# 486. Predict the Winner (Medium)

https://leetcode.com/problems/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." li="">
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.

## Solutions

``````public class Solution {
public boolean PredictTheWinner(int[] nums) {
int len = nums.length;

// store all the calculated value in case of computation overhead
int[][] track = new int[len][len];

for (int i = 0; i < len; i++) {
Arrays.fill(track[i], -1);
}

// first one's turn id is 1, later one's turn id is -1
// player 1 uses points of positive type, player 2 uses negative type
return winner(nums, 0, len - 1, 1, track) >= 0;
}

public int winner(int[] nums, int start, int end, int turn, int[][] track) {
if (track[start][end] >= 0) {
return turn * track[start][end];
}

if (start == end) {
return turn * nums[start];
}

// winner() return the difference of points of player 1 and play 2
// winner() returning a positive value x indicates that player 1 is
// x points ahead of player 2
int a = turn * nums[start] + winner(nums, start + 1, end, -turn, track);
int b = turn * nums[end] + winner(nums, start, end - 1, -turn, track);

int val = turn * Math.max(turn * a, turn * b);

// for convenience, all the values are kept as positive.
track[start][end] = turn * val;

return val;
}
}
``````