leetcode1130 Minimum Cost Tree From Leaf Values

思路：

区间dp。

实现：

 class Solution
 {
 public:
     int mctFromLeafValues(vector<int>& arr)
     {
         int n = arr.size();
         vector<vector<int>> maxn(n, vector<int>(n, ));
         for (int i = n - ; i >= ; i--)
         {
             for (int j = i; j < n; j++)
             {
                 if (j == i) maxn[i][j] = arr[i];
                 else
                 {
                     maxn[i][j] = max(maxn[i][j - ], arr[j]);
                 }
             }
         }
         vector<vector<int>> dp(n, vector<int>(n, INT_MAX));
         for (int i = n - ; i >= ; i--)
         {
             for (int j = i; j < n; j++)
             {
                 if (j == i) dp[i][j] = arr[i];
                 else if (j == i + ) dp[i][j] = arr[i] * arr[j];
                 else
                 {
                     dp[i][j] = min(dp[i][j], dp[i + ][j] + arr[i] * maxn[i + ][j]);
                     dp[i][j] = min(dp[i][j], dp[i][j - ] + arr[j] * maxn[i][j - ]);
                     for (int k = i + ; k < j - ; k++)
                     {
                         dp[i][j] = min(dp[i][j], dp[i][k] + dp[k + ][j] + maxn[i][k] * maxn[k + ][j]);
                     }
                 }
             }
         }
         return dp[][n - ];
     }
 }