HDU 3516 四边形优化 解题报告

Tree Construction

Time Limit: 4000/2000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 1369 Accepted Submission(s): 760

Problem Description

Consider a two-dimensional space with a set of points (xi, yi) that satisfy xi < xj and yi > yj for all i < j. We want to have them all connected by a directed tree whose edges go toward either right (x positive) or upward (y positive). The figure below shows an example tree.

Write a program that finds a tree connecting all given points with the shortest total length of edges.

Input

The input begins with a line that contains an integer n (1 <= n <= 1000), the number of points. Then n lines follow. The i-th line contains two integers xi and yi (0 <= xi, yi <= 10000), which give the coordinates of the i-th point.

Output

Print the total length of edges in a line.

Sample Input

5
1 5
2 4
3 3
4 2
5 1
1
10000 0

Sample Output

12
0
【解题报告】
四边形优化
http://download.csdn.net/detail/onepointo/9846259

代码如下：

#include<cstdio>    #include<cstring>    #include<algorithm>  using namespace std;  #define INF 0x3f3f3f3fint x[1005],y[1005],s[2005][2005],dp[2005][2005];int n,i,j,k,l,ans;    int main(){      while(scanf("%d",&n)!=EOF)    {          memset(dp,INF,sizeof(dp));          for(i=1;i<=n;i++)        {              scanf("%d%d",&x[i],&y[i]);              dp[i][i]=dp[i+n][i+n]=0;              s[i][i]=i,s[i+n][i+n]=i+n;          }          for(l=2;l<=2*n;l++)        {                                 for(i=1;i<=2*n-l+1;++i)            {                             j=i+l-1;                  for(k=s[i][j-1];k<=s[i+1][j];++k)                {                      if(dp[i][j]>dp[i][k]+dp[k+1][j]+(y[k]-y[j])+(x[k+1]-x[i]))                    {                          dp[i][j]=dp[i][k]+dp[k+1][j]+(y[k]-y[j])+(x[k+1]-x[i]);                          s[i][j]=k;                      }                  }              }          }          printf("%d\n",dp[1][n]);      }      return 0;  }  

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