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#include <bits/stdc++.h> using namespace std; int main() { int t; cin >> t; while (t--) { int n; cin >> n; int prevp, prevc; bool ok = true; for (int i = 0; i < n; i++) { int p, c; cin >> p >> c; if (c > p) { ok = false; } if (i == 0) { prevp = p; prevc = c; continue; } if (p < prevp || c < prevc) { ok = false; } if (p - prevp < c - prevc) { ok = false; } prevp = p; prevc = c; } if (ok) cout << "YES" << endl; else cout << "NO" << endl; } return 0; }
#include <bits/stdc++.h> using namespace std; int main() { long long t; cin >> t; while (t--) { long long f = 0; long long n; cin >> n; long long a[n], b[n]; for (long long i = 0; i < n; i++) cin >> a[i] >> b[i]; if (b[0] <= a[0]) { for (long long i = 1; i < n; i++) { if (b[i] <= a[i] && a[i] - a[i - 1] >= b[i] - b[i - 1]) { if (a[i] > a[i - 1] && b[i] >= b[i - 1]) { continue; } else if (a[i] == a[i - 1] && b[i] == b[i - 1]) { continue; } else { f = 1; break; } } else { f = 1; break; } } if (f) cout << "NO\n"; else cout << "YES\n"; } else cout << "NO\n"; } }
#include <bits/stdc++.h> using namespace std; int main() { int t, n, i, ck = 0; cin >> t; while (t--) { cin >> n; int p[n], c[n]; for (i = 0; i < n; i++) cin >> p[i] >> c[i]; if (n == 1) { if (p[n - 1] >= c[n - 1]) ck = 1; else ck = 0; } else { for (i = 0; i < n - 1; i++) { if ((p[i + 1] >= p[i] && c[i + 1] >= c[i]) && (p[i + 1] - p[i] >= c[i + 1] - c[i]) && (p[i] >= c[i])) ck = 1; else { ck = 0; break; } } } if (ck) cout << "YES" << endl; else cout << "NO" << endl; } return 0; }
#include <bits/stdc++.h> #pragma GCC optimize(2) #pragma GCC optimize(3) using namespace std; template <class nmsl> inline void read(nmsl &x) { x = 0; char ch = getchar(), w = 0; while (!isdigit(ch)) w = (ch == '-'), ch = getchar(); while (isdigit(ch)) x = (x << 1) + (x << 3) + (ch ^ 48), ch = getchar(); x = w ? -x : x; } int main() { ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0); ; int t; cin >> t; while (t--) { int n; cin >> n; int i; int prev = 0; int prevc = 0; int f = 1; for (int i = 0; i < int(n); i++) { int x, y; cin >> x >> y; if (x >= prev && (y - prevc <= x - prev) && y <= x && y >= prevc) { prev = x; prevc = y; continue; } else { f = 0; } } if (f == 0) cout << "NO" << endl; else cout << "YES" << endl; } return 0; }
#include <bits/stdc++.h> using namespace std; int main() { long long int t, i, j, k, l, n, m; cin >> t; while (t--) { cin >> n; long long int p[n], c[n]; for (i = 0; i < n; i++) cin >> p[i] >> c[i]; int fl = 1; for (i = 0; i < n; i++) { if (c[i] > p[i]) { fl = 0; break; } } for (i = 1; i < n; i++) { if (p[i] < p[i - 1] || c[i] < c[i - 1]) { fl = 0; break; } } for (i = 1; i < n; i++) { k = p[i] - p[i - 1]; l = c[i] - c[i - 1]; if (k < l) { fl = 0; break; } } if (fl) cout << "YES\n"; else cout << "NO\n"; } return 0; }
#include <bits/stdc++.h> using namespace std; void Fastio() { ios::sync_with_stdio(0); cin.tie(0); cout.tie(0); } long long fact[1000006], inv[1000006]; long long fp(long long base, long long exp) { if (exp == 0) return 1; long long ans = fp(base, exp / 2); ans = (ans * ans) % 998244353; if (exp % 2 != 0) ans = (ans * (base % 998244353)) % 998244353; return ans; } void calcFacAndInv(long long n) { fact[0] = inv[0] = 1; for (long long i = 1; i <= n; i++) { fact[i] = (i * fact[i - 1]); inv[i] = fp(fact[i], 998244353 - 2); } } long long ncr(long long n, long long r) { return ((fact[n] * inv[r]) % 998244353 * inv[n - r]) % 998244353; } long long npr(long long n, long long r) { return (fact[n] * inv[n - r]) % 998244353; } long double NCR(int n, int m) { long double res = 1; m = min(m, n - m); for (int i = 0; i < m; i++) { res = res * (n - i) / (i + 1); } return res; } long long tol(string a) { long long res = 0; while (a[0] == '0') { a.erase(a.begin()); } if (a == "") a = "0"; for (int i = 0; i < a.size(); i++) { res *= 10; res += a[i] - '0'; } return res; } int check(string a, string b) { for (int i = 0; i < a.size(); i++) { if (a[i] > b[i]) return 1; if (b[i] > a[i]) return -1; } return 0; } class data { public: long long v, d, p; data() {} data(long long vv, long long dd, long long pp) { v = vv; d = dd; p = pp; } }; int primeFactors(int n) { long long c = 0; while (n % 2 == 0) { c++; n = n / 2; } for (int i = 3; i * i <= n; i = i + 2) { while (n % i == 0) { c++; n = n / i; } } if (n > 2) c++; return c; } int main() { Fastio(); int t; cin >> t; while (t--) { int n; cin >> n; pair<int, int> arr[n]; bool st = 1; for (int i = 0; i < n; i++) { cin >> arr[i].first >> arr[i].second; if (!i) { if (arr[i].first < arr[i].second) st = 0; continue; } int tmp1, tmp2; tmp1 = arr[i].first - arr[i - 1].first; tmp2 = arr[i].second - arr[i - 1].second; if (tmp1 < 0 || tmp2 < 0) st = 0; if (tmp1 < tmp2) st = 0; } if (st) cout << "YES\n"; else cout << "NO\n"; } return 0; }
#include <bits/stdc++.h> using namespace std; int main() { int t; cin >> t; while (t--) { int n; cin >> n; int p, c; cin >> p >> c; bool f = true; if (p < c) f = false; for (int i = 2; i <= n; i++) { int a, b; cin >> a >> b; if (a - p < b - c) { f = false; } if (a < p || b < c) { f = false; } if (a < b) f = false; p = a; c = b; } if (f) cout << "YES" << endl; else cout << "NO" << endl; } }
#include <bits/stdc++.h> using namespace std; const long long mod = 1000000007; long long powmod(long long a, long long b) { long long res = 1; a %= mod; assert(b >= 0); for (; b; b >>= 1) { if (b & 1) res = res * a % mod; a = a * a % mod; } return res; } long long gcd(long long a, long long b) { return b ? gcd(b, a % b) : a; } int t; int n; int x, y; int main() { scanf("%d", &t); while (t--) { scanf("%d", &n); scanf("%d%d", &x, &y); bool f = false; int prex = x, prey = y; if (x < y) f = true; for (int i = 1; i < n; i++) { scanf("%d%d", &x, &y); if (x < y) f = true; if (x >= prex && y < prey) f = true; if (x < prex) f = true; int maxx = x - prex + prey; if (x >= prex && y > maxx) f = true; prex = x; prey = y; } if (f) printf("NO\n"); else printf("YES\n"); } return 0; }
#include <bits/stdc++.h> using namespace std; long long int n, k, m, d, t; vector<pair<long long int, long long int> > v; long long int p[105]; long long int c[105]; int main() { cin >> t; while (t--) { cin >> n; for (int i = 0; i < n; i++) { cin >> p[i] >> c[i]; } int flag = 1; if (n == 1) { if (c[0] > p[0]) { flag = 0; } } for (int i = 0; i < (n - 1); i++) { if ((p[i + 1] < p[i]) || (c[i + 1] < c[i])) { flag = 0; break; } if ((c[i + 1] - c[i]) > (p[i + 1] - p[i])) { flag = 0; break; } if (c[i] > p[i]) { flag = 0; break; } } if (c[n - 1] > p[n - 1]) { flag = 0; } if (flag) { cout << "YES" << endl; } else { cout << "NO" << endl; } } return 0; }
#include <bits/stdc++.h> using namespace std; using ll = long long; using Vi = vector<int>; using Pii = pair<int, int>; int uplg(int n) { return 32 - __builtin_clz(n); } int uplg(ll n) { return 64 - __builtin_clzll(n); } void run(); int main() { cin.sync_with_stdio(0); cin.tie(0); cout << fixed << setprecision(18); run(); return 0; } void run() { int t; cin >> t; while (t--) { int n; cin >> n; vector<Pii> stats(n); for (auto& k : (stats)) cin >> k.first >> k.second; bool ans = 1; if (stats[0].first < stats[0].second) { ans = 0; } else { for (int i = (1); i < (n); i++) { int a = stats[i].first - stats[i - 1].first; int b = stats[i].second - stats[i - 1].second; if (a < 0 || b < 0 || a < b) { ans = 0; break; } } } cout << (ans ? "YES\n" : "NO\n"); } }
