ZJOI2007仓库建设

斜率优化

# include <stdio.h>
# include <stdlib.h>
# include <iostream>
# include <string.h>
# include <algorithm>
# define IL inline
# define RG register
# define Fill(a, b) memset(a, b, sizeof(a))
using namespace std;
typedef long long ll;

IL ll Read(){
    RG char c = getchar(); RG ll x = 0, z = 1;
    for(; c > '9' || c < '0'; c = getchar()) z = c == '-' ? -1 : 1;;
    for(; c >= '0' && c <= '9'; c = getchar()) x = (x << 1) + (x << 3) + c - '0';
    return x * z;
}

const int MAXN(1000010);
const ll INF(1e18);
int n, cnt, Q[MAXN], tail, head;
ll f[MAXN], c[MAXN], p[MAXN], x[MAXN], s[MAXN], g[MAXN];

IL double Calc(RG int i, RG int j){
    return 1.0 * (f[i] + g[i] - f[j] - g[j]) / (p[i] - p[j]);
}

int main(){
    n = Read();
    for(RG int i = 1; i <= n; i++){
        x[i] = Read(); p[i] = Read(); c[i] = Read();
        p[i] += p[i - 1];
        s[i] = s[i - 1] + p[i - 1] * (x[i] - x[i - 1]);
        g[i] = x[i] * p[i] - s[i];
    }
    for(RG int i = 1; i <= n; i++){
        while(head < tail && Calc(Q[head], Q[head + 1]) <= x[i]) head++;
        f[i] = f[Q[head]] + c[i] + s[i] + g[Q[head]] - x[i] * p[Q[head]];
        while(head < tail && Calc(Q[tail - 1], Q[tail]) > Calc(Q[tail], i)) tail--;
        Q[++tail] = i;
    }
    printf("%lld\n", f[n]);
    return 0;
}