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

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

/*
*/