#include <bits/stdc++.h> using namespace std; vector<string> solve(const vector<vector<pair<int, int>>> _data) { vector<string> res; int last_t = 0; int last_w = 0; bool a = false; for (vector<pair<int, int>> vec : _data) { last_t = vec[0].first; last_w = vec[0].second; if (last_w > last_t) { res.push_back("NO"); continue; } else { if (vec.size() > 1) { a = false; for (int i = 1; i < vec.size(); ++i) { last_w = vec[i - 1].second; last_t = vec[i - 1].first; if (last_t <= vec[i].first && last_w <= vec[i].second) { if ((vec[i].second - last_w) > (vec[i].first - last_t)) { res.push_back("NO"); a = true; break; } } else { res.push_back("NO"); a = true; break; } } if (!a) res.push_back("YES"); } else if (vec.size() == 1) { res.push_back("YES"); continue; } } } return res; } int main() { ios::sync_with_stdio(0); cin.tie(0); int t; cin >> t; vector<vector<pair<int, int>>> data(t); for (int k = 0; k < t; ++k) { int n; cin >> n; for (int i = 0; i < n; ++i) { int v1, v2; cin >> v1 >> v2; data[k].push_back(make_pair(v1, v2)); } } vector<string> _res = solve(data); for (string s : _res) cout << s << "\n"; return 0; }
#include <bits/stdc++.h> using namespace std; int main() { ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0); int n, q; cin >> q; int p, c, p1, c1; while (q--) { cin >> n; bool ans = true; cin >> p >> c; if (c > p) ans = false; for (int i = 1; i < n; i++) { cin >> p1 >> c1; if (c1 > p1) ans = false; if (!((p1 > p && c1 == c) || (p1 == p && c1 == c) || (c1 > c && p1 > p && p1 - p >= c1 - c))) ans = false; c = c1; p = p1; } if (ans) { cout << "YES\n"; } else { cout << "NO\n"; } } }
#include <bits/stdc++.h> using namespace std; void solve() { int n; cin >> n; int p[n]; int c[n]; for (int i = 0; i < n; i++) { cin >> p[i] >> c[i]; } if (p[0] < c[0]) { cout << "NO\n"; return; } for (int i = 1; i < n; i++) { if ((p[i] < p[i - 1]) || (c[i] < c[i - 1]) || (p[i] - p[i - 1] < c[i] - c[i - 1])) { cout << "NO\n"; return; } } cout << "YES\n"; } int main() { int t; cin >> t; while (t--) { solve(); } }
#include <bits/stdc++.h> using namespace std; int main() { int t; cin >> t; while (t > 0) { int n; cin >> n; int a[n], b[n]; for (int i = 0; i < n; i++) { cin >> a[i] >> b[i]; } if (a[0] < b[0]) { cout << "NO" << endl; goto label; } for (int i = 1; i < n; i++) { if (a[i] < a[i - 1]) { cout << "NO" << endl; goto label; } if (b[i] < b[i - 1]) { cout << "NO" << endl; goto label; } if (a[i] - a[i - 1] < b[i] - b[i - 1]) { cout << "NO" << endl; goto label; } } cout << "YES" << endl; label: t--; } }
#include <bits/stdc++.h> using namespace std; long long int a[105], b[105]; int main() { long long int t; cin >> t; while (t--) { long long int n, i, count; cin >> n; for (i = 1; i <= n; i++) { cin >> a[i] >> b[i]; } count = 0; for (i = 1; i <= n; i++) if (a[i] >= a[i - 1] && b[i] >= b[i - 1] && a[i] - a[i - 1] >= b[i] - b[i - 1]) { continue; } else { count = 1; } if (count) cout << "NO" << endl; else cout << "YES" << endl; } return 0; }
#include <bits/stdc++.h> using namespace std; int main() { int q; cin >> q; for (int w = 0; w < q; w++) { int n; cin >> n; int p[n], c[n]; for (int i = 0; i < n; i++) { cin >> p[i] >> c[i]; } bool isValid = true; if (p[0] < c[0]) { isValid = false; cout << "NO\n"; continue; } for (int i = 1; i < n; i++) { if (p[i] < p[i - 1] || c[i] < c[i - 1] || c[i] > p[i] || (c[i] - c[i - 1]) > (p[i] - p[i - 1])) { isValid = false; break; } } if (isValid) cout << "YES\n"; else cout << "NO\n"; } return 0; }
#include <bits/stdc++.h> using namespace std; int main() { int t; cin >> t; while (t--) { int cr; cin >> cr; int p[cr], c[cr]; for (int i = 0; i < cr; i++) { cin >> p[i] >> c[i]; } string ans = "YES"; for (int i = 1; i < cr; i++) { if (((p[i] < p[i - 1]) || ((c[i] < c[i - 1]) || (c[i] - c[i - 1] > p[i] - p[i - 1])))) { ans = "NO"; break; } } if (c[0] > p[0]) cout << "NO" << endl; else cout << ans << endl; } }
#include <bits/stdc++.h> using namespace std; int p[105], c[105]; int main() { ios::sync_with_stdio(false); int t; cin >> t; while (t--) { int n; cin >> n; for (int i = 1; i <= n; i++) cin >> p[i] >> c[i]; int f = 1; for (int i = 1; i <= n; i++) { if (c[i] > p[i]) f = 0; if (p[i] < p[i - 1] || c[i] < c[i - 1]) f = 0; if (p[i] - p[i - 1] < c[i] - c[i - 1]) f = 0; } if (f) puts("YES"); else puts("NO"); } return 0; }
#include <bits/stdc++.h> using namespace std; signed main() { ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL); int tcase; cin >> tcase; while (tcase--) { long long int n, i; cin >> n; vector<pair<long long int, long long int> > v; for (i = 0; i < n; i++) { long long int x, y; cin >> x >> y; v.push_back(make_pair(x, y)); } if (n == 1) { if (v[0].first >= v[0].second) cout << "YES\n"; else cout << "NO\n"; } else { if (v[0].first >= v[0].second) { bool flag = true; for (i = 1; i < n; i++) { if (v[i].first >= v[i - 1].first and v[i].second >= v[i - 1].second and v[i].first >= v[i].second and v[i].first - v[i - 1].first >= v[i].second - v[i - 1].second) continue; else { flag = false; break; } } if (!flag) cout << "NO\n"; else cout << "YES\n"; } else cout << "NO\n"; } } }
#include <bits/stdc++.h> using namespace std; int main() { ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0); long long int t; cin >> t; while (t--) { long long int n; cin >> n; long long int a[n][2]; for (int i = (0); i < (n); i++) cin >> a[i][0] >> a[i][1]; if (a[0][0] < a[0][1]) { cout << "NO" << endl; continue; } for (int i = (1); i < (n); i++) { if (a[i][0] < a[i - 1][0] || a[i][1] < a[i - 1][1]) { cout << "NO" << endl; goto out; } else if ((a[i][0] - a[i - 1][0]) < (a[i][1] - a[i - 1][1])) { cout << "NO" << endl; goto out; } } cout << "YES" << endl; out:; } return 0; }
#include <bits/stdc++.h> using namespace std; int c[120], p[120]; int main() { ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL); cout.precision(16); ; int t; cin >> t; while (t--) { int n, flag = 0; cin >> n; for (int i = 0; i < n; i++) cin >> p[i] >> c[i]; for (int i = 0; i < n; i++) if (c[i] > p[i]) { flag = 1; break; } for (int i = 1; i < n; i++) { if (c[i] - c[i - 1] > p[i] - p[i - 1] || p[i] < p[i - 1] || c[i] < c[i - 1]) { flag = 1; break; } } if (flag) cout << "NO" << endl; else cout << "YES" << endl; } return 0; }
#include <bits/stdc++.h> using namespace std; using ll = long long; using i2 = pair<int, int>; int main() { ios_base::sync_with_stdio(false); cin.tie(0); int T; cin >> T; while (T--) { int n; cin >> n; int pp = 0, pc = 0; bool ok = true; for (int i = 1; i <= n; i++) { int np, nc; cin >> np >> nc; if (np - pp < nc - pc || nc - pc < 0) ok = false; pp = np; pc = nc; } cout << (ok ? "YES\n" : "NO\n"); } return 0; }
#include <bits/stdc++.h> using namespace std; int main() { ios::sync_with_stdio(0); cin.tie(0); int t; cin >> t; while (t--) { int n; cin >> n; int prp, prc; cin >> prp >> prc; bool flag = false; if (prp < prc) { flag = true; } for (int i = 1; i < n; i++) { int p, c; cin >> p >> c; if (p < prp || c < prc) { flag = true; } if (p < c) { flag = true; } if (abs(prp - p) < abs(prc - c)) { flag = true; } prp = p; prc = c; } if (flag) { cout << "NO\n"; } else { cout << "YES\n"; } } return 0; }
#include <bits/stdc++.h> using namespace std; int main() { int n; cin >> n; for (int i = 0; i < n; ++i) { int k; cin >> k; bool ok = true; int pa = 0, pb = 0; for (int j = 0; j < k; ++j) { int a, b; cin >> a >> b; if (a < pa || b < pb) ok = false; if (a == pa && b != pb) ok = false; if (a > pa && (a - pa) < (b - pb)) ok = false; pa = a; pb = b; } cout << (ok ? "YES" : "NO") << endl; } }
