hdu3516 Tree Construction (四边形不等式)

题意：给定一些点(xi,yi)(xj,yj)满足:i<j,xi<xj,yi>yj。用下面的连起来，使得所有边的长度最小？

题解：直接给出吧

f[i][j]=min(f[i][k]+f[k+1][j]+cost(i,j)

cost(i,j)=a[k].y-a[j].y+a[k+1].x-a[i].x;

明显了吧

证明一下，搞一搞，四边形性质就出来了，模板题吧。

 #include<cstdio>
 #include<cstring>
 #include<iostream>
 #include<algorithm>
 #include<cstring>
 #include<cstdlib>
 #define N 1007
 #define M 500007
 #define inf 2000000009
 using namespace std;

 int n;
 int f[N][N],s[N][N];
 struct Node{int x,y;}a[M];

 int cost(int i,int j,int k)
 {
     if (k>=j) return inf;
     return a[k].y-a[j].y+a[k+].x-a[i].x;
 }
 int main()
 {
     while (~scanf("%d",&n))
     {
         for (int i=;i<=n;i++)
             scanf("%d%d",&a[i].x,&a[i].y);
         for (int i=;i<=n;i++)
             s[i][i]=i;
         memset(f,,sizeof f);
         for (int L=;L<=n;L++)
             for (int i=;i+L-<=n;i++)
              {
                 int j=L+i-;f[i][j]=inf;
                 for (int k=s[i][j-];k<=s[i+][j];k++)
                 {
                     int tmp=f[i][k]+f[k+][j]+cost(i,j,k);
                     if (tmp<f[i][j]) f[i][j]=tmp,s[i][j]=k;
                 }
             }
         printf("%d\n",f[][n]);
     }
 }