제출 #788990

#제출 시각아이디문제언어결과실행 시간메모리
788990AlcabelAliens (IOI16_aliens)C++17
4 / 100
12 ms364 KiB
#include <bits/stdc++.h> #ifndef LOCAL #include "aliens.h" #endif using namespace std; const long long inf = 1e13; const int maxiters = 200; struct Line { int a; long double b; Line() {} Line(int _a, long double _b) { a = _a, b = _b; } long double f(int x) { return a * 1ll * x + b; } ~Line() {} }; const long double eps = 1e-9; int sign(long double x) { if (x > eps) { return 1; } if (x < eps) { return -1; } return 0; } long long intersect(const Line& A, const Line& B) { // x = (B.b - A.b) / (A.a - B.a) long double numer = B.b - A.b, denom = A.a - B.a; return ceill(numer / denom); /*int sn = sign(numer), sd = sign(denom); numer *= sn, denom *= sd; if (sn * sd < eps) { return numer / denom * -1; } return (numer + denom - 1) / denom;*/ } long long take_photos(int n, int m, int k, vector<int> rows, vector<int> cols) { vector<int> maxRight(m, -1); for (int i = 0; i < n; ++i) { int l = min(rows[i], cols[i]); int r = max(rows[i], cols[i]); maxRight[l] = max(maxRight[l], r + 1); } vector<pair<int, int>> segs; for (int l = 0; l < m; ++l) { if (maxRight[l] != -1 && (segs.empty() || segs.back().second < maxRight[l])) { segs.emplace_back(l, maxRight[l]); } } n = segs.size(); k = min(k, n); vector<pair<long double, int>> dp(n); vector<Line> lines; vector<long double> optX; vector<int> cntSegs; long double left = -inf, right = inf; long long ans = (segs.back().second - segs[0].first) * 1ll * (segs.back().second - segs[0].first); for (int iter = 0; iter < maxiters; ++iter) { long double mid = left + (right - left) / 2; lines = {}; optX = {}; cntSegs = {}; dp[0] = {(segs[0].second - segs[0].first) * 1ll * (segs[0].second - segs[0].first) + mid, 1}; for (int i = 1, ptr = 0; i < n; ++i) { // cerr << "i: " << i << '\n'; int lenInter = max(0, segs[i - 1].second - segs[i].first); Line l(-2 * segs[i].first, dp[i - 1].first - lenInter * 1ll * lenInter + segs[i].first * 1ll * segs[i].first); while (!lines.empty() && sign(intersect(lines.back(), l) - optX.back()) != 1) { optX.pop_back(); lines.pop_back(); cntSegs.pop_back(); } if (!lines.empty()) { optX.emplace_back(intersect(lines.back(), l)); } else { optX.emplace_back(-1); } lines.emplace_back(l); cntSegs.emplace_back(dp[i - 1].second); // cerr << "inserted!\n"; ptr = min(ptr, (int)lines.size() - 1); while (ptr + 1 < (int)lines.size() && optX[ptr + 1] <= segs[i].second) { ++ptr; } // cerr << "found!\n"; dp[i] = {lines[ptr].f(segs[i].second) + segs[i].second * 1ll * segs[i].second + mid, cntSegs[ptr] + 1}; if (sign((segs[i].second - segs[0].first) * 1ll * (segs[i].second - segs[0].first) + mid - dp[i].first) != 1) { dp[i] = {(segs[i].second - segs[0].first) * 1ll * (segs[i].second - segs[0].first) + mid, 1}; } } if (dp[n - 1].second <= k) { right = mid; long long cur = floorl(dp.back().first - dp.back().second * mid); if (sign(dp.back().first - dp.back().second * mid - cur) == 1) { ++cur; } ans = min(ans, cur); } else { left = mid; } /*cerr << "g: " << g << ", subtracted:\n"; for (int i = g - 1; i < n; ++i) { cerr << dp[layer ^ 1][i] - dp[layer][i] << ' '; } cerr << '\n'; ans = min(ans, dp[layer][n - 1]);*/ } return ans; } /* void solve() { int n, m, k; cin >> n >> m >> k; vector<int> r(n), c(n); for (int i = 0; i < n; ++i) { cin >> r[i] >> c[i]; } cout << take_photos(n, m, k, r, c) << '\n'; } int main() { ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0); #ifdef LOCAL freopen("input.txt", "r", stdin); freopen("output.txt", "w", stdout); int T = 1; cin >> T; while (T--) { solve(); cerr << "-----------\n"; cout << "-----------\n"; } #else int T = 1; cin >> T; while (T--) { solve(); } #endif return 0; } */
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