#include <bits/stdc++.h> using namespace std; #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") void input(long long int n, long long int a[]) { for (long long int i = 0; i < n; ++i) cin >> a[i]; } long long int bin_expo(long long int A, long long int B, long long int M) { long long int result = 1ll; while (B > 0) { if (B % 2 == 1) { result = (result * A) % M; } A = (A * A) % M; B = B / 2; } return result; } 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 * b) / gcd(a, b); } int main() { ios_base::sync_with_stdio(0); long long int t; cin >> t; while (t--) { long long int n; cin >> n; pair<long long int, long long int> pa[n]; for (long long int i = 0; i < n; ++i) cin >> pa[i].first >> pa[i].second; long long int flag = 0; for (long long int i = 0; i < n; ++i) { if (pa[i].first < pa[i].second) { flag = 1; break; } } for (int i = 1; i < n; i++) { long long int tot_plays = pa[i].first - pa[i - 1].first; long long int tot_score = pa[i].second - pa[i - 1].second; if (tot_plays >= 0 && tot_score >= 0 && tot_score <= tot_plays) continue; flag = 1; break; } if (flag) cout << "NO" << endl; else cout << "YES" << endl; } return 0; }
#include <bits/stdc++.h> #pragma GCC optimize("-O3") using ll = long int; using namespace std; ll m; int main() { ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0); ll t, x, a, b, q, r, f, l, h; cin >> t; while (t--) { ll n; q = 0; cin >> n; int bl = 1; r = 0; ll p[n], c[n]; h = 0; for (ll i = 0; i < n; i++) { cin >> p[i] >> c[i]; } for (ll i = 0; i < n; i++) { a = p[i]; b = c[i]; if (b >= r and a >= q and a - h >= b and a >= b) { h = a - b; q = a; r = b; } else bl = 0; } if (bl == 1) cout << "Yes\n"; else cout << "No\n"; } return 0; }
#include <bits/stdc++.h> using namespace std; const int MAXN = 1e6 + 5; int n, m, t; int v[MAXN]; char s[MAXN]; int main() { cin >> t; while (t--) { cin >> n; int a, b; cin >> a >> b; int flag = a >= b; for (int i = 1; i <= n - 1; i++) { int tmpa, tmpb; cin >> tmpa >> tmpb; if (tmpa < a || tmpb < b || tmpb - b > tmpa - a) flag = 0; a = tmpa, b = tmpb; } if (flag) cout << "YES"; else cout << "NO"; cout << endl; } }
#include <bits/stdc++.h> using namespace std; long long t, a, b, c, n, lasta = -1, lastb = -1; bool ok = 1; int main() { ios_base::sync_with_stdio(0); cin.tie(); cout.tie(); cin >> t; while (t--) { ok = 1; cin >> n; lasta = -1, lastb = -1; for (long long i = 0; i < n; i++) { cin >> a >> b; if (lasta == -1 and lastb == -1) { lasta = a; lastb = b; } if (lasta <= a and lastb <= b and a >= b and (a - lasta) >= (b - lastb)) { lasta = a; lastb = b; } else { ok = 0; } } if (ok) cout << "YES\n"; else cout << "NO\n"; } return 0; }
#include <bits/stdc++.h> using namespace std; int main() { int i, n, m, j, k, t, p, c, nowp, nowc; bool flag = true; scanf("%d", &t); while (t--) { flag = true; nowp = nowc = 0; scanf("%d", &n); for (i = 1; i <= n; i++) { scanf("%d%d", &p, &c); if (!flag) continue; if (p >= nowp && c >= nowc) { if (p - nowp < c - nowc) { flag = false; } if (nowp < p) nowp = p; if (nowc < c) nowc = c; } else { flag = false; } } if (flag) printf("YES\n"); else printf("NO\n"); } }
#include <bits/stdc++.h> using namespace std; int main() { int t; cin >> t; while (t-- > 0) { int n; cin >> n; vector<int> a(n); vector<int> b(n); for (int i = 0; i < n; i++) { cin >> a[i] >> b[i]; } int i = 0; int val1 = a[i], val2 = b[i]; if (val1 < val2) { cout << "NO" << endl; continue; } for (i = 1; i < n; i++) { if ((a[i] < b[i]) or (a[i] < val1) or (b[i] < val2) or (a[i] - val1 < b[i] - val2)) { break; cout << "hahahah" << endl; } else { val1 = a[i], val2 = b[i]; } } if (i != n) { cout << "NO"; } else { cout << "YES"; } cout << "\n"; } return 0; }
#include <bits/stdc++.h> using namespace std; int main() { long long int t, n, i, a, b; cin >> t; while (t--) { cin >> n; bool f = false; vector<long long int> p(n), c(n); for (i = 0; i < n; i++) { cin >> a >> b; p[i] = a, c[i] = b; } for (i = 1; i < n; i++) { if (p[i] < p[i - 1]) { f = true; cout << "NO" << "\n"; break; } if (c[i] < c[i - 1]) { f = true; cout << "NO" << "\n"; break; } } if (!f) { for (i = 0; i < n; i++) { if (c[i] > p[i]) { f = true; cout << "NO" << "\n"; break; } } } if (!f) { for (i = 0; i < n - 1; i++) { if (c[i + 1] - c[i] > p[i + 1] - p[i]) { f = true; cout << "NO" << "\n"; break; } } } if (!f) cout << "YES" << "\n"; } }
#include <bits/stdc++.h> using namespace std; int main() { ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0); int n, t; cin >> t; while (t--) { cin >> n; vector<pair<int, int>> a(n); for (int i = 0; i < (int)n; i++) cin >> a[i].first >> a[i].second; bool ok = 1; if (n == 1 && (a[0].first < a[0].second)) ok = 0; for (int i = 0; i < (int)n - 1; i++) { if (a[i + 1].first - a[i].first < a[i + 1].second - a[i].second) ok = 0; if (a[i + 1].second > a[i].second) { if (a[i + 1].first <= a[i].first) ok = 0; } else if (a[i + 1].second < a[i].second) ok = 0; if (a[i + 1].first < a[i].first) ok = 0; if (a[i].first < a[i].second) ok = 0; } cout << (ok ? "YES\n" : "NO\n"); } }
#include <bits/stdc++.h> using namespace std; int main() { ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0); long long t; cin >> t; while (t--) { long long n, flag = 1; cin >> n; long long p[n + 1], c[n + 1]; long long diff1 = 0, diff2 = 0; for (long long i = 1; i <= n; i++) { cin >> p[i] >> c[i]; } for (long long i = 1; i <= n; i++) { diff1 = p[i] - diff1; diff2 = c[i] - diff2; if (diff1 < diff2 || diff1 < 0 || diff2 < 0) { flag = 0; break; } diff1 = p[i]; diff2 = c[i]; } if (flag == 1) cout << "YES" << endl; else cout << "NO" << endl; } return 0; }
#include <bits/stdc++.h> using namespace std; int main() { int t; cin >> t; while (t--) { int n, x = 0, y = 0, p = 0, q = 0; cin >> n; bool ans = true; for (int i = 1; i <= n; i++) { cin >> p >> q; if (p < x || q < y) ans = false; else if (q - y > p - x) ans = false; x = p; y = q; } if (ans == true) cout << "YES" << endl; else cout << "NO" << endl; } }
#include <bits/stdc++.h> using namespace std; int32_t main() { ios_base::sync_with_stdio(NULL); cin.tie(NULL); cout.tie(NULL); long long t; cin >> t; while (t--) { long long n; cin >> n; long long p, c, lp, lc; long long pos = 0; for (long long i = 0; i < n; i++) { cin >> p >> c; if (i > 0) { if (p < c) { pos = 1; continue; } if (c < lc) { pos = 1; continue; } if (p < lp) { pos = 1; continue; } if (c - lc > p - lp) { pos = 1; } } if (i == 0) { if (p < c) { pos = 1; continue; } } lc = c; lp = p; } if (pos) cout << "NO\n"; else cout << "YES\n"; } }
#include <bits/stdc++.h> using namespace std; int main() { long long int t; cin >> t; while (t--) { long long int n; cin >> n; long long int a, b; long long int c = 0, d = 0; bool f = true; for (long long int i = 0; i < n; i++) { cin >> a >> b; if (a < c || b < d || a - c < b - d) f = false; c = a, d = b; } if (f) cout << "YES" << endl; else cout << "NO" << endl; } }
#include <bits/stdc++.h> using namespace std; int main() { int t; cin >> t; while (t--) { int num; cin >> num; int min1 = -1, min2 = -1; int temp1, temp2; bool val = true; for (int i = 0; i < num; i++) { cin >> temp1 >> temp2; int avoid = ((temp1 - min1) - (temp2 - min2)); if (i != 0) { if (temp1 < min1 || temp2 < min2 || avoid < 0) { val = false; } } if (temp2 > temp1) val = false; min1 = temp1; min2 = temp2; } if (val) cout << "YES" << endl; else cout << "NO" << endl; } return 0; }
