predict-the-winner

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Algorithms

You are given an integer array <code>nums</code>.

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 current player takes the number at either end of the array (i.e., <code>nums[0]</code> or <code>nums[nums.length - 1]</code>), removing it from the array and adding it to their own score. The game ends when there are no more elements in the array.

Return <code>true</code> if Player 1&#39;s final score is greater than or equal to Player 2&#39;s final score, and <code>false</code> otherwise.

Note that a tie counts as a win for Player 1. You may assume that both players play optimally.

&nbsp;
Example 1:

<div class="example-block">
Input: nums = [1,5,2]

Output: false

Explanation:

<ul>
	<li>Player 1 must open by taking either 1 or 2, and both choices lead to the same result.</li>
	<li>If Player 1 takes 1, the array becomes <code>[5,2]</code>. Player 2 takes 5, leaving 2 for Player 1.</li>
	<li>If Player 1 takes 2, the array becomes <code>[1,5]</code>. Player 2 takes 5, leaving 1 for Player 1.</li>
	<li>Either way, Player 1 finishes with <code>1 + 2 = 3</code> and Player 2 finishes with <code>5</code>. Player 1 can never win, so return <code>false</code>.</li>
</ul>
</div>

Example 2:

<div class="example-block">
Input: nums = [1,5,233,7]

Output: true

Explanation:

<ul>
	<li>Player 1 first takes 1, leaving <code>[5,233,7]</code>. Player 2 must then choose between 5 and 7, and no matter which number Player 2 chooses, Player 1 can take 233 on the next turn.</li>
	<li>Player 1 finishes with a higher score (234) than Player 2 (12), so return <code>true</code>.</li>
</ul>
</div>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= nums.length &lt;= 20</code></li>
	<li><code>0 &lt;= nums[i] &lt;= 107</code></li>
</ul>

predictTheWinner

Predict the Winner

Can I Win

can-i-win

我能赢吗

Find the Winning Player in Coin Game

find-the-winning-player-in-coin-game

求出硬币游戏的赢家

Find the Number of Winning Players

find-the-number-of-winning-players

求出胜利玩家的数目

Count The Number of Winning Sequences

count-the-number-of-winning-sequences

统计能获胜的出招序列数

Recursion

Minimax

Array

Math

Dynamic Programming

Game Theory

零和博弈

给你一个整数数组 <code>nums</code>。

玩家 1 和玩家 2 基于这个数组设计了一个游戏。

玩家 1 和玩家 2 轮流进行自己的回合，玩家 1 先手。开始时，两个玩家的初始分值都是 <code>0</code> 。

每一回合，玩家从数组的 任意一端 取一个数字（即，<code>nums[0]</code> 或 <code>nums[nums.length - 1]</code>），取到的数字将会从数组中 移除（数组长度减 <code>1</code> ）。玩家选中的数字将会加到他的得分上。当数组中没有剩余数字可取时，游戏结束。

如果玩家 1 能成为赢家，返回 <code>true</code> 。

注意，如果两个玩家得分相等，同样认为玩家 1 是游戏的赢家。你可以假设每个玩家的玩法都会使他的分数最大化。

&nbsp;

示例 1：

<div class="example-block">
输入：nums = [1,5,2]

输出：false

解释：

<ul>
	<li>玩家 1 必须先取 1 或 2，两种选择都会导致相同的结果。</li>
	<li>如果玩家 1 取 1，数组变为&nbsp;<code>[5, 2]</code>。玩家 2 取 5，剩下 2 给玩家 1。</li>
	<li>如果玩家 1 取 2，数组变为&nbsp;<code>[1, 5]</code>。玩家 2 取 5，剩下 1 给玩家 1。</li>
	<li>无论哪种情况，玩家 1 最终得到&nbsp;<code>1 + 2 = 3</code>，玩家 2 得到&nbsp;<code>5</code>。玩家 1 永远无法获胜，所以返回&nbsp;<code>false</code>。</li>
</ul>
</div>

示例 2：

<div class="example-block">
输入：nums = [1,5,233,7]

输出：true

解释： 

<ul>
	<li>玩家 1 先取 1，剩下&nbsp;<code>[5,233,7]</code>。然后玩家 2 必须在 5 和 7 之间选择，无论玩家 2 选择哪个数字，玩家 1 在下一次回合都可以取 233。</li>
	<li>玩家 1 的得分（234）高于玩家 2（12），所以返回&nbsp;<code>true</code>。</li>
</ul>
</div>

&nbsp;

提示：

<ul>
	<li><code>1 &lt;= nums.length &lt;= 20</code></li>
	<li><code>0 &lt;= nums[i] &lt;= 107</code></li>
</ul>