CEOI2004锯木厂选址

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(20010), INF(2e9);
int n, Q[MAXN], tail, head, w[MAXN], d[MAXN];
int dis[MAXN], s[MAXN], ans, f[MAXN], c[MAXN], g[MAXN];

IL double Calc(RG int i, RG int j){
    return 1.0 * (c[i] - c[j]) / (w[i] - w[j]);
}

int main(){
    n = Read();
    for(RG int i = 1; i <= n; i++)
        w[i] = w[i - 1] + Read(), d[i] = Read();
    for(RG int i = 1; i <= n + 1; i++){
        dis[i] = dis[i - 1] + d[i - 1];
        s[i] = s[i - 1] + w[i - 1] * d[i - 1];
        c[i] = w[i] * dis[i];
    }
    for(RG int i = 1; i <= n; i++)
        g[i] = s[n + 1] + c[i] - w[i] * dis[n + 1];
    ans = INF;
    Q[0] = 1;
    for(RG int i = 2; i <= n; i++){
        while(head < tail && Calc(Q[head], Q[head + 1]) <= dis[i]) head++;
        RG int j = Q[head];
        ans = min(ans, g[i] + c[j] - w[j] * dis[i]);
        while(head < tail && Calc(Q[tail - 1], Q[tail]) >= Calc(Q[tail], i)) tail--;
        Q[++tail] = i;
    }
    printf("%d\n", ans);
    return 0;
}