#include <bits/stdc++.h> using namespace std; const int MOD = 1e9 + 7; const long double PI = 4 * atan((long double)1); long long int get_hash(string s) { long long int N = 1000001; long long int base[N], A = 11, MD = 1110111110111; base[0] = 1; for (int i = (1); i < (N); ++i) base[i] = (base[i - 1] * A) % MD; long long int hs = 0; for (int i = (0); i < (s.size()); ++i) { hs += (s[i] * base[i]); hs %= MD; } return hs; } long long power(long long a, long long n) { long long res = 1; while (n) { if (n % 2) res *= a; a *= a; n /= 2; } return res; } int main() { ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0); ; int t; cin >> t; while (t--) { int n; cin >> n; int e = 0; long long int x[n], y[n]; for (int i = (0); i < (n); ++i) { cin >> x[i] >> y[i]; if (x[i] < y[i]) { e = 1; } } if (e == 1) { cout << "NO\n"; continue; } long long int a[n - 1], b[n - 1]; for (int i = (1); i < (n); ++i) { a[i - 1] = x[i] - x[i - 1]; b[i - 1] = y[i] - y[i - 1]; } for (int i = (0); i < (n - 1); ++i) { if (a[i] < 0 || b[i] < 0) { e = 1; break; } if (b[i] > a[i]) { e = 1; break; } } if (e == 1) cout << "NO"; else cout << "YES"; cout << "\n"; } return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 100; int t, n; int main() { ios_base::sync_with_stdio(0); cin.tie(0); cin >> t; while (t--) { cin >> n; int lp = 0, lc = 0; int pi, ci; bool poss = true; for (int i = 0; i < n; i++) { cin >> pi >> ci; if (ci - lc > pi - lp) { poss = false; } if (lc > ci || lp > pi) { poss = false; } lc = ci; lp = pi; } if (poss) { cout << "YES\n"; } else { cout << "NO\n"; } } return 0; }
#include <bits/stdc++.h> #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") using namespace std; long long q, n; int main() { ios_base::sync_with_stdio(0); cin.tie(0); cin >> q; while (q--) { cin >> n; long long p = 0, c = 0; long long ap, ac; bool t = 1; for (long long i = 0; i < n; ++i) { cin >> ap >> ac; if (ap < ac) t = 0; if ((ap < p) || (ac < c)) t = 0; if ((ap - p) < (ac - c)) t = 0; p = ap; c = ac; } cout << (t ? "YES" : "NO") << "\n"; } }
#include <bits/stdc++.h> using namespace std; int main() { int testcases; cin >> testcases; while (testcases--) { int n, flag = 0; cin >> n; int x[n], y[n]; cin >> x[0] >> y[0]; if (y[0] > x[0]) { flag = 1; } for (int i = 1; i < n; ++i) { cin >> x[i] >> y[i]; if ((x[i] < x[i - 1]) or (y[i] < y[i - 1]) or ((y[i] - y[i - 1]) > (x[i] - x[i - 1]))) { flag = 1; } } if (flag) { cout << "NO\n"; } else { cout << "YES\n"; } } return 0; }
#include <bits/stdc++.h> using namespace std; int main() { int t, n, i, j, a, a1, b, b1, f = 0; cin >> t; for (i = 0; i < t; i++) { cin >> n; cin >> a1 >> b1; if (a1 < b1) { f++; } for (j = 1; j < n; j++) { cin >> a >> b; if (a < b || a - a1 < b - b1) { f++; } else if ((a > a1 && b >= b1) || (a == a1 && b == b1)) { a1 = a; b1 = b; } else { f++; } } if (f == 0) { cout << "YES" << endl; } else { cout << "NO" << endl; } f = 0; } }
#include <bits/stdc++.h> using namespace std; const int M = 100005; long long int N = 1e9 + 7; long long int Z = 998244353; int gcd(int a, int b) { if (b == 0) return a; return gcd(b, a % b); } void precompute() {} int max3(int x, int y, int z) { return max(x, max(y, z)); } long long int power(long long int x, unsigned int y, int p) { long long int res = 1; x = x % p; while (y > 0) { if (y & 1) res = (res * x) % p; y = y >> 1; x = (x * x) % p; } return res; } long long int modinv(long long int x, int p) { return (power(x, p - 2, p)); } bool compare(const pair<int, int> &p1, const pair<int, int> &p2) { return (p1.first > p2.first); } int main() { ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL); int t; cin >> t; precompute(); while (t--) { int n, x = 0, y = 0, prevx = 0, prevy = 0; cin >> n; int flag = 0; for (int i = 0; i < n; i++) { cin >> x >> y; if (((x - prevx) >= 0) && ((y - prevy) >= 0) && (y - prevy) <= (x - prevx)) { } else { flag = 1; } prevx = x; prevy = y; } if (flag == 1) { cout << "NO\n"; } else { cout << "YES\n"; } } return 0; }
#include <bits/stdc++.h> using namespace std; using ll = long long; using Vi = vector<int>; using Vl = vector<ll>; using Pii = pair<int, int>; using Pll = pair<ll, ll>; constexpr int I_INF = numeric_limits<int>::max(); constexpr ll L_INF = numeric_limits<ll>::max(); constexpr double PI = 3.1415926535897932384626433832795028841971; void solve() { int Q; cin >> Q; cout << setprecision(20); while (Q--) { double N; cin >> N; double phi = 0; ll cnt = 0; while (phi < PI / 4.0) { phi += PI / N; ++cnt; } double z = PI / (2.0 * N) + PI / N * (N / 2 - cnt); double th = PI / 4.0 - z; double ans = cos(th) / sin(PI / (2.0 * N)); cout << ans << "\n"; } } int main() { cin.tie(0), cout.tie(0); ios::sync_with_stdio(false); solve(); cout << flush; return 0; }
#include <bits/stdc++.h> using namespace std; struct edge { int t, f, w; bool operator<(const edge& e) const { return w > e.w; } edge(int from, int to, int weight) { t = to; f = from; w = weight; } }; const double EPS = (1e-5); struct line { double a, b, c; }; struct point { double x, y; point() { x = y = 0.0; } point(double _x, double _y) : x(_x), y(_y) {} bool operator==(point other) const { return (fabs(x - other.x) < EPS && (fabs(y - other.y) < EPS)); } }; double dist(point p1, point p2) { return fabs(p1.x - p2.x) * fabs(p1.x - p2.x) + fabs(p1.y - p2.y) * fabs(p1.y - p2.y); } void pointsToLine(point p1, point p2, line& l) { if (fabs(p1.x - p2.x) < EPS) { l.a = 1.0; l.b = 0.0; l.c = -p1.x; } else { l.a = -(double)(p1.y - p2.y) / (p1.x - p2.x); l.b = 1.0; l.c = -(double)(l.a * p1.x) - p1.y; } } bool areParallel(line l1, line l2) { return (fabs(l1.a - l2.a) < EPS) && (fabs(l1.b - l2.b) < EPS); } bool areSame(line l1, line l2) { return areParallel(l1, l2) && (fabs(l1.c - l2.c) < EPS); } bool areIntersect(line l1, line l2, point& p) { if (areParallel(l1, l2)) return false; p.x = (l2.b * l1.c - l1.b * l2.c) / (l2.a * l1.b - l1.a * l2.b); if (fabs(l1.b) > EPS) p.y = -(l1.a * p.x + l1.c); else p.y = -(l2.a * p.x + l2.c); return true; } long long binpowmod(long long a, long long b, long long m) { a %= m; long long res = 1; while (b > 0) { if (b & 1) res = res * a % m; a = a * a % m; b >>= 1; } return res; } long long binpow(long long a, long long b) { long long res = 1; while (b > 0) { if (b & 1) res = res * a; a = a * a; b >>= 1; } return res; } int findXOR(int n) { switch (n % 4) { case 0: return n; case 1: return 1; case 2: return n + 1; case 3: return 0; } } int rangeXOR(int l, int r) { return (findXOR(l - 1) ^ findXOR(r)); } int getbit(int mask, int bit) { return (mask & (1 << bit)); } void setbit(int& mask, int bit, int val) { if (val) mask |= (1 << bit); else mask &= ~(1 << bit); } const int N = 1e5 + 10; const int M = 2e5 + 10; const long long INF = 9999999; int BIT[N]; void update(int x, int val) { ++x; while (x <= N) { BIT[x] += val; x += (x & -x); } } int query(int x) { ++x; int res = 0; while (x > 0) { res += BIT[x]; x -= (x & -x); } return res; } void solve() { int n; cin >> n; cout << setprecision(10) << fixed << 1 / (2 * sin(acos(-1) / 4 / n)) << endl; } int main(void) { int tc = 1; cin >> tc; while (tc--) { solve(); } }
#include <bits/stdc++.h> using namespace std; int main() { ios_base::sync_with_stdio(0), cin.tie(0); int t; cin >> t; while (t--) { int n; cin >> n; cout << fixed << setprecision(9) << cos(3.14159265358979323846 / (4 * n)) / sin(3.14159265358979323846 / (2 * n)) << "\n"; } return 0; }
#include <bits/stdc++.h> using namespace std; int main() { ios::sync_with_stdio(NULL); cin.tie(NULL); cout.tie(NULL); int tc; cin >> tc; while (tc--) { double n; cin >> n; double pi = acos(-1.0); n *= 2; double angle = 360 / n; angle /= 2; double biglen = 0.5 / (sin(angle * pi / 180)); double ans = 1e9; for (double i = 0; i <= angle * 2; i += 0.0001) { double ans1, ans2; ans1 = biglen * cos(i * pi / 180); double a = 0.5 * i / angle; ans2 = a / sin(i * pi / 180); ans = min(ans, max(ans1, ans2)); } cout << fixed << setprecision(9) << ans * 2 << "\n"; } }
