树形动态规划

 1 #include <stdio.h>
 2 #include <string.h>
 3 
 4 int a[30];
 5 int dp[30][30];//dp[i][j] 表示某子树的中序遍历为i-->j    那么dp[i][i]则表示i为叶子结点
 6 int root[30][30];
 7 
 8 void print(int i, int j)
 9 {
10     if(i>j)return;
11     if(root[i][j]==-1) return;
12     printf("%d ",root[i][j]+1);
13     print(i,root[i][j]-1);
14     print(root[i][j]+1,j);
15 }
16 int main()
17 {
18     int n,i,j,k,t;
19     while(scanf("%d",&n)!=EOF)
20     {
21         memset(dp,-1,sizeof(dp));
22         memset(root,-1,sizeof(root));
23         for(i=0; i<n; ++i)
24         {
25             scanf("%d",&a[i]);
26             dp[i][i] = a[i];
27             root[i][i] = i;
28         }    
29         for(t=1; t<n; ++t)//枚举长度
30             for(i=0; i<n-t; ++i)//枚举起点
31             {
32                 j = t + i;//区间总长度
33                 for(k=i+1; k<j; ++k)
34                     if(dp[i][j] < (dp[i][k-1]*dp[k+1][j]+a[k]))
35                     {
36                         dp[i][j] = dp[i][k-1]*dp[k+1][j]+a[k];
37                         root[i][j] = k;
38                     }
39                 if(dp[i][j] < dp[i][j-1] + a[j])
40                 {
41                     dp[i][j] = dp[i][j-1] + a[j];
42                     root[i][j] = j;
43                 }
44                 if(dp[i][j] < dp[i+1][j] + a[i])
45                 {
46                     dp[i][j] = dp[i+1][j] + a[i];
47                     root[i][j] = i;
48                 }
49             }
50         printf("%d\n",dp[0][n-1]);
51         print(0,n-1);
52     }
53 }