312. 戳气球（区间dp）

class Solution {
    public int maxCoins(int[] nums) {
        int n = nums.length + 2;
        int[] points = new int[n];
        points[0] = 1;
        points[n-1] = 1;
        for(int i = 1; i <= n - 2; i++) points[i] = nums[i-1];
        int[][] dp = new int[n][n];  // dp[i][j] 戳破（i，j）之间的气球最大多少分 假设最后一个戳破的是k
                                     // dp[i][j] = dp[i][k]+dp[k][j]+points[k]*points[i]*points[j]
        for(int i = n; i >= 0; i--) {
            for(int j = i + 2;  j < n; j++) {
                for(int k = i + 1; k < j; k++) {
                    dp[i][j] = Math.max(dp[i][j],
                    dp[i][k] + dp[k][j] + points[k] * points[i] * points[j]);
                }
            }
        }
        return dp[0][n-1];
    }
}