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  • HNOI2008玩具装箱

    斜率优化

    # include <stdio.h>
    # include <stdlib.h>
    # include <iostream>
    # include <string.h>
    # include <algorithm>
    # define Sqr(x) (1LL * (x) * (x))
    # 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(50010);
    int n, L, Q[MAXN], head, tail;
    ll f[MAXN], sum[MAXN], INF, b[MAXN], a[MAXN];
    
    IL double K(RG int i, RG int j){
        RG ll y1 = Sqr(b[i]) + f[i], y2 = Sqr(b[j]) + f[j], x1 = 2 * b[i], x2 = 2 * b[j];
        return 1.0 * (y2 - y1) / (x2 - x1);
    }
    
    int main(){
        n = Read(); L = Read();
        for(RG int i = 1; i <= n; i++){
            sum[i] = sum[i - 1] + Read();
            b[i] = sum[i] + i; a[i] = b[i] - L - 1;
        }
        Fill(f, 127); INF = f[0]; f[0] = Q[0] = 0;
        for(RG int i = 1; i <= n; i++){
            while(head < tail && K(Q[head], Q[head + 1]) <= a[i]) head++;
            RG int j = Q[head];
            f[i] = f[j] + Sqr(a[i] - b[j]);
            while(head < tail && K(Q[tail - 1], Q[tail]) >= K(Q[tail], i)) tail--;
            Q[++tail] = i;
        }
        printf("%lld
    ", f[n]);
        return 0;
    }
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  • 原文地址:https://www.cnblogs.com/cjoieryl/p/8206396.html
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