#include <bits/stdc++.h> using namespace std; void fastio() { ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0); cout << fixed; cout.precision(9); } int main() { fastio(); int t; cin >> t; while (t--) { double n; cin >> n; n *= 2; double angle = (3.141592653589793 - 2 * 3.141592653589793 / n) / 2; double ans = sin(3.141592653589793 / 2 * (n - 1) / n) * 1 / (sin(3.141592653589793 / n)); cout << ans << "\n"; } return 0; }
#include <bits/stdc++.h> using namespace std; bool comp(int x, int y) { return x > y; } int main() { ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0); ; int t = 1; cin >> t; while (t--) { double n; cin >> n; cout << fixed << setprecision(9) << cos(3.1415926535 / (4 * n)) / sin(3.1415926535 / (2 * n)) << '\n'; } }
#include <bits/stdc++.h> using namespace std; double sides[405]; int main() { std::cout << std::fixed; std::cout << std::setprecision(10); double theta = 0; for (int i = 2; i < 405; i++) { sides[i] = cos(2 * acos(0) / (i * 2)) / sin(2 * acos(0) / (i)); } int T; int n; cin >> T; while (T--) { cin >> n; n = n << 1; cout << sides[n] << "\n"; } return 0; }
#include <bits/stdc++.h> using namespace std; int main() { int t; cin >> t; while (t--) { int n; cin >> n; double x = (3.14159265358979323846 / (double)n); double r = 0.5 / cos((3.14159265358979323846 - x) / 2.0); double ans = r * sin((3.14159265358979323846 - x) / 2.0 + x / 4.0) * 2.0; cout << fixed << setprecision(9) << ans << endl; } }
#include <bits/stdc++.h> using namespace std; const int MODA = 1000000007; long long int ncr(long long int, long long int); long long int power(long long int, long long int); long long int modi(long long int); long long int powm(long long int, unsigned int); long long int gcd(long long int, long long int); long long int kadane(long long int[], long long int); bool isPrime(long long int); bool isPowerTwo(long long int); bool isSubstring(string, string); void generateFactors(long long int); void generatePrimeFactors(long long int); void facto(long long int); void SieveOfEratosthenes(long long int); void mo_dfs(long long int, long long int); long long int fact[1025] = {}; bool prime[105]; long long int timer; long long int S[100], T[100], FT[200]; vector<int> ADJ[100]; vector<long long int> factors; vector<long long int> primefactors; int main() { ios_base::sync_with_stdio(false); cin.tie(0); int tc = 1; cin >> tc; while (tc--) { int n; cin >> n; cout << fixed << setprecision(10) << cos(3.1415926535897932384626433832795 / (4 * n)) / sin(3.1415926535897932384626433832795 / (2 * n)) << "\n"; } return 0; } void facto(long long int n) { fact[0] = 1; for (int i = 1; i <= n; i++) fact[i] = (i * 1ll * fact[i - 1]) % MODA; } long long int power(long long int a, long long int b) { long long int res = 1; while (b) { if (b & 1) res = (res * a) % MODA; a = (a * a) % MODA; b >>= 1; } return res; } long long int modi(long long int a) { return powm(a, MODA - 2); } long long int powm(long long int x, unsigned int y) { if (y == 0) return 1; long long int p = power(x, y / 2) % MODA; p = (p * p) % MODA; return (y % 2 == 0) ? p : (x * p) % MODA; } long long int gcd(long long int a, long long int b) { if (a == 0) return b; return gcd(b % a, a); } bool isPowerTwo(long long int x) { return (x && !(x & (x - 1))); } long long int kadane(long long int a[], long long int size) { long long int max_so_far = INT_MIN, max_ending_here = 0; for (long long int i = 0; i < size; i++) { max_ending_here = max_ending_here + a[i]; if (max_so_far < max_ending_here) max_so_far = max_ending_here; if (max_ending_here < 0) max_ending_here = 0; } return max_so_far; } void generateFactors(long long int n) { factors.clear(); for (long long int i = 2; i * i <= n; i++) { if (n % i == 0) { factors.push_back(i); if (n / i != i) factors.push_back(n / i); } } factors.push_back(1); factors.push_back(n); sort(factors.begin(), factors.end()); } void generatePrimeFactors(long long int n) { primefactors.clear(); for (long long int i = 2; i * i <= n; i++) { if (n % i == 0) { primefactors.push_back(i); while (n % i == 0) n = n / i; } } if (n != 1) primefactors.push_back(n); } void SieveOfEratosthenes(long long int n) { memset(prime, true, sizeof(prime)); for (long long int p = 2; p * p <= n; p++) { if (prime[p] == true) { for (long long int i = p * p; i <= n; i += p) prime[i] = false; } } } long long int ncr(long long int n, long long int r) { if (r == 0) return 1; fact[0] = 1; for (int i = 1; i <= n; i++) fact[i] = fact[i - 1] * i % MODA; return (fact[n] * modi(fact[r]) % MODA * modi(fact[n - r]) % MODA) % MODA; } bool isPrime(long long int n) { if (n < 2) return false; for (long long int i = 2; i * i <= n; i++) if (n % i == 0) return false; return true; } void mo_dfs(long long int node, long long int parent) { S[node] = timer; FT[timer] = node; timer++; for (long long int child : ADJ[node]) { if (child != parent) mo_dfs(child, node); } T[node] = timer; FT[timer] = node; timer++; } bool isSubstring(string s1, string s2) { if (s1.find(s2) != string::npos) return true; else return false; }
#include <bits/stdc++.h> using namespace std; const long long int mod = 1e9 + 7; const int inf = 1e9; const int N = 2e5; int main() { ios_base::sync_with_stdio(false); cin.tie(NULL); int t; cin >> t; while (t--) { long long int n; cin >> n; long double res = 0; long double pi = 3.14159265; res = 1.0 / (2 * sin(pi / (4.0 * n))); cout << setprecision(9) << res << "\n"; } return 0; }
#include <bits/stdc++.h> using namespace std; const double PI = 3.14159265; int main() { ios::sync_with_stdio(false); int t; cin >> t; while (t--) { int n; cin >> n; cout << fixed << setprecision(7) << (cos(PI / (4 * n)) / sin(PI / (2 * n))) << endl; } }
#include <bits/stdc++.h> using namespace std; using ll = long long; int main() { int t; scanf("%d\n", &t); for (int itr = 0; itr < t; ++itr) { int n; scanf("%d", &n); double len_1 = 1.0, len_2 = 0.0; double b_angle = 3.14159265359 / (double)n; double angle = b_angle; for (int i = 0; i < n / 2; ++i) { len_1 += 2.0 * cos(angle); len_2 += 2.0 * sin(angle); angle += b_angle; } double th = 3.14159265359 / 4.0, low = 0.0, high = 3.14159265359 / 2.0; double a = len_1 * cos(th), b = len_2 * cos(th) + sin(th); while (fabs(a - b) > 0.0000000001) { if (a > b) { low = th; } else { high = th; } th = (low + high) / 2.0; a = len_1 * cos(th), b = len_2 * cos(th) + sin(th); } printf("%lf\n", a); } return 0; }
#include <bits/stdc++.h> using namespace std; int main() { long long int t, n; long double size, theta, theta1, theta2, x, y, r; cin >> t; while (t--) { cin >> n; theta = M_PI / n; r = 1 / (2 * sin(theta / 2)); theta1 = (M_PI * floor(n / 2)) / n; theta2 = M_PI - theta1; x = r * (sin(theta1 / 2)); y = r * (sin(theta2 / 2)); cout << fixed << setprecision(9) << (x + y) * sqrt(2) << endl; } return 0; }
