486. Predict the Winner

Given an array of scores that are non-negative integers. Player 1 picks one of the numbers from either end of the array followed by the player 2 and then player 1 and so on. Each time a player picks a number, that number will not be available for the next player. This continues until all the scores have been chosen. The player with the maximum score wins.

Given an array of scores, predict whether player 1 is the winner. You can assume each player plays to maximize his score.

Example 1:

Input: [1, 5, 2]
Output: False
Explanation: Initially, player 1 can choose between 1 and 2. 
If he chooses 2 (or 1), then player 2 can choose from 1 (or 2) and 5. If player 2 chooses 5, then player 1 will be left with 1 (or 2). 
So, final score of player 1 is 1 + 2 = 3, and player 2 is 5. 
Hence, player 1 will never be the winner and you need to return False.

Example 2:

Input: [1, 5, 233, 7]
Output: True
Explanation: Player 1 first chooses 1. Then player 2 have to choose between 5 and 7. No matter which number player 2 choose, player 1 can choose 233.
Finally, player 1 has more score (234) than player 2 (12), so you need to return True representing player1 can win.

Note:

1. 1 <= length of the array <= 20.
2. Any scores in the given array are non-negative integers and will not exceed 10,000,000.
3. If the scores of both players are equal, then player 1 is still the winner.

 本题思维上面还是有点难度的，我开始的思路是按照can I win的想法来做的，然而做不出来，原因是player2没有办法赋值。本题的解法里面，首先用到了动态规划的方法，采用自顶向下方法，从start和从end开始取较大值，代码如下：

public class Solution {
    public boolean PredictTheWinner(int[] nums) {
        return helper(nums,0,nums.length-1,new Integer[nums.length][nums.length])>=0;
    }
    public int helper(int[] nums,int s,int e,Integer[][] dp){
        if(dp[s][e]==null){
            dp[s][e] = s==e?nums[e]:Math.max(nums[s]-helper(nums,s+1,e,dp),nums[e]-helper(nums,s,e-1,dp));
        }
        return dp[s][e];
    }
}