Stone Game II

Description

There is a stone game.At the beginning of the game the player picks n piles of stones in a circle.

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

At each step of the game,the player can merge two adjacent piles to a new pile.
The score is the number of stones in the new pile.
You are to determine the minimum of the total score.

Example

Example 1:

Input:

[1,1,4,4]

Output:18

Explanation:

1. Merge second and third piles => [2, 4, 4], score +2

2. Merge the first two piles => [6, 4]，score +6

3. Merge the last two piles => [10], score +10

Example 2:

Input:

[1, 1, 1, 1]

Output:8

Explanation:

1. Merge first and second piles => [2, 1, 1], score +2

2. Merge the last two piles => [2, 2]，score +2

3. Merge the last two piles => [4], score +4
思路：动态规划。
dp[i][j]代表从i合并到j的最少花费。
转移方程为dp[i][j] = min（dp[i][k] + dp[k+1][j] + sum[j + 1] - sum[i]）

public class Solution {

    /**

     * @param A an integer array

     * @return an integer

     */

    public int stoneGame2(int[] A) {

        // Write your code here

        int n = A.length;

        if (n <= 1)

            return 0;

        int[][] dp = new int[2 * n][2 * n];

        int[] sum = new int[2 * n + 1];

        for (int i = 1; i <= 2 * n; ++i) {

            sum[i] = sum[i - 1] + A[(i - 1) % n];

        }

        for (int i = 0; i < 2 * n; ++i) {

            dp[i][i] = 0;

        }

        for(int len = 2; len <= 2 * n; ++len)

            for(int i= 0;i < 2 * n && i + len - 1 < 2 * n; ++i) {

                int j = i + len - 1;

                dp[i][j] = Integer.MAX_VALUE;

                for (int k = i; k < j; ++k) {

                    if (dp[i][k] + dp[k+1][j] + sum[j + 1] - sum[i] < dp[i][j])

                        dp[i][j] = dp[i][k] + dp[k+1][j] + sum[j + 1] - sum[i];

                }

        }

        int ans = Integer.MAX_VALUE;

        for (int i = 0; i < n; ++i)

            if (dp[i][i + n - 1] < ans)

                ans = dp[i][i + n - 1];

        return ans;

    }

}

巴特西

Stone Game II

Description

Example

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