#include <bits/stdc++.h> using namespace std; const long long int inf = 9e18; const long double pi = 2 * acos(0.0); long long int t, n; long double ans, angle, diff, dis, l, r; bool check(long double l, long double r) { if (abs(r - l) <= (1.0 / 1.0e9)) { return false; } else { return true; } } void solve() { cin >> n; angle = pi / n; diff = 1.0 / 1.0e5; dis = sin(pi / (2 * n)); ans = 2.0 * (sin((pi - angle) / 2.0) / (sin(angle))); l = 0.000000, r = angle; while (check(l, r)) { long double r1 = r * 1e6; long double l1 = l * 1e6; long double mid1 = ((2.0 * l1) + r1) / 3.0; long double mid2 = (l1 + (2.0 * r1)) / 3.0; mid1 /= 1.0e6; mid2 /= 1.0e6; long double x_left = 1.0e+99, x_right = -1.0e+99, y_left = 1.0e+99, y_right = -1.0e+99; for (long double j = 0; j < (2.0 * n); j += 1.0) { long double px = cos(((pi * j) / n) + mid1); long double py = sin(((pi * j) / n) + mid1); x_left = min(x_left, px); x_right = max(x_right, px); y_left = min(y_left, py); y_right = max(y_right, py); } long double ans1 = (max(x_right - x_left, y_right - y_left) / dis) / 2.0; x_left = 1.0e+99, x_right = -1.0e+99, y_left = 1.0e+99, y_right = -1.0e+99; for (long double j = 0; j < (2.0 * n); j += 1.0) { long double px = cos(((pi * j) / n) + mid2); long double py = sin(((pi * j) / n) + mid2); x_left = min(x_left, px); x_right = max(x_right, px); y_left = min(y_left, py); y_right = max(y_right, py); } long double ans2 = (max(x_right - x_left, y_right - y_left) / dis) / 2.0; if (ans1 <= ans2) { r = mid2; } else { l = mid1; } ans = min(ans, min(ans1, ans2)); } cout << fixed << setprecision(9) << ans << "\n"; } int32_t main(void) { ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL); ; cin >> t; while (t--) { solve(); } }
#include <bits/stdc++.h> double dist(double x1, double y1, double x2, double y2) { return sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2)); } int main() { int T; scanf("%d", &T); while (T--) { int n; scanf("%d", &n); n *= 2; double angle = 2 * acos(-1.0) / n, lo = 0.0, hi = angle / 2; double xtop = cos((n / 4 + 1) * angle), ytop = sin((n / 4 + 1) * angle); double x0 = 1.0, y0 = 0.0; double x1 = -1.0, y1 = 0.0; while (hi - lo > 1e-12) { double m1 = tan((hi + lo) / 2), m2 = -1 / m1; double xm = (m1 * xtop - ytop - m2 * x0 + y0) / (m1 - m2); double ym = m1 * xm - m1 * xtop + ytop; double xn = (m1 * xtop - ytop - m2 * x1 + y1) / (m1 - m2); double yn = m1 * xn - m1 * xtop + ytop; double xp = -xn, yp = -yn; double mn = dist(xm, ym, xn, yn), mp = dist(xm, ym, xp, yp); if (mn > mp) lo = (hi + lo) / 2; else hi = (hi + lo) / 2; } double m1 = tan((hi + lo) / 2), m2 = -1 / m1; double xm = (m1 * xtop - ytop - m2 * x0 + y0) / (m1 - m2); double ym = m1 * xm - m1 * xtop + ytop; double xn = (m1 * xtop - ytop - m2 * x1 + y1) / (m1 - m2); double yn = m1 * xn - m1 * xtop + ytop; double mn = dist(xm, ym, xn, yn); printf("%.9lf\n", mn / dist(x0, y0, cos(angle), sin(angle))); } return 0; }
#include <bits/stdc++.h> using namespace std; const double pi = 3.14159265359; int main() { ios::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL); int t; cin >> t; while (t--) { int n; cin >> n; cout << fixed << setprecision(10) << cos(pi / (4 * n)) / sin(pi / (n * 2)) << '\n'; } return 0; }
#include <bits/stdc++.h> const long long big = 998244353; using namespace std; long long power(long long a, long long n) { if (n == 0) return 1; if (n % 2 == 1) return (power(a, n - 1) * a) % big; else { long long b = power(a, n / 2); return (b * b) % big; } } void solve() { int n; cin >> n; double k = n; cout.precision(10); double r = 1 / sin(acos(-1) / (2 * k)); double a = 2 * r * r * (1 - cos(acos(-1) / k * (k - 1) / 2)); double b = 2 * r * r * (1 - cos(acos(-1) / k * (k + 1) / 2)); cout << (sqrt(a / 2) + sqrt(b / 2)) / 2 << '\n'; } int main() { ios_base::sync_with_stdio(false); cin.tie(NULL); long long t = 1; cin >> t; while (t--) { solve(); } }
#include <bits/stdc++.h> using namespace std; const int inf = 0x3f3f3f3f, mod = 1000000007; const double pi = 3.1415926535897932, eps = 1e-6; void chmax(int &x, int y) { if (x < y) x = y; } void chmin(int &x, int y) { if (x > y) x = y; } int T, n; void solve() { scanf("%d", &n); double deg = 360.0 / (n + n); double ans = 0; for (int(i) = (1); (i) <= (n / 2); (i)++) { double S = sin((deg * i - deg / 2.0) / 180.0 * pi); ans += S; } double ans1 = 2 * ans + 1.0; double rotate = deg / 4.0; ans1 = ans1 * cos(rotate / 180.0 * pi); printf("%.12lf\n", ans1); } int main() { scanf("%d", &T); while (T--) solve(); return 0; }
#include <bits/stdc++.h> using namespace std; double solvre(int n) { double ans = 0; ans += 1; double del = 3.14159265358979 / (n); double ang = del; while (ang < (3.14159265358979 / 2) - 10e-9) { ans += 2 * cos(ang); ang += del; } return ans * cos(del / 4); } int main() { int t; cin >> t; while (t--) { int n; scanf("%d", &n); printf("%.10lf\n", solvre(n)); } return 0; }
#include <bits/stdc++.h> using namespace std; long long int gcd(long long int a, long long int b) { return b == 0 ? a : gcd(b, a % b); } long long int lcm(long long int a, long long int b) { return a * (b / gcd(a, b)); } void solve() { double pi = atan(1) * 4; cout << setprecision(15); long long int n; cin >> n; double ans = 1 / (1.0 * sin(pi / (2.0 * n))); double temp = cos(pi / (4.0 * n)); cout << ans * temp << '\n'; } int main() { ios_base::sync_with_stdio(false), cin.tie(NULL), cout.tie(NULL); long long int TESTS = 1; cin >> TESTS; while (TESTS--) { solve(); } return 0; }
#include <bits/stdc++.h> using namespace std; long long int MOD = 998244353; long long int mod = 1e9 + 7; long long int INF = 1e18; long long int dx[] = {1, -1, 0, 0}; long long int dy[] = {0, 0, 1, -1}; int main() { ios_base::sync_with_stdio(false); cin.tie(NULL); long long int t; cin >> t; while (t--) { long long int n; cin >> n; double p = 3.14159265358979; double ans = 0.0; ans = sin(p / (4 * n)); ans = 1.0 / ans; ans = ans * 0.5; cout << setprecision(15) << ans << endl; ; } return 0; }
#include <bits/stdc++.h> using namespace std; int main() { long double t; cin >> t; while (t--) { long double n; cin >> n; long double res1 = cos(3.1415926535 / (4 * n)); long double res2 = sin(3.1415926535 / (2 * n)); cout << fixed << setprecision(10); cout << res1 / res2 << endl; } return 0; }
#include <bits/stdc++.h> const double pi = acos(-1.0); using namespace std; long long int gcd(long long int a, long long int b) { return b == 0 ? a : gcd(b, a % b); } long long int lcm(long long int a, long long int b) { return a * b / gcd(a, b); } double answer(long long int n) { double pro; if (n % 4 == 0) { pro = pi * (180.0 / n) / 180; } else { pro = pi * (180.0 / (2 * n)) / 180; } double x = 1.0e+99, x1 = -1.0e+99, y = 1.0e+99, y1 = -1.0e+99; for (long long int i = 0; i < n; i++) { double px = cos(2 * pi * i / n + pro); double py = sin(2 * pi * i / n + pro); x = min(x, px); x1 = max(x1, px); y = min(y, py); y1 = max(y1, py); } double res = max(x1 - x, y1 - y); double ans = res / sin(pi / n) / 2; return ans; } void solve() { long long int n; cin >> n; n = n * 2; cout << fixed << setprecision(10); cout << answer(n) << endl; } int main() { ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0); int t; cin >> t; int tc = 1; while (t--) { solve(); tc++; } return 0; }
#include <bits/stdc++.h> using namespace std; int main() { ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0); int TESTS = 1; cin >> TESTS; while (TESTS--) { long long n; cin >> n; double x = 3.1415926535897932 / (2 * n); double t = tan(x); double p = sin(x); double ans = n * 4; ; double dia = 1 / p; long long i = n / 2; double k = dia * (sin(i * x) + sin((n - i) * x)) / sqrt(2); ans = min(ans, k); cout << setprecision(20) << ans << endl; } return 0; }
#include <bits/stdc++.h> using namespace std; double side_len(double radius, double angle) { return 2.0 * radius * sin(M_PI * angle / (2 * 180)); } int main() { ios::sync_with_stdio(0); cin.tie(0); int t; cin >> t; while (t--) { double n; double ans; cin >> n; double radius = 1.0 / (2.0 * sin(M_PI / (2 * n))); double angle = 180 / n; double l = side_len(radius, (n - 1) / 2 * angle); double r = side_len(radius, (n + 1) / 2 * angle); cout << fixed << setprecision(9) << (l * M_SQRT1_2) + (r * M_SQRT1_2) << "\n"; } return 0; }
