feat: solve No.486

Author: BaffinLee

Diff for: 401-500/486. Predict the Winner.md

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+# 486. Predict the Winner
+
+- Difficulty: Medium.
+- Related Topics: Array, Math, Dynamic Programming, Recursion, Game Theory.
+- Similar Questions: Can I Win.
+
+## Problem
+
+You are given an integer array `nums`. Two players are playing a game with this array: player 1 and player 2.
+
+Player 1 and player 2 take turns, with player 1 starting first. Both players start the game with a score of `0`. At each turn, the player takes one of the numbers from either end of the array (i.e., `nums[0]` or `nums[nums.length - 1]`) which reduces the size of the array by `1`. The player adds the chosen number to their score. The game ends when there are no more elements in the array.
+
+Return `true` if Player 1 can win the game. If the scores of both players are equal, then player 1 is still the winner, and you should also return `true`. You may assume that both players are playing optimally.
+
+ 
+Example 1:
+
+```
+Input: nums = [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: nums = [1,5,233,7]
+Output: true
+Explanation: Player 1 first chooses 1. Then player 2 has 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.
+```
+
+ 
+**Constraints:**
+
+
+	
+- `1 <= nums.length <= 20`
+	
+- `0 <= nums[i] <= 107`
+
+
+
+## Solution
+
+```javascript
+/**
+ * @param {number[]} nums
+ * @return {boolean}
+ */
+var PredictTheWinner = function(nums) {
+    return maxDiff(nums, 0, nums.length - 1) >= 0;
+};
+
+var maxDiff = function(nums, left, right) {
+    if (left === right) return nums[left];
+    return Math.max(
+        nums[left] - maxDiff(nums, left + 1, right),
+        nums[right] - maxDiff(nums, left, right - 1),
+    );
+};
+```
+
+**Explain:**
+
+nope.
+
+**Complexity:**
+
+* Time complexity : O(n ^ 2).
+* Space complexity : O(n ^ 2).