent(rhs->depth - lhs->depth); } } if (lhs->depth == 0 || lhs == rhs) { return lhs; } int l = 1, r = lhs->depth; while (l != r) { int mid = (l + r) / 2; if (lhs->KStepParent(mid) != rhs->KStepParent(mid)) { l = mid + 1; } else { r = mid; } } return lhs->KStepParent(l); } class LCAKaryTree { public: LCAKaryTree(vector<pair<int, int>>& edges) { for (int i = 0; i < 30; ++i) { lookup[1 << i] = i; } n = edges.size() + 1; connect.resize(n); for (auto& pa : edges) { connect[pa.first - 1].push_back(pa.second - 1); connect[pa.second - 1].push_back(pa.first - 1); } for (int i = 0; i < n; ++i) { auto ptr = new Node(); ptr->id = i; nodes[i] = ptr; } nodes[0]->depth = 0; for (int nxt : connect[0]) { dfs(nodes[nxt], nodes[0]); } } ~LCAKaryTree() { for (auto& pa : nodes) { delete pa.second; } } int Distance(int x, int y) { long long res = x; res *= n; res += y; auto iter = distance_cache_.find(res); if (iter != distance_cache_.end()) { return iter->second; } auto lhs = nodes[x]; auto rhs = nodes[y]; auto lca = LCA(lhs, rhs); int dist = lhs->depth + rhs->depth - 2 * lca->depth; distance_cache_[res] = dist; return dist; } private: void dfs(Node* cur, Node* par) { cur->depth = par->depth + 1; cur->parent.push_back(par); int steplog = 0; Node* trace = par; while (trace->parent.size() > steplog) { cur->parent.push_back(trace->parent[steplog]); trace = trace->parent[steplog]; steplog++; } for (int nxt : connect[cur->id]) { if (nxt == par->id) { continue; } dfs(nodes[nxt], cur); } } std::unordered_map<long long, int> distance_cache_; int n; std::vector<std::vector<int>> connect; std::map<int, Node*> nodes; }; bool ok(int distance, int k) { return distance <= k && !((k - distance) & 1); } class Solver { public: void solve() { ios_base::sync_with_stdio(false); cin.tie(NULL); int n; vector<pair<int, int>> edg; cin >> n; int l, r; for (int i = 1; i < n; ++i) { cin >> l >> r; edg.emplace_back(l, r); } LCAKaryTree lca(edg); int q; cin >> q; while (q--) { int x, y, a, b, k; cin >> x >> y >> a >> b >> k; x--; y--; a--; b--; int d1 = lca.Distance(a, b); if (ok(d1, k)) { cout << "YES" << endl; continue; } int d2 = lca.Distance(x, a) + lca.Distance(y, b) + 1; if (ok(d2, k)) { cout << "YES" << endl; continue; } int d3 = lca.Distance(y, a) + lca.Distance(x, b) + 1; if (ok(d3, k)) { cout << "YES" << endl; } else { cout << "NO" << endl; } } } }; int main() { Solver sol; sol.solve(); return 0; }
#include <bits/stdc++.h> using namespace std; vector<vector<int>> edge; vector<int> dist; vector<int> et; vector<int> first; void inedge(int n, int m) { edge.resize(n + 1); dist.resize(n + 1, -1); first.resize(n + 1); int a, b; for (int i = 0; i < m; i++) { cin >> a >> b; edge[a].push_back(b); edge[b].push_back(a); } } void dfs(int v, int p, int h) { if (dist[v] != -1) return; dist[v] = h; first[v] = et.size(); et.push_back(v); for (int i = 0; i < edge[v].size(); i++) { if (p - edge[v][i]) { dfs(edge[v][i], v, h + 1); et.push_back(v); } } } vector<int> t; int n; void build(vector<int>& vv) { n = vv.size(); t.resize(2 * n, INT_MAX); for (int i = 0; i < n; i++) t[i + n] = vv[i]; for (int i = n - 1; i > 0; i--) { t[i] = min(t[i << 1], t[i << 1 | 1]); } } int rq(int l, int r) { int res = INT_MAX; r++; for (l += n, r += n; l < r; l >>= 1, r >>= 1) { if (l & 1) res = min(res, t[l++]); if (r & 1) res = min(res, t[--r]); } return res; } int dt(int a, int b) { if (first[a] > first[b]) swap(a, b); int dlca = rq(first[a], first[b]); return dist[a] + dist[b] - 2 * dlca; } int main() { int n; cin >> n; inedge(n, n - 1); dfs(1, -1, 0); vector<int> vv; for (int i = 0; i < et.size(); i++) vv.push_back(dist[et[i]]); build(vv); int q, x, y, a, b, k; cin >> q; while (q--) { cin >> x >> y >> a >> b >> k; int d1 = dt(a, b); int d2 = dt(a, x) + dt(y, b) + 1; int d3 = dt(a, y) + dt(x, b) + 1; if (d1 <= k && (d1 % 2 == k % 2)) { cout << "YES\n"; } else if (d2 <= k && (d2 % 2 == k % 2)) { cout << "YES\n"; } else if (d3 <= k && (d3 % 2 == k % 2)) { cout << "YES\n"; } else cout << "NO\n"; } }
#include <bits/stdc++.h> using namespace std; int lev[100005]; void dfs(int u, int p, int **memo, int log, vector<int> *g) { memo[u][0] = p; for (int i = 1; i <= log; i++) memo[u][i] = memo[memo[u][i - 1]][i - 1]; for (int v : g[u]) { if (v != p) { lev[v] = lev[u] + 1; dfs(v, u, memo, log, g); } } } int lca(int u, int v, int log, int **memo) { if (lev[u] < lev[v]) swap(u, v); for (int i = log; i >= 0; i--) if ((lev[u] - pow(2, i)) >= lev[v]) u = memo[u][i]; if (u == v) return u; for (int i = log; i >= 0; i--) { if (memo[u][i] != memo[v][i]) { u = memo[u][i]; v = memo[v][i]; } } return memo[u][0]; } int main() { int n; cin >> n; vector<int> g[n + 1]; int log = (int)ceil(log2(n)); int **memo = new int *[n + 1]; for (int i = 0; i < n + 1; i++) memo[i] = new int[log + 1]; for (int i = 0; i <= n; i++) memset(memo[i], -1, sizeof memo[i]); int a, b; for (int i = 0; i < n - 1; i++) { cin >> a >> b; g[b].push_back(a); g[a].push_back(b); } dfs(1, 1, memo, log, g); int q; cin >> q; while (q--) { int x, y, k; cin >> x >> y >> a >> b >> k; int lc = lca(a, b, log, memo); int disab = *(lev + a) + *(lev + b) - (*(lev + lc)) - (*(lev + lc)); if (disab == k) { cout << "YES\n"; continue; } else if (disab < k) { if ((k - disab) % 2 == 0) { cout << "YES\n"; continue; } } lc = lca(a, x, log, memo); int disax = *(lev + a) + *(lev + x) - (*(lev + lc)) - (*(lev + lc)); int lc1 = lca(y, b, log, memo); int disyb = *(lev + y) + *(lev + b) - (*(lev + lc1)) - (*(lev + lc1)); disab = 1 + disax + disyb; if (disab == k) { cout << "YES\n"; continue; } else if (disab < k) { if ((k - disab) % 2 == 0) { cout << "YES\n"; continue; } } lc = lca(a, y, log, memo); disax = *(lev + a) + *(lev + y) - (*(lev + lc)) - (*(lev + lc)); lc1 = lca(x, b, log, memo); disyb = *(lev + x) + *(lev + b) - (*(lev + lc1)) - (*(lev + lc1)); disab = 1 + disax + disyb; if (disab == k) { cout << "YES\n"; continue; } else if (disab < k) { if ((k - disab) % 2 == 0) { cout << "YES\n"; continue; } } cout << "NO\n"; } return 0; }
#include <bits/stdc++.h> using namespace std; inline long long read() { char c = getchar(); long long ans = 0, tag = 1; while (!isdigit(c)) tag = (c == '-' ? -1 : 1), c = getchar(); while (isdigit(c)) ans = (ans << 3) + (ans << 1) + c - '0', c = getchar(); return ans * tag; } const long long maxn = 1e5 + 5; long long n, cnt, head[maxn]; long long tot, fa[21][maxn], dep[maxn]; struct edge { long long to, next; } e[maxn << 1]; void add(long long x, long long y) { e[++cnt] = (edge){y, head[x]}; head[x] = cnt; } void dfs(long long x, long long f) { dep[x] = dep[f] + 1; fa[0][x] = f; for (long long i = 1; i <= tot; i++) { fa[i][x] = fa[i - 1][fa[i - 1][x]]; } for (long long i = head[x]; i; i = e[i].next) { if (e[i].to == f) continue; dfs(e[i].to, x); } } long long lca(long long x, long long y) { if (dep[x] < dep[y]) swap(x, y); for (long long i = tot; i >= 0; i--) { if (dep[fa[i][x]] >= dep[y]) x = fa[i][x]; } if (x == y) return x; for (long long i = tot; i >= 0; i--) { if (fa[i][x] != fa[i][y]) { x = fa[i][x]; y = fa[i][y]; } } return fa[0][x]; } long long dist(long long x, long long y) { return dep[x] + dep[y] - 2 * dep[lca(x, y)]; } bool check(long long dis, long long k) { return (dis <= k && ((dis & 1) == (k & 1))); } int main() { n = read(); tot = log(n) / log(2) + 1; for (long long i = 1, x, y; i < n; i++) { x = read(), y = read(); add(x, y); add(y, x); } dfs(1, 0); long long q = read(); while (q--) { long long x = read(), y = read(), a = read(), b = read(), k = read(); if (check(dist(a, b), k) || check(dist(a, x) + 1 + dist(b, y), k) || check(dist(a, y) + 1 + dist(b, x), k)) { puts("YES"); } else puts("NO"); } return 0; }
#include <bits/stdc++.h> using namespace std; vector<int> g; class segment_tree_min { private: vector<int> m; int n; public: segment_tree_min() {} segment_tree_min(int nn) { n = 1; while (n < nn) { n *= 2; } m.assign(2 * n, 1e9); } segment_tree_min(vector<int> d) { n = 1; while (n < d.size()) { n *= 2; } m.assign(2 * n, 1e9); for (int i = 0; i < d.size(); i++) { update(i, d[i]); } } int get_min(int l, int r) { if (l > r) { swap(l, r); } l += n; r += n; int ans = 1e9; while (l <= r) { if (l % 2 == 1) { ans = min(ans, m[l]); l++; } if (r % 2 == 0) { ans = min(ans, m[r]); r--; } l /= 2; r /= 2; } return ans; } void update(int i, int val) { i += n; while (i >= 1) { m[i] = min(m[i], val); i /= 2; } } }; class rmq { private: segment_tree_min min_tree; vector<int> h; vector<int> d; vector<int> di; int n; void dfs(const vector<vector<int> >& g, int x, int l, int p) { di[x] = d.size(); h[x] = l; d.push_back(l); for (int y : g[x]) { if (y != p) { dfs(g, y, l + 1, x); d.push_back(l); } } } public: rmq(const vector<vector<int> >& g) { int n = g.size(); h.assign(n, 0); di.assign(n, 0); dfs(g, 0, 0, -1); min_tree = segment_tree_min(d); } int get_dist(int x, int y) { int parent_h = min_tree.get_min(di[x], di[y]); return h[x] - parent_h + h[y] - parent_h; } }; bool check(int l, int k) { if (l <= k && ((k - l) % 2 == 0)) { return true; } else { return false; } } void solve() { int n; cin >> n; vector<vector<int> > g(n); for (int i = 0; i < n - 1; i++) { int x, y; cin >> x >> y; g[x - 1].push_back(y - 1); g[y - 1].push_back(x - 1); } rmq r(g); int m; cin >> m; for (int i = 0; i < m; i++) { int x, y, a, b, k; cin >> x >> y >> a >> b >> k; int ab = r.get_dist(a - 1, b - 1); int ax = r.get_dist(a - 1, x - 1); int ay = r.get_dist(a - 1, y - 1); int bx = r.get_dist(b - 1, x - 1); int by = r.get_dist(b - 1, y - 1); int xy = 1; if (check(ab, k) || check(ax + xy + by, k) || check(ay + xy + bx, k) || check(ax + xy + ay + ab, k)) { cout << "YES"; } else { cout << "NO"; } cout << endl; } } int main() { ios::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr); solve(); cout << endl; return 0; }
#include <bits/stdc++.h> using namespace std; long long level[1 << 18]; long long dp[1 << 18][18]; long long n; vector<vector<long long>> g; void dfs(long long u, long long par) { if (par == -1) level[u] = 0; else level[u] = level[par] + 1; dp[u][0] = par; for (auto it : g[u]) { if (it == par) continue; dfs(it, u); } } void build_table() { long long max_jumps = ceil(log2(n)); for (long long i = 0; i < max_jumps - 1; i++) { for (long long j = 1; j <= n; j++) { if (dp[j][i] != -1) dp[j][i + 1] = dp[dp[j][i]][i]; } } } long long LCA(long long u, long long v) { long long max_jumps = ceil(log2(n)); if (level[u] < level[v]) swap(u, v); long long diff = level[u] - level[v]; for (long long i = 0; i < max_jumps; i++) { if (diff & (1 << i)) u = dp[u][i]; } if (u == v) return u; for (long long i = max_jumps - 1; i >= 0; i--) { if (dp[u][i] != dp[v][i]) { u = dp[u][i]; v = dp[v][i]; } } return dp[u][0]; } long long dist(long long u, long long v) { return (level[u] + level[v] - 2 * level[LCA(u, v)]); } int main() { ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL); ; long long q, u, v, x, y, a, b, k; cin >> n; g.resize(n + 1); for (long long i = 0; i < n - 1; i++) { cin >> u >> v; g[u].push_back(v); g[v].push_back(u); } memset(dp, -1, sizeof(dp)); dfs(1, -1); build_table(); cin >> q; while (q--) { cin >> x >> y >> a >> b >> k; pair<long long, long long> p = {0x3f3f3f3f, 0x3f3f3f3f}; long long d = dist(a, b); if (d % 2) p.second = d; else p.first = d; d = dist(a, x) + 1 + dist(y, b); if (d % 2) p.second = min(d, p.second); else p.first = min(d, p.first); d = dist(a, y) + 1 + dist(x, b); if (d % 2) p.second = min(d, p.second); else p.first = min(d, p.first); bool flag = (k % 2) ? (p.second != 0x3f3f3f3f && k >= p.second) : (p.first != 0x3f3f3f3f && k >= p.first); flag ? cout << "YES\n" : cout << "NO\n"; } return 0; }
#include <bits/stdc++.h> using namespace std; vector<vector<int>> graf; vector<int> timein; vector<int> timeout; int timer = 0; const int kolvo = 2e5; int binup[kolvo][19]; int a, l; int rast[kolvo]; void dfs(int v, int deep, int p = 0) { rast[v] = deep; timein[v] = timer++; binup[v][0] = p; for (int q = 1; q <= l; q++) { binup[v][q] = binup[binup[v][q - 1]][q - 1]; } for (int q = 0; q < graf[v].size(); q++) { if (graf[v][q] != p) { dfs(graf[v][q], deep + 1, v); } } timeout[v] = timer++; } bool check(int v1, int v2) { return timein[v1] <= timein[v2] && timeout[v1] >= timeout[v2]; } int lca(int v1, int v2) { if (check(v1, v2)) { return v1; } if (check(v2, v1)) { return v2; } for (int q = l; q >= 0; q--) { if (!check(binup[v1][q], v2)) { v1 = binup[v1][q]; } } return binup[v1][0]; } int rrast(int a, int b) { return rast[a] + rast[b] - 2 * rast[lca(a, b)]; } int main() { ios_base::sync_with_stdio(false); cin.tie(0); rast[0] = 0; int b, c, t; cin >> a; graf.resize(a); for (int q = 1; q < a; q++) { cin >> b >> c; graf[c - 1].push_back(b - 1); graf[b - 1].push_back(c - 1); } timeout.resize(a); timein.resize(a); while ((1 << l) < a) { l++; } dfs(0, 0, 0); cin >> t; int d, e, f, g; while (t--) { cin >> c >> d >> e >> f >> g; if (rrast(e - 1, f - 1) % 2 == g % 2 && rrast(e - 1, f - 1) <= g) { cout << "YES" << endl; } else if ((rrast(e - 1, c - 1) + rrast(f - 1, d - 1) + 1) % 2 == g % 2 && (rrast(e - 1, c - 1) + rrast(f - 1, d - 1) + 1) <= g) { cout << "YES" << endl; } else if ((rrast(f - 1, c - 1) + rrast(e - 1, d - 1) + 1) % 2 == g % 2 && (rrast(f - 1, c - 1) + rrast(e - 1, d - 1) + 1) <= g) { cout << "YES" << endl; } else { cout << "NO" << endl; } } }
#include <bits/stdc++.h> using namespace std; const long long maxn = 1e5 + 5, mod = 1e9 + 7, inf = 0x3f3f3f3f; long long n, m, Q, K, T; long long read() { long long x = 0, f = 1; char c = getchar(); while (c < '0' || c > '9') { if (c == '-') f = -1; c = getchar(); } while (c >= '0' && c <= '9') { x = x * 10 + c - '0'; c = getchar(); } return x * f; } long long e = 1, to[maxn << 1], hed[maxn], nxt[maxn << 1]; void add(long long x, long long y) { to[++e] = y; nxt[e] = hed[x]; hed[x] = e; to[++e] = x; nxt[e] = hed[y]; hed[y] = e; } long long fa[maxn], dep[maxn], siz[maxn], son[maxn], top[maxn]; void dfs1(long long x, long long fu, long long deep) { siz[x] = 1, fa[x] = fu; dep[x] = deep; for (long long i = hed[x]; i; i = nxt[i]) { if (to[i] == fu) continue; dfs1(to[i], x, deep + 1); siz[x] += siz[to[i]]; if (siz[to[i]] > siz[son[x]]) son[x] = to[i]; } return; } void dfs2(long long x, long long topx) { top[x] = topx; if (!son[x]) return; dfs2(son[x], topx); for (long long i = hed[x]; i; i = nxt[i]) { if (to[i] == fa[x] || to[i] == son[x]) continue; dfs2(to[i], to[i]); } return; } long long lca(long long x, long long y) { while (top[x] != top[y]) { if (dep[top[x]] < dep[top[y]]) swap(x, y); x = fa[top[x]]; } if (dep[x] > dep[y]) swap(x, y); return x; } long long dis(long long x, long long y) { return dep[x] + dep[y] - dep[lca(x, y)] * 2; } bool check(long long x, long long y, long long a, long long b, long long k) { long long goal = (k & 1); long long k1 = ((dis(a, b))), k2 = ((dis(a, x) + dis(b, y) + 1)); long long k3 = ((dis(a, y) + dis(b, x) + 1)); if (k1 <= k && k1 % 2 == goal) return true; if (k2 <= k && k2 % 2 == goal) return true; if (k3 <= k && k3 % 2 == goal) return true; return false; } signed main() { n = read(); for (long long i = (1); i <= (n - 1); ++i) add(read(), read()); dfs1(1, 0, 1); dfs2(1, 1); Q = read(); while (Q--) { long long x = read(), y = read(), a = read(), b = read(), k = read(); puts((check(x, y, a, b, k)) ? "YES" : "NO"); } return 0; }
#include <bits/stdc++.h> using namespace std; vector<vector<int>> edge; vector<int> dist; vector<int> et; vector<int> first; void inedge(int n, int m) { edge.resize(n + 1); dist.resize(n + 1, -1); first.resize(n + 1); int a, b; for (int i = 0; i < m; i++) { cin >> a >> b; edge[a].push_back(b); edge[b].push_back(a); } } void dfs(int v, int p, int h) { if (dist[v] != -1) return; dist[v] = h; first[v] = et.size(); et.push_back(h); for (int i = 0; i < edge[v].size(); i++) { if (p - edge[v][i]) { dfs(edge[v][i], v, h + 1); et.push_back(h); } } } vector<int> t; int n; void build(vector<int>& vv) { n = vv.size(); t.resize(2 * n, INT_MAX); for (int i = 0; i < n; i++) t[i + n] = vv[i]; for (int i = n - 1; i > 0; i--) { t[i] = min(t[i << 1], t[i << 1 | 1]); } } int rq(int l, int r) { int res = INT_MAX; r++; for (l += n, r += n; l < r; l >>= 1, r >>= 1) { if (l & 1) res = min(res, t[l++]); if (r & 1) res = min(res, t[--r]); } return res; } int dt(int a, int b) { if (first[a] > first[b]) swap(a, b); int dlca = rq(first[a], first[b]); return dist[a] + dist[b] - 2 * dlca; } int main() { int n; cin >> n; inedge(n, n - 1); dfs(1, -1, 0); build(et); int q, x, y, a, b, k; cin >> q; while (q--) { cin >> x >> y >> a >> b >> k; int d1 = dt(a, b); int d2 = dt(a, x) + dt(y, b) + 1; int d3 = dt(a, y) + dt(x, b) + 1; if (d1 <= k && (d1 % 2 == k % 2)) { cout << "YES\n"; } else if (d2 <= k && (d2 % 2 == k % 2)) { cout << "YES\n"; } else if (d3 <= k && (d3 % 2 == k % 2)) { cout << "YES\n"; } else cout << "NO\n"; } }
#include <bits/stdc++.h> #pragma comment(linker, "/stack:200000000") #pragma GCC optimize("Ofast") #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native") using namespace std; constexpr int maxl = 21; signed main() { std::ios::sync_with_stdio(false); cin.tie(0); int n; cin >> n; vector<vector<int>> graph(n); for (int i = 0; i < n - 1; i++) { int a, b; cin >> a >> b; a--; b--; graph[a].push_back(b); graph[b].push_back(a); } vector<array<int, maxl>> step(n); vector<int> tin(n), tout(n), depth(n, -1); int time = 0; function<void(int, int)> dfs = [&](int v, int p) { step[v][0] = p; for (int i = 0; i < maxl - 1; i++) step[v][i + 1] = step[step[v][i]][i]; depth[v] = depth[p] + 1; tin[v] = time++; for (int ne : graph[v]) if (ne != p) dfs(ne, v); tout[v] = time++; }; dfs(0, 0); auto anc = [&](int high, int low) { return tin[high] <= tin[low] and tout[low] <= tout[high]; }; auto lca = [&](int u, int v) { if (anc(u, v)) return u; if (anc(v, u)) return v; for (int i = maxl - 1; i >= 0; i--) if (!anc(step[u][i], v)) u = step[u][i]; return step[u][0]; }; auto dist = [&](int u, int v) { return depth[u] + depth[v] - 2 * depth[lca(u, v)]; }; int tt; cin >> tt; while (tt--) { int x, y, a, b, k; cin >> x >> y >> a >> b >> k; x--; y--; a--; b--; vector<int> ds = {dist(a, b), dist(a, x) + dist(y, b) + 1, dist(b, x) + dist(y, a) + 1}; bool gud = false; for (int d : ds) gud |= d % 2 == k % 2 and d <= k; cout << (gud ? "YES" : "NO") << "\n"; } }
#include <bits/stdc++.h> int dr[] = {2, 2, -2, -2, 1, -1, 1, -1}; int dc[] = {1, -1, 1, -1, 2, 2, -2, -2}; int dr1[] = {0, 0, 1, 1, 1, -1, -1, -1}; int dc1[] = {1, -1, 1, 0, -1, 0, 1, -1}; int dr2[] = {0, 0, 1, -1}; int dc2[] = {1, -1, 0, 0}; using namespace std; vector<long long> adj[500005]; long long lev[500005], tr[500005][20]; void dfs(long long u, long long par) { long long i, j; for (i = 0; i < adj[u].size(); i++) { long long p = adj[u][i]; if (p == par) continue; lev[p] = lev[u] + 1; tr[p][0] = u; dfs(p, u); } } void build(long long n) { memset(tr, -1, sizeof(tr)); dfs(1, -1); long long i, j; for (j = 1; (1 << j) <= n; j++) { for (i = 1; i <= n; i++) { if (tr[i][j - 1] != -1) tr[i][j] = tr[tr[i][j - 1]][j - 1]; } } } long long query(long long p, long long q) { if (lev[q] > lev[p]) swap(p, q); long long i, j; for (i = 16; i >= 0; i--) { if (lev[p] - (1 << i) >= lev[q]) { p = tr[p][i]; } } if (p == q) return p; for (i = 16; i >= 0; i--) { if (tr[p][i] != tr[q][i] && tr[p][i] != -1 && tr[q][i] != -1) { p = tr[p][i]; q = tr[q][i]; } } return tr[p][0]; } long long dis(long long x, long long y) { long long p = query(x, y); return lev[x] + lev[y] - 2 * lev[p]; } int main() { ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0); long long tc, n, i, j, m, q; while (cin >> n) { for (i = 1; i < n; i++) { long long u, v; cin >> u >> v; adj[u].push_back(v); adj[v].push_back(u); } build(n); cin >> q; while (q--) { long long x, y, a, b, k; cin >> x >> y >> a >> b >> k; long long d = dis(a, b); if (d <= k && d % 2 == k % 2) { cout << "YES" << endl; continue; } long long p1 = dis(x, a) + dis(y, b) + 1; long long p2 = dis(x, b) + dis(y, a) + 1; if (p1 <= k && p1 % 2 == k % 2) { cout << "YES" << endl; continue; } if (p2 <= k && p2 % 2 == k % 2) { cout << "YES" << endl; continue; } cout << "NO" << endl; } } return 0; }
#include <bits/stdc++.h> using namespace std; int n, x, y, q, a, b, k, in[100009], out[100009], parent[100009][19], timer, H[100009]; vector<int> v[100009]; void go(int x) { timer++; in[x] = timer; for (int i = 2; i <= 17; i++) { parent[x][i] = parent[parent[x][i - 1]][i - 1]; } for (int i = 0; i < v[x].size(); i++) { if (v[x][i] != parent[x][1]) { parent[v[x][i]][1] = x; go(v[x][i]); } } timer++; out[x] = timer; } bool check(int a, int b) { return (in[a] <= in[b] && out[b] <= out[a]); } int lca(int a, int b) { if (check(a, b)) return a; if (check(b, a)) return b; for (int i = 17; i >= 1; i--) { if (!check(parent[a][i], b)) a = parent[a][i]; } return parent[a][1]; } void High(int x, int h) { H[x] = h; for (int i = 0; i < v[x].size(); i++) { if (H[v[x][i]] == 0) High(v[x][i], h + 1); } } bool find(int a, int b, int k) { int p = lca(a, b); int depth = H[a] + H[b] - 2 * H[p]; if (k % 2 == depth % 2 && k >= depth) return true; else return false; } int main() { ios::sync_with_stdio(0); cin >> n; for (int i = 1; i < n; i++) { cin >> x >> y; v[x].push_back(y); v[y].push_back(x); } in[0] = 0; out[0] = 3 * n; go(1); High(1, 1); cin >> q; while (q--) { cin >> x >> y >> a >> b >> k; if (find(a, b, k)) { cout << "YES" << endl; continue; } int p = lca(a, x); int depth = H[a] + H[x] - 2 * H[p]; depth++; if (depth <= k) { if (find(y, b, k - depth)) { cout << "YES" << endl; continue; } } p = lca(a, y); depth = H[a] + H[y] - 2 * H[p]; depth++; if (depth <= k) { if (find(x, b, k - depth)) { cout << "YES" << endl; continue; } } cout << "NO" << endl; } return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 1e5 + 7; const int M = 1e3 + 1; const int base = 1e9 + 7; const long long mod = 1e9 + 7; int n, m = 20; vector<int> ke[N]; int f[N][25], pa[N], h[N]; void khoitao() { for (int i = 1; i <= n; i++) for (int j = 0; j <= m; j++) f[i][j] = -1; for (int i = 1; i <= n; i++) f[i][0] = pa[i]; for (int j = 1; j <= m; j++) for (int i = 1; i <= n; i++) if (f[i][j - 1] != -1) f[i][j] = f[f[i][j - 1]][j - 1]; } void dfs(int u, int cha, int hi) { h[u] = hi; for (int v : ke[u]) { if (v == cha) continue; if (h[v]) continue; pa[v] = u; dfs(v, u, hi + 1); } } int lca(int u, int v) { if (h[u] < h[v]) swap(u, v); int x = 0; while ((1 << x) <= h[u]) x++; x--; for (int i = x; i >= 0; i--) if (h[u] - h[v] >= (1 << i)) u = f[u][i]; if (u == v) return u; for (int i = x; i >= 0; i--) { if (f[u][i] != -1 && f[u][i] != f[v][i]) { u = f[u][i]; v = f[v][i]; } } return pa[u]; } int x, y, a, b, k, r, r1, r2, r3, r4, tmp; int main() { ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0); cin >> n; for (int i = 1; i < n; i++) { int u, v; cin >> u >> v; ke[u].push_back(v); ke[v].push_back(u); } for (int i = 1; i <= n; i++) h[i] = 0; h[1] = 1; dfs(1, -1, 1); khoitao(); int q; cin >> q; while (q--) { cin >> a >> b >> x >> y >> k; r = lca(x, y); int d = h[x] + h[y] - 2 * h[r]; r1 = h[x] + h[a] - 2 * h[lca(a, x)]; r2 = h[y] + h[b] - 2 * h[lca(b, y)]; r3 = h[x] + h[b] - 2 * h[lca(x, b)]; r4 = h[y] + h[a] - 2 * h[lca(y, a)]; tmp = min(r1 + r2, r3 + r4) + 1; int res = base; if ((d + k) % 2 == 0) { res = d; } if ((tmp + k) % 2 == 0) res = min(res, tmp); if (res <= k) { cout << "YES" << '\n'; } else cout << "NO" << '\n'; } return 0; }
#include <bits/stdc++.h> using namespace std; long long MOD = (1e9) + 7; const long long N = 1e5 + 5; const long long level = 25; long long par[N][level], depth[N]; vector<long long> a[N]; void dfs(long long c, long long p) { depth[c] = depth[p] + 1; par[c][0] = p; for (long long i = 1; i < level; i++) par[c][i] = par[par[c][i - 1]][i - 1]; for (auto ne : a[c]) { if (ne == p) continue; dfs(ne, c); } } long long lca(long long u, long long v) { if (depth[v] < depth[u]) swap(u, v); long long diff = depth[v] - depth[u]; for (long long i = 0; i < level; i++) if ((diff >> i) & 1) v = par[v][i]; if (u == v) return u; for (long long i = level - 1; i >= 0; i--) if (par[u][i] != par[v][i]) { u = par[u][i]; v = par[v][i]; } return par[u][0]; } long long dist(long long u, long long v) { if (u == v) return 0; long long res = 0; if (depth[u] > depth[v]) swap(u, v); long long l = lca(u, v); return depth[u] + depth[v] - (2 * depth[l]); } signed main() { ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL); long long tc = 1; for (long long ti = 1; ti <= tc; ti++) { long long n; cin >> n; for (long long i = 1; i < n; i++) { long long x, y; cin >> x >> y; a[x].push_back(y); a[y].push_back(x); } dfs(1, 0); long long q; cin >> q; while (q--) { long long x, y, a, b, k; cin >> x >> y >> a >> b >> k; long long chk = dist(a, b); if (chk <= k && !((k - chk) % 2)) { cout << "YES" << endl; continue; } chk = dist(a, x) + dist(y, b) + 1; if (chk <= k && !((k - chk) % 2)) { cout << "YES" << endl; continue; } chk = dist(a, y) + dist(x, b) + 1; if (chk <= k && !((k - chk) % 2)) { cout << "YES" << endl; continue; } cout << "NO" << endl; } } return 0; }
#include <bits/stdc++.h> using namespace std; const int K = 20; const int N = 1e5 + 7; vector<int> g[N]; int h[N]; int tin[N]; int tout[N]; int p[N]; int up[K][N]; int timer = 0; void dfs(int cur, int pr, int ch) { h[cur] = ch; p[cur] = pr; tin[cur] = timer; timer++; for (auto t : g[cur]) { if (t != p[cur]) { dfs(t, cur, ch + 1); } } tout[cur] = timer; timer++; } void init(int n) { for (int i = 0; i < n; i++) { up[0][i] = p[i]; } for (int i = 1; i < K; i++) { for (int j = 0; j < n; j++) { int mid = up[i - 1][j]; if (mid != -1) { up[i][j] = up[i - 1][mid]; } else { up[i][j] = -1; } } } } bool anc(int u, int v) { return tin[u] <= tin[v] && tout[v] <= tout[u]; } int get(int a, int b) { if (anc(a, b)) { return a; } else if (anc(b, a)) { return b; } else { for (int i = K - 1; i >= 0; i--) { if (up[i][a] != -1 && !anc(up[i][a], b)) { a = up[i][a]; } } return p[a]; } } int ln(int a, int b) { return h[a] + h[b] - 2 * h[get(a, b)]; } int ok(int ln, int k) { return ln <= k && (ln % 2) == (k % 2); } signed main() { ios_base::sync_with_stdio(false); cin.tie(0); int n; cin >> n; for (int i = 0; i + 1 < n; i++) { int u, v; cin >> u >> v; u--; v--; g[u].push_back(v); g[v].push_back(u); } dfs(0, -1, 0); init(n); int q; cin >> q; while (q--) { int x, y, a, b, k; cin >> x >> y >> a >> b >> k; x--; y--; a--; b--; int ans = 0; ans |= ok(ln(a, b), k); ans |= ok(ln(a, x) + 1 + ln(y, b), k); swap(x, y); ans |= ok(ln(a, x) + 1 + ln(y, b), k); if (ans) cout << "YES\n"; else cout << "NO\n"; } }
#include <bits/stdc++.h> using namespace std; int first[(100 * 1000 + 5)], height[(100 * 1000 + 5)], tim = 0; vector<int> euler, g[(100 * 1000 + 5)]; void dfs(int u, int p = -1, int h = 0) { first[u] = tim++; euler.push_back(u); height[u] = h; for (int v : g[u]) { if (v != p) { dfs(v, u, h + 1); euler.push_back(u); tim++; } } } int main() { ios_base::sync_with_stdio(false); cin.tie(0); int n; cin >> n; for (int i = 0; i < n - 1; i++) { int u, v; cin >> u >> v; g[u].push_back(v); g[v].push_back(u); } dfs(1); int sz = 1; int m = euler.size(); while (sz <= m) { sz *= 2; } vector<pair<int, int>> tree(2 * sz, {((int)1e9), -1}); for (int i = 0; i < m; i++) { tree[i + sz] = make_pair(height[euler[i]], euler[i]); } for (int i = sz - 1; i > 0; i--) { tree[i] = min(tree[2 * i], tree[2 * i + 1]); } auto lca = [&](int u, int v) { int L = first[u] + sz, R = first[v] + sz; assert(L && R); if (L > R) swap(L, R); pair<int, int> ans = {((int)1e9), -1}; while (L <= R) { if (L % 2 == 1) ans = min(ans, tree[L++]); if (R % 2 == 0) ans = min(ans, tree[R--]); L /= 2, R /= 2; } assert(ans.second != -1); return ans.second; }; auto dist = [&](int u, int v) { return height[u] + height[v] - 2 * height[lca(u, v)]; }; int queries; cin >> queries; while (queries--) { int x, y, a, b, k; cin >> x >> y >> a >> b >> k; vector<int> options = {dist(a, b), dist(a, x) + dist(b, y) + 1, dist(a, y) + dist(b, x) + 1}; bool ok = false; for (int d : options) { ok |= d <= k && d % 2 == k % 2; } cout << (ok ? "YES" : "NO") << '\n'; } }