#include <bits/stdc++.h> using namespace std; double sn(double a) { double param, result; param = a; result = sin(param * 3.14159265 / 180.0); return result; } int Q; int main() { cin >> Q; while (Q--) { double n; cin >> n; double e = (180 * (2 * n - 2)) / (n * 2); double a = (180 * (2 * n - 2)) / (n * 2); double p1 = 0, p2 = 0; double n1 = (int)n / 2; double n2 = n - n1; if ((int)n1 % 2 == 1) { p1++; n1--; a = a - 90; } else a = a / 2; for (double k = 2; k <= n1; k += 2) { p1 += 2 * (sn(a)); a = e - (90 - a) - 90; } e = (180 * (2 * n - 2)) / (n * 2); a = (180 * (2 * n - 2)) / (n * 2); if ((int)n2 % 2 == 1) { p2++; n2--; a = a - 90; } else a = a / 2; for (double k = 2; k <= n2; k += 2) { p2 += (double)2.0 * (sn(a)); a = e - (90.0 - a) - 90.0; } p1 = p1 * (sqrt(2)) / 2; p2 = p2 * (sqrt(2)) / 2; cout << fixed; cout << setprecision(6) << (double)(p1 + p2) << endl; } return 0; }
#include <bits/stdc++.h> using namespace std; const double pi = acos(-1.0); double nGon(int N) { double proAngleVar; if (N % 4 == 0) { proAngleVar = pi * (180.0 / N) / 180; } else { proAngleVar = pi * (180.0 / (2 * N)) / 180; } double negX = 1.0e+99, posX = -1.0e+99, negY = 1.0e+99, posY = -1.0e+99; for (int j = 0; j < N; ++j) { double px = cos(2 * pi * j / N + proAngleVar); double py = sin(2 * pi * j / N + proAngleVar); negX = min(negX, px); posX = max(posX, px); negY = min(negY, py); posY = max(posY, py); } double opt2 = max(posX - negX, posY - negY); return (double)opt2 / sin(pi / N) / 2; } int main() { int test, i, j, k, n; cin >> test; while (test--) { cin >> n; cout << fixed << setprecision(6); cout << nGon(2 * n) << endl; } }
#include <bits/stdc++.h> using namespace std; template <typename T> string tos(T a) { stringstream ss; string ret; ss << a; ss >> ret; return ret; } void read(int &_a) { int temp = scanf("%d", &_a); } void read(int &_a, int &_b) { int temp = scanf("%d %d", &_a, &_b); } void read(int &_a, int &_b, int &_c) { int temp = scanf("%d %d %d", &_a, &_b, &_c); } int main() { int T; read(T); double n; while (T--) { cin >> n; double ang = 3.141592653589793238 / (4.0 * n); double l = 0.5 / sin(ang); printf("%.10lf\n", l); } return 0; }
#include <bits/stdc++.h> std::mt19937 rng( (int)std::chrono::steady_clock::now().time_since_epoch().count()); int main() { std::ios_base::sync_with_stdio(false); std::cin.tie(NULL); int t; std::cin >> t; std::cout << std::fixed << std::setprecision(10); while (t--) { int n; std::cin >> n; n *= 2; std::cout << (1.0 / sin(acos(-1) / n / 2)) / 2 << '\n'; } }
#include <bits/stdc++.h> using namespace std; int main() { ios::sync_with_stdio(0), cin.tie(0); int n, t; double pi = 3.1415926535897932; cin >> t; while (t--) { cin >> n; if (n % 2) cout << setprecision(16) << fixed << cos(pi / (4 * n)) / sin(pi / (2 * n)) << '\n'; else cout << setprecision(16) << fixed << 1 / tan(pi / (n * 2)) << '\n'; } }
#include <bits/stdc++.h> #pragma GCC optimize(3, "Ofast", "inline") using namespace std; const double pi = acos(-1); const double sq2 = sqrt(2); void solve() { int n; cin >> n; double tt = pi / n, k = 1.0 / 2 / sin(tt / 2); double a = n / 2, b = n - a; cout << setiosflags(ios::fixed) << setprecision(9) << k * (sqrt(1 - cos(tt * a)) + sqrt(1 - cos(tt * b))) << '\n'; } int main() { ios::sync_with_stdio(false); int t; cin >> t; while (t--) solve(); return 0; }
#include <bits/stdc++.h> const long long inf = 1 << 28; using namespace std; int main() { long long t; cin >> t; while (t--) { long long n; cin >> n; cout << std::fixed << std::setprecision(9) << (cos(3.14159265358979323846 / (4 * n)) / sin(3.14159265358979323846 / (2 * n))) << endl; } return 0; }
#include <bits/stdc++.h> using namespace std; int main() { int t; cin >> t; double pi = acos(-1); while (t--) { int n; cin >> n; float temp = 0; int i = 1; cout << fixed << setprecision(9) << cos(pi / (4 * n)) / sin(pi / (2 * n)) << endl; } return 0; }
#include <bits/stdc++.h> using namespace std; int ini() { int x; scanf("%d", &x); return x; } long long inl() { long long x; scanf("%lld", &x); return x; } int main() { int t = ini(); while (t--) { long double x, ang; cin >> x; ang = 360 / (x * 4); ang = ang * acos(-1) / 180.0; long double ans1 = 0.25 / sin(ang * 0.5); ans1 *= 2.0; printf("%0.9Lf\n", ans1); } return 0; }
#include <bits/stdc++.h> using namespace std; void solve() { long long n; cin >> n; const long double pi = 3.14159265359; long double deg = 180 * 1.0 / n; long double rad = (pi * 1.0) / n; long double tans = tan(rad); tans = 1 / tans; long double res = cos(pi / (4 * n)) / sin(pi / (2 * n)); cout << res << "\n"; } int main() { ios_base::sync_with_stdio(false); cin.tie(NULL); if (fopen("input.txt", "r")) { freopen("input.txt", "r", stdin); freopen("output.txt", "w", stdout); } cout << setprecision(20); long long t = 1; cin >> t; while (t--) { solve(); } return 0; }
#include <bits/stdc++.h> using namespace std; void solve() { int n; cin >> n; double ans; if (n & 1) { ans = cos(0.78539816339744830962 / n) / sin(1.57079632679489661923 / n); } else { ans = 1.0 / tan(1.57079632679489661923 / n); } printf("%.9f\n", ans); } int main() { ios_base::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr); int t; cin >> t; while (t--) { solve(); } return 0; }
#include <bits/stdc++.h> using namespace std; int a[100005], b[100005]; int main() { ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0); int t, n; cin >> t; while (t--) { cin >> n; double ans = .5 / sin(3.14159265358979323846 / (4 * n)); cout.precision(8); cout << fixed << ans << endl; } }
#include <bits/stdc++.h> int T; int n; int Max(int a, int b) { return a > b ? a : b; } int Min(int a, int b) { return a < b ? a : b; } int Abs(int a) { return a < 0 ? -a : a; } const double PI = 3.1415926535897932; int main() { scanf("%d", &T); while (T--) { scanf("%d", &n); if (!(n & 1)) { double a = (180.0 - (180.0 / (double)n)) / 2.0; double ans = 0.5 * tan(PI / 180 * a); printf("%.9lf\n", ans * 2.0); } else { double x = (PI / 4.0) / n; double ans1 = 0, ans2 = 0; double _x = x; for (int i = 1; i <= n; ++i) ans1 += sin(_x), _x += PI / n; _x = x; for (int i = 1; i < n; ++i) ans2 += cos(_x), _x += PI / n; printf("%.9lf\n", ans1 > ans2 ? ans1 : ans2); } } }
#include <bits/stdc++.h> using namespace std; const double pi = acos(-1); int T, n; int main() { scanf("%d", &T); while (T--) { scanf("%d", &n); double ct = pi / (double)n; double cct = (double)round((double)n / 4.0) * ct; double x = 0.5 / sin(0.5 * ct); double ans1 = (sin(cct) * x / (sin(pi / 4.0))); double ans2 = (sin(pi / 2.0 - cct) * x / sin((pi / 4.0))); printf("%.9f\n", ans1 + ans2); } return 0; }
#include <bits/stdc++.h> const double PI = acos(-1.0); int main() { int T; scanf("%d", &T); while (T--) { int n; scanf("%d", &n); printf("%.12lf\n", cos(PI / 4.0 / n) / sin(PI / 2.0 / n)); } return 0; }
#include <bits/stdc++.h> using namespace std; int main() { int t; cin >> t; while (t) { int n; cin >> n; double pi = 2 * asin(1); double area = cos(pi / (4 * n)) / sin(pi / (2 * n)); printf("%0.15f\n", area); t--; } return 0; }
#include <bits/stdc++.h> using namespace std; int main() { int t, n; cin >> t; while (t--) { cin >> n; n *= 2; float theta = (float)180 / n; float den = sin(theta * 3.141592653 / 180); den = 1 / den; int i = 1; float ang; ang = 3 * (float)90 / n; ang = 90 + theta - ang; float num = sin(ang * 3.141592653 / 180); printf("%0.9f\n", num * den); } }
#include <bits/stdc++.h> using namespace std; int main() { ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL); cout.precision(10); double PI = acos(-1.0); int t; cin >> t; while (t--) { int n; cin >> n; printf("%.9f\n", (cos(PI / (4.0 * n)) / sin(PI / (2.0 * n)))); } return 0; }
