제출 #254201

#	제출 시각	아이디	문제	언어	결과	실행 시간	메모리
254201		NONAME	새로운 문제 (COCI19_akvizna)	C++14	130 / 130	70 ms	3584 KiB

Main

#include <bits/stdc++.h>
#define m first
#define b second
#define dbg(x) cerr << #x << " = " << x << "\n"
#define fast_io ios_base::sync_with_stdio(0); cin.tie(0); cout.tie()
using namespace std;
using ll = long long;
using ld = long double;
typedef pair <double, double> line;

const int N = int(2e5) + 500;
const int base = int(1e9) + 7;

double dp[N];
int n, k;
int cnt[N], which[N];
line lines[N];

double intersect(line f, line s) { return (f.m == s.m) ? 1e18 : (f.b - s.b) / (s.m - f.m); }
double val(line a, double x) { return (a.m * x + a.b); }

void solve(double cost) {
    int l = 0, r = 0;
    dp[0] = cnt[0] = 0;
    for (int i = 1; i <= n; ++i) {
        line nline = {dp[i - 1], -i};
        while (r - l > 1 && intersect(nline, lines[r - 1]) < intersect(lines[r - 1], lines[r - 2]))
            --r;
        which[r] = i - 1;
        lines[r++] = nline;
        while (r - l > 1 && val(lines[l], i) <= val(lines[l + 1], i))
            ++l;
        dp[i] = (val(lines[l], i) + i + 1) / i - cost;
        cnt[i] = cnt[which[l]] + 1;
    }
}

int main() {
    fast_io;

    cin >> n >> k;
    double low = 0, high = 20;

    while (high - low >= 1e-12) {
        double md = (low + high) / 2;
        solve(md);

        if (cnt[n] <= k) high = md;
            else low = md;
    }

    solve(high);
    cout.precision(20); cout << fixed;
    cout << dp[n] + cnt[n] * high << "\n";
}

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