HDU 3516 DP 四边形不等式优化 Tree Construction

设d(i, j)为连通第i个点到第j个点的树的最小长度，则有状态转移方程：

d(i, j) = min{ d(i, k) + d(k + 1, j) + p[k].y - p[j].y + p[k+1].x - p[i].x }

然后用四边形不等式优化之。。

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <map>
#define MP make_pair
#define x first
#define y second
using namespace std;

typedef pair<int, int> PII;

const int maxn = 1000 + 10;
const int INF = 0x3f3f3f3f;
int n;

PII p[maxn];

int d[maxn][maxn], s[maxn][maxn];

int main()
{
    while(scanf("%d", &n) == 1 && n)
    {
        for(int i = 1; i <= n; i++) scanf("%d%d", &p[i].x, &p[i].y);
        for(int i = 1; i <= n; i++)
        {
            s[i][i + 1] = i;
            d[i][i + 1] = p[i+1].x - p[i].x + p[i].y - p[i+1].y;
        }

        for(int l = 3; l <= n; l++)
        {
            for(int i = 1; i + l - 1 <= n; i++)
            {
                int j = i + l - 1;
                d[i][j] = INF;
                for(int k = s[i][j-1]; k <= s[i+1][j]; k++)
                {
                    int t = d[i][k] + d[k+1][j] + p[k].y - p[j].y + p[k+1].x - p[i].x;
                    if(t < d[i][j])
                    {
                        d[i][j] = t;
                        s[i][j] = k;
                    }
                }
            }
        }

        printf("%d
", d[1][n]);
    }

    return 0;
}