Problem312.java

import java.util.List;
import java.util.ArrayList;

class Problem312 {
	public static void main(String[] args) {
		int[] nums = {3,1,5,8};
		System.out.println(new Problem312().maxCoins(nums));
	}

	public int maxCoins(int[] nums) {
 List<Integer> list = new ArrayList<>();
 list.add(1);
 for (int i = 0; i < nums.length; i++) {
 	list.add(nums[i]);
 }
 list.add(1);

 int[][] dp = new int[list.size()][list.size()];

 int sum = helper(list, 1, nums.length, dp);
 	return sum;
 }


 	int helper(List<Integer> list, int left, int right, int[][] dp) {
 	
 if (left > right) return 0;
 if (dp[left][right] > 0) return dp[left][right];

 	for (int i = left; i <= right; i++) {
 int l = helper(list, left, i-1, dp);
 int r = helper(list, i+1, right, dp);

 		int val = list.get(i) * list.get(left-1) * list.get(right+1);
 		dp[left][right] = Math.max(dp[left][right], val + l + r);
 	}
 	return dp[left][right];
 }
}