1 解題思想

開學了，我又迴歸了。
這道題的意思是給了一個數組，兩個人玩，每個人可以在當前的陣列的頭部或者尾部選擇一個數，作為自己的分數，然後換人，已經被選過的數字不能再用。
現在有兩個人玩，Player1和Player2，問給了當前的陣列後，Player1能不能保證勝利？

解題方法，就是需要做一個決策，看Player1有沒有一個必勝的選擇決策，這個只需要遞迴下去選就好。
所謂的必勝，就是當前選到的分數，大於對手能選擇到的。

2 原題

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

3 AC解

public class Solution {
    public boolean PredictTheWinner(int[] nums) {
        return helper(nums, 0, nums.length-1)>=0;
    }

    private int helper(int[] nums, int start, int end){  
        if(start==end){
            return nums[start];
        } else{
            return Math.max(nums[start] - helper(nums,start+1,end),nums[end] - helper(nums,start,end-1));
        }
    }
}