leetcode-problemset/leetcode-cn/originData/alice-and-bob-playing-flower-game.json

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            "title": "Alice and Bob Playing Flower Game",
            "titleSlug": "alice-and-bob-playing-flower-game",
            "content": "<p>Alice and Bob are playing a turn-based game on a field, with two lanes of flowers between them. There are <code>x</code> flowers in the first lane between Alice and Bob, and <code>y</code> flowers in the second lane between them.</p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2025/08/27/3021.png\" style=\"width: 300px; height: 150px;\" /></p>\n\n<p>The game proceeds as follows:</p>\n\n<ol>\n\t<li>Alice takes the first turn.</li>\n\t<li>In each turn, a player must choose either one of the lane&nbsp;and pick one flower from that side.</li>\n\t<li>At the end of the turn, if there are no flowers left at all in either lane, the <strong>current</strong> player captures their opponent and wins the game.</li>\n</ol>\n\n<p>Given two integers, <code>n</code> and <code>m</code>, the task is to compute the number of possible pairs <code>(x, y)</code> that satisfy the conditions:</p>\n\n<ul>\n\t<li>Alice must win the game according to the described rules.</li>\n\t<li>The number of flowers <code>x</code> in the first lane must be in the range <code>[1,n]</code>.</li>\n\t<li>The number of flowers <code>y</code> in the second lane must be in the range <code>[1,m]</code>.</li>\n</ul>\n\n<p>Return <em>the number of possible pairs</em> <code>(x, y)</code> <em>that satisfy the conditions mentioned in the statement</em>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 3, m = 2\n<strong>Output:</strong> 3\n<strong>Explanation:</strong> The following pairs satisfy conditions described in the statement: (1,2), (3,2), (2,1).\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 1, m = 1\n<strong>Output:</strong> 0\n<strong>Explanation:</strong> No pairs satisfy the conditions described in the statement.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= n, m &lt;= 10<sup>5</sup></code></li>\n</ul>\n",
            "translatedTitle": "Alice 和 Bob 玩鲜花游戏",
            "translatedContent": "<p>Alice 和 Bob 在一片田野上玩一个回合制游戏，他们之间有两排花。Alice 和 Bob 之间第一排有 <code>x</code> 朵花，第二排有 <code>y</code> 朵花。</p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2025/08/27/3021.png\" style=\"width: 300px; height: 150px;\" /></p>\n\n<p>游戏过程如下：</p>\n\n<ol>\n\t<li>Alice 先行动。</li>\n\t<li>每一次行动中，当前玩家必须选择其中一排，然后在这边摘一朵鲜花。</li>\n\t<li>一次行动结束后，如果两排上都没有剩下鲜花，那么 <strong>当前</strong>&nbsp;玩家抓住对手并赢得游戏的胜利。</li>\n</ol>\n\n<p>给你两个整数&nbsp;<code>n</code>&nbsp;和&nbsp;<code>m</code>&nbsp;，你的任务是求出满足以下条件的所有&nbsp;<code>(x, y)</code>&nbsp;对：</p>\n\n<ul>\n\t<li>按照上述规则，Alice 必须赢得游戏。</li>\n\t<li>第一排的鲜花数目&nbsp;<code>x</code>&nbsp;必须在区间&nbsp;<code>[1,n]</code>&nbsp;之间。</li>\n\t<li>第二排的鲜花数目 <code>y</code>&nbsp;必须在区间&nbsp;<code>[1,m]</code>&nbsp;之间。</li>\n</ul>\n\n<p>请你返回满足题目描述的数对&nbsp;<code>(x, y)</code>&nbsp;的数目。</p>\n\n<p>&nbsp;</p>\n\n<p><strong class=\"example\">示例