Stone Game

There is a stone game.At the beginning of the game the player picksnpiles of stones in a line.

The goal is to merge the stones in one pile observing the following rules:

1. At each step of the game,the player can merge two adjacent piles to a new pile.
2. The score is the number of stones in the new pile.

You are to determine the minimum of the total score.

Example

For[4, 1, 1, 4], in the best solution, the total score is18:

1. Merge second and third piles =
>
 [4, 2, 4], score +2
2. Merge the first two piles =
>
 [6, 4]，score +6
3. Merge the last two piles =
>
 [10], score +10

Other two examples:
[1, 1, 1, 1]return8
[4, 4, 5, 9]return43

public int stoneGame(int[] A) {
    if(A == null || A.length == 0) {
        return 0;
    }
    int n = A.length;
    int[][] dp = new int[n][n];
    int[][] sum = new int[n][n];
    for(int i = 0; i < n; i++) {
        sum[i][i] = A[i];
        for(int j = i + 1; j < n; j++) {
            sum[i][j] = sum[i][j - 1] + A[j];
        }
    }
    for(int i = 0; i < n; i++) {
        for(int j = 0; j < n; j++) {
            dp[i][j] = Integer.MAX_VALUE;
        }
    }
    for(int i = 0; i < n; i++) {
        dp[i][i] = 0;
    }
    return search(A, 0, n - 1, dp, sum);
}
public int search(int[] A, int start, int end, int[][] dp, int[][] sum) {
    if(dp[start][end] != Integer.MAX_VALUE) {
        return dp[start][end];
    }
    if(start == end) {
        return dp[start][end];
    }
    int value = Integer.MAX_VALUE;
    for(int i = start; i < end; i++) {
        value = Math.min(value, search(A, start, i, dp, sum) + search(A, i + 1, end, dp, sum) + sum[start][end]);
    }
    dp[start][end] = value;
    return dp[start][end];
}