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: FalseExplanation: 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: TrueExplanation: 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.

动态规划的思路，采用自顶向下，使用memoize。当前问题划分成子问题，然后找最优解。返回true的条件是，第一个用户所能够得到的分数是否大于等于第二个人的。而两个人取值的方式，都是尽可能的让结果大。

代码：

    Integer[][] memo;    public boolean PredictTheWinner(int[] nums) {        memo = new Integer[nums.length][nums.length];        return helper(nums, 0, nums.length-1) >=0;    }    private int helper(int[] nums, int i, int j) {        if(memo[i][j] == null)        memo[i][j] =  i == j ? nums[i] : Math.max(nums[i]-helper(nums, i+1, j),                                            nums[j]-helper(nums, i, j-1));        return memo[i][j];    }