#ifndef LOCAL #pragma GCC optimize("O3,unroll-loops") #endif #include <bits/stdc++.h> #define fi first #define se second #define pn printf("\n") #define ssize(x) int(x.size()) #define all(x) x.begin(),x.end() #define rall(x) x.rbegin(),x.rend() #define bitcount(x) __builtin_popcount(x) #define clz(x) __builtin_clz(x) #define ctz(x) __builtin_ctz(x) #define mp make_pair //~ #define r(x) resize(x) //~ #define rf(x, c) resize(x, c) using namespace std; typedef long long ll; typedef pair<int, int> pii; typedef pair<int, ll> pil; typedef pair<ll, int> pli; typedef pair<ll, ll> pll; typedef double db; typedef long double ldb; #define V vector int inf = 2e09; ll infll = 2e18; int mod = (1<<23)*119+1; int add(int a, int b){return a+b >= mod ? a+b - mod : a+b;} int sub(int a, int b){return a-b < 0 ? a-b + mod : a-b;} int mul(int a, int b){return int(a * ll(b) % mod);} int fpow(int a, ll b){ int ret = 1; while(b){ if(b & 1) ret = mul(ret, a); b >>= 1, a = mul(a, a); } return ret; } int inv(int a){ return fpow(a, mod-2); } struct coeff{ V<int> fac, invfac; coeff(int n){ fac.resize(n+1), invfac.resize(n+1); fac[0] = 1, invfac[0] = 1; for(int i = 1; i <= n; ++i) fac[i] = mul(fac[i-1], i); invfac[n] = inv(fac[n]); for(int i = n-1; i; --i) invfac[i] = mul(invfac[i+1], i+1); } int get(int n, int k){ if(n < k) return 0; return mul(fac[n], mul(invfac[n-k], invfac[k])); } }; void answer(){ int n = 200000; scanf("%d", &n); V<int> t(n+1); for(int i = 1; i <= n; ++i) scanf("%d", &t[i]); int req = 0; for(int i = 1; i <= n; ++i) if(t[i]) ++req; int C = 1000; V<ll> c_2(C+1, 0), c_3(C+1, 0); for(int c = 0; c <= C; ++c) c_2[c] = (c*(c-1))/2, c_3[c] = (c*(c-1)*(c-2))/6; int l = 1, r = 1e06, k; // do zmiany! while(l < r){ k = (l+r)/2; V<V<pii>> p(n+1); // dodam asserta, czy jest 1 przedzial p[0].emplace_back(0, 0); V<pii> curr; int cnt = 0; for(int i = 1; i <= n; ++i){ curr.clear(); if(!t[i]) for(pii u : p[i-1]) curr.emplace_back(u); else for(int c = 1; c <= C; ++c){ // dodalem else, twierdze, ze jest poprawnie ll guaranteed = c_3[c]+c_2[c]*(req-1)+ll(cnt)*c*(req-cnt-1); ldb delta = (c*ldb(k)-c*c)*(c*ldb(k)-c*c)+ 4*ldb(c)*(c_2[c]*(k-c) + c_3[c] - t[i]); if(delta < 0) continue; int x1 = (int) max(0ll, ll(ceil((c*ldb(k)-c*c - sqrtl(delta)) / (2*c)))); int x2 = (int) min(ll(k), ll(floor((c*ldb(k)-c*c + sqrtl(delta)) / (2*c)))); // if(c == 2) // printf("%Lf, %Lf %Lf\n", delta, (c*ldb(k)-c*c +sqrtl(delta))/(2*c), floor((c*ldb(k)-c*c +sqrtl(delta))/(2*c))), // printf("%d, %d: %d %d\n", k, c, x1, x2); if(x1 <= x2) for(pii u : p[i-1]){ if(x2 < u.fi || u.se < x1) continue; curr.emplace_back(max(x1, u.fi)+c, min(x2, u.se)+c); } if(ll(t[i]) < guaranteed) break; } if(t[i]) ++cnt; sort(all(curr)); for(pii u : curr){ if(!ssize(p[i]) || p[i].back().se+1 < u.fi) p[i].emplace_back(u); else p[i].back().se = max(p[i].back().se, u.se); } // assert(ssize(p[i]) <= 1); } // printf("%d:\n", k); // for(int i = 1; i <= n; ++i){ // for(pii u : p[i]) // printf("%d %d, ", u.fi, u.se); // pn; // } bool ok = 0; if(ssize(p[n])){ for(pii u : p[n]) if(u.fi <= k) ok = 1; } if(ok) r = k; else l = k+1; // trzeba wiecej ludzi // break; } printf("%d\n", l); } int main(){ int T = 1; scanf("%d", &T); //~ ios_base::sync_with_stdio(0); cin.tie(0); cin >> T; for(++T; --T; ) answer(); return 0; }
