Codeforces 643C Levels and Regions 斜率优化dp

Levels and Regions

把dp方程列出来， 把所有东西拆成前缀的形式， 就能看出可以斜率优化啦。

#include<bits/stdc++.h>
#define LL long long
#define fi first
#define se second
#define mk make_pair
#define PLL pair<LL, LL>
#define PLI pair<LL, int>
#define PII pair<int, int>
#define SZ(x) ((int)x.size())
#define ull unsigned long long

using namespace std;

const int N = 2e5 + 7;
const int inf = 0x3f3f3f3f;
const LL INF = 0x3f3f3f3f3f3f3f3f;
const int mod = 1e9 + 7;
const double eps = 1e-8;
const double PI = acos(-1);

int n, k, be, ed, que[N];
double sum[N], prefix[N], dp[N][51], t[N];

double calc(int k, int j, int c) {
    return ((dp[j][c] + sum[j] * prefix[j]) - (dp[k][c] + sum[k] * prefix[k])) / (sum[j] - sum[k]);
}

int main() {
    be = 1, ed = 0;
    scanf("%d%d", &n, &k);
    for(int i = 1; i <= n; i++) scanf("%lf", &t[i]);
    for(int i = 1; i <= n; i++) prefix[i] = prefix[i - 1] + 1 / t[i];
    for(int i = 1; i <= n; i++) sum[i] = sum[i - 1] + t[i];
    dp[0][0] = 0;
    que[++ed] = 0;
    for(int j = 1; j <= k; j++) {
        int p = j - 1;
        for(int i = j; i <= n; i++) {
            while(j > 1 && p < i) {
                while(ed - be + 1 >= 2 && calc(que[ed-1], que[ed], j-1) > calc(que[ed], p, j-1)) ed--;
                que[++ed] = p;
                p++;
            }
            while(ed - be + 1 >= 2 && calc(que[be], que[be+1], j-1) < prefix[i]) be++;
            int who = que[be];
            dp[i][j] = dp[who][j - 1] - sum[who] * (prefix[i] - prefix[who]);
        }
        be = 1; ed = 0;
    }
    double ans = dp[n][k];
    for(int i = 1; i <= n; i++) ans += sum[i] / t[i];
    printf("%.12f
", ans);
    return 0;
}

/*
*/