#include <bits/stdc++.h> using namespace std; const long long inf = 0x3f3f3f3f3f3f3f3f; mt19937 rng(chrono::steady_clock::now().time_since_epoch().count()); void zz() { ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0); } const double pi = 3.1415926535897932; double polydiagonal(double n, double a) { if (a < 0 && n < 0) return -1; double rad = (pi / n); return (double)(1 / sin(rad)); } int32_t main() { zz(); long long t; cin >> t; while (t--) { long long n; cin >> n; double x = pi / (4 * n); double ans = sin(x) * 2; ans = 1 / ans; cout << fixed << setprecision(10) << ans << endl; } }
#include <bits/stdc++.h> using namespace std; const long long N = 1e5 + 10; const double pi = 3.141592653589793; double x, z, l; long long T, y, n; signed main() { cin >> T; while (T--) { cin >> n; x = 0; z = pi / 2 / n; l = 1.0 / 2 / sin(pi / 2 / n); while (z <= pi / 2) x = max(x, l * 2 * (cos(z) + sin(z))), z += pi / n; printf("%.9lf\n", x * sqrt(2) / 2); } return 0; }
#include <bits/stdc++.h> using namespace std; int main() { ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0); int t = 1; cin >> t; while (t--) { double n, i, j, ans; cin >> n; i = cos(3.14159265358979323846 / (4 * n)); j = sin(3.14159265358979323846 / (2 * n)); ans = i / j; cout << fixed << setprecision(9) << ans << "\n"; } }
#include <bits/stdc++.h> using namespace std; const int inf = 1 << 30; const long long linf = 1LL << 62; const int MAX = 510000; long long dy[8] = {0, 1, 0, -1, 1, -1, 1, -1}; long long dx[8] = {1, 0, -1, 0, 1, -1, -1, 1}; const double pi = acos(-1); const double eps = 1e-7; template <typename T1, typename T2> inline bool chmin(T1 &a, T2 b) { if (a > b) { a = b; return true; } else return false; } template <typename T1, typename T2> inline bool chmax(T1 &a, T2 b) { if (a < b) { a = b; return true; } else return false; } template <typename T1, typename T2> inline void print2(T1 a, T2 b) { cout << a << " " << b << "\n"; } template <typename T1, typename T2, typename T3> inline void print3(T1 a, T2 b, T3 c) { cout << a << " " << b << " " << c << endl; } const int mod = 998244353; void solve() { int n; cin >> n; double ans = 1.0 / sin(pi / (double)(2 * n)) * cos(pi / (double)n / 4.0); printf("%.10f\n", ans); } int main() { int t = 1; cin >> t; while (t--) { solve(); } }
#include <bits/stdc++.h> using namespace std; const double pi = acos(-1); int main() { int t, n; scanf("%d", &t); while (t--) { scanf("%d", &n); double t1 = cos(pi / (4.0 * n)); double t2 = sin(pi / (2.0 * n)); double ans = t1 / t2; printf("%.9f\n", ans); } return 0; }
#include <bits/stdc++.h> using namespace std; long long power(long long x, long long y, long long m) { long long r = 1; for (; y; y >>= 1) { if (y & 1) r = r * x % m; x = x * x % m; } return r; } const long long N = 1e3 + 5, M = 1e9 + 7; int main() { ios_base::sync_with_stdio(false), cin.tie(0), cout.tie(0); srand(time(NULL)); ; long long n, k, m = 0, x = 0, i, t = 1, ans = 0, j, y = 0, z = 0, c = 0, w, last = -1; double pi = acos(-1.0); cin >> t; while (t--) { cin >> n; n *= 4; cout << fixed << setprecision(9) << 0.5 / sin(pi / n); cout << "\n"; } }
#include <bits/stdc++.h> using namespace std; using ll = long long; using ull = unsigned long long; const double pi = 3.14159265358979323846; int main() { ios_base::sync_with_stdio(0); cin.tie(0); int t; cin >> t; while (t--) { double n; cin >> n; double x = pi / n; double r = ((1.0 / 2.0) * 1.0) * (1.0 / tan(x)); double R = cos(pi / (4.0 * n)) / sin(pi / (2.0 * n)); double dif = R + R - r - r; dif /= 4.0; cout << setprecision(12) << R << endl; } }
#include <bits/stdc++.h> using namespace std; int main() { int test; cin >> test; for (int t = 0; t < test; t++) { int n; cin >> n; double ans = 0; ans = cos(M_PI_4 / n) / (sin(M_PI_2 / n)); cout << setprecision(25) << ans << endl; } return 0; }
#include <bits/stdc++.h> using namespace std; int main() { double T, n, i; cin >> T; while (T--) { double par, len, val; long long int N; cin >> n; n = 2 * n; par = 3.14159265358979323846 / n; len = 1 / sin(par); N = (n / 2 - 1) / 2; if (N % 2 == 0) { N = N + 1; N = N / 2; val = par + (double)(N)*par * 2; } else { N = N + 1; val = par + (double)(N / 2 - 1) * par * 2; } val = 3.14159265358979323846 / 2 - val; val = val - 3.14159265358979323846 / 4; i = cos(val) * len; printf("%.10f\n", i); } return 0; }
#include <bits/stdc++.h> using namespace std; const long long int N = 2e5 + 5; void solve() { long long int n; cin >> n; double ans, pi = 3.14159265358979323846; double rad = (2.0 * sin(pi / (2.0 * (double)n))); ans = (cos(pi / (4.0 * n))) / sin(pi / (2.0 * (double)n)); cout << fixed << setprecision(15) << ans << '\n'; } signed main() { ios_base::sync_with_stdio(0), cin.tie(NULL), cout.tie(NULL); long long int t = 1; cin >> t; while (t--) { solve(); } }
#include <bits/stdc++.h> using namespace std; int main() { int t; cin >> t; while (t--) { int n; cin >> n; double x = n; x = M_PI_2 / x; double ans = sin((n / 2) * x + M_PI_4) / sin(x); printf("%0.9lf\n", ans); } }
#include <bits/stdc++.h> using namespace std; const int N = 1e3 + 15; const double PI = acos(-1); struct Gauss { long long n, f = 0; double a[10][10], b[10]; void init(long long nn) { n = nn; for (int i = 1; i <= n; i++) { for (int j = 1; j <= n; j++) cin >> a[i][j]; cin >> b[i]; } } void solve() { for (int i = 1; i <= n; i++) { long long r = i; for (int j = i + 1; j <= n; j++) { if (fabs(a[j][i]) > fabs(a[r][i])) r = j; } if (r != i) { for (int j = 1; j <= n; j++) swap(a[i][j], a[r][j]); swap(b[i], b[r]); } if (abs(a[i][i] - 0.0) < 0.00001) { cout << "No Solution" << endl; f = 1; return; } for (int j = 1; j <= n; j++) { if (j == i) continue; double d = 1.0 * a[j][i] / a[i][i]; for (int k = i; k <= n; k++) a[j][k] = a[j][k] - a[i][k] * d; b[j] = b[j] - b[i] * d; } } for (int i = 1; i <= n; i++) b[i] = 1.0 * b[i] / a[i][i]; } void print() { if (f == 1) return; for (int i = 1; i <= n; i++) printf("%.2lf\n", b[i]); } }; long long n, m, p; int num[N]; int main() { int T; cin >> T; while (T--) { cin >> n; double d1 = n * 1.0 * 2.0 + 1.0; double d2 = 4.0 * n; double d3 = d1 / d2; double temp = cos(PI * d3); double ans = 1.0 / (2.0 * temp); ans *= -1.0; printf("%.9f\n", ans); } return 0; }
#include <bits/stdc++.h> using namespace std; unsigned long long n, m, k; vector<long long> a(1e5 + 1); int main() { unsigned int t; cin >> t; while (t--) { cin >> n; double f_2 = 0.5 * 3.14159265358979323846 / (double)n; double a; if (n % 2) { double f_3 = 1.57079632679489661923 - ceil(0.5 * (0.78539816339744830962 - f_2) / f_2) * 2.0 * f_2; a = 0.5 / sin(f_2); double d_2 = a * (sin(f_3) + cos(f_3)); a = d_2 / sin(0.78539816339744830962); } else a = 1.0 / tan(f_2); printf("%.8lf\n", a); } return 0; }
#include <bits/stdc++.h> using namespace std; const int M = 1e9 + 7; const long long INF = 1e18; const double pi_2 = 1.57079632679489661923; long long biex(long long a, long long b) { if (b == 0) return 1; long long ans = biex(a, b / 2); ans = (ans * ans) % M; if (b & 1) return (ans * a) % M; else return ans; } void solve() { int n; cin >> n; double a = pi_2 / n; double d = sin(a); double nu = sin(pi_2 / 2 + a * 2); for (int i = 2; i <= (n - 1) / 2; i++) { nu = max(nu, sin(pi_2 / 2 + a * 2 * i)); } cout << fixed << setprecision(9) << (double)nu / (double)d << "\n"; return; } int main() { ios_base::sync_with_stdio(false); cin.tie(NULL); int t = 1; cin >> t; for (int i = 1; i <= t; i++) solve(); return 0; }