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 | #ifndef LOCAL #pragma GCC optimize("O3,unroll-loops") #endif #include <bits/stdc++.h> #define fi first #define se second #define pn printf("\n") #define ssize(x) int(x.size()) #define all(x) x.begin(),x.end() #define rall(x) x.rbegin(),x.rend() #define bitcount(x) __builtin_popcount(x) #define clz(x) __builtin_clz(x) #define ctz(x) __builtin_ctz(x) #define mp make_pair //~ #define r(x) resize(x) //~ #define rf(x, c) resize(x, c) using namespace std; typedef long long ll; typedef pair<int, int> pii; typedef pair<int, ll> pil; typedef pair<ll, int> pli; typedef pair<ll, ll> pll; typedef double db; typedef long double ldb; #define V vector int inf = 2e09; ll infll = 2e18; int mod = (1<<23)*119+1; int add(int a, int b){return a+b >= mod ? a+b - mod : a+b;} int sub(int a, int b){return a-b < 0 ? a-b + mod : a-b;} int mul(int a, int b){return int(a * ll(b) % mod);} int fpow(int a, ll b){ int ret = 1; while(b){ if(b & 1) ret = mul(ret, a); b >>= 1, a = mul(a, a); } return ret; } int inv(int a){ return fpow(a, mod-2); } struct coeff{ V<int> fac, invfac; coeff(int n){ fac.resize(n+1), invfac.resize(n+1); fac[0] = 1, invfac[0] = 1; for(int i = 1; i <= n; ++i) fac[i] = mul(fac[i-1], i); invfac[n] = inv(fac[n]); for(int i = n-1; i; --i) invfac[i] = mul(invfac[i+1], i+1); } int get(int n, int k){ if(n < k) return 0; return mul(fac[n], mul(invfac[n-k], invfac[k])); } }; void answer(){ int n = 200000; scanf("%d", &n); V<int> t(n+1); for(int i = 1; i <= n; ++i) scanf("%d", &t[i]); int req = 0; for(int i = 1; i <= n; ++i) if(t[i]) ++req; int C = 1000; V<ll> c_2(C+1, 0), c_3(C+1, 0); for(int c = 0; c <= C; ++c) c_2[c] = (c*(c-1))/2, c_3[c] = (c*(c-1)*(c-2))/6; int l = 1, r = 1e06, k; // do zmiany! while(l < r){ k = (l+r)/2; V<V<pii>> p(n+1); // dodam asserta, czy jest 1 przedzial p[0].emplace_back(0, 0); V<pii> curr; int cnt = 0; for(int i = 1; i <= n; ++i){ curr.clear(); if(!t[i]) for(pii u : p[i-1]) curr.emplace_back(u); else for(int c = 1; c <= C; ++c){ // dodalem else, twierdze, ze jest poprawnie ll guaranteed = c_3[c]+c_2[c]*(req-1)+ll(cnt)*c*(req-cnt-1); ldb delta = (c*ldb(k)-c*c)*(c*ldb(k)-c*c)+ 4*ldb(c)*(c_2[c]*(k-c) + c_3[c] - t[i]); if(delta < 0) continue; int x1 = (int) max(0ll, ll(ceil((c*ldb(k)-c*c - sqrtl(delta)) / (2*c)))); int x2 = (int) min(ll(k), ll(floor((c*ldb(k)-c*c + sqrtl(delta)) / (2*c)))); // if(c == 2) // printf("%Lf, %Lf %Lf\n", delta, (c*ldb(k)-c*c +sqrtl(delta))/(2*c), floor((c*ldb(k)-c*c +sqrtl(delta))/(2*c))), // printf("%d, %d: %d %d\n", k, c, x1, x2); if(x1 <= x2) for(pii u : p[i-1]){ if(x2 < u.fi || u.se < x1) continue; curr.emplace_back(max(x1, u.fi)+c, min(x2, u.se)+c); } if(ll(t[i]) < guaranteed) break; } if(t[i]) ++cnt; sort(all(curr)); for(pii u : curr){ if(!ssize(p[i]) || p[i].back().se+1 < u.fi) p[i].emplace_back(u); else p[i].back().se = max(p[i].back().se, u.se); } // assert(ssize(p[i]) <= 1); } // printf("%d:\n", k); // for(int i = 1; i <= n; ++i){ // for(pii u : p[i]) // printf("%d %d, ", u.fi, u.se); // pn; // } bool ok = 0; if(ssize(p[n])){ for(pii u : p[n]) if(u.fi <= k) ok = 1; } if(ok) r = k; else l = k+1; // trzeba wiecej ludzi // break; } printf("%d\n", l); } int main(){ int T = 1; scanf("%d", &T); //~ ios_base::sync_with_stdio(0); cin.tie(0); cin >> T; for(++T; --T; ) answer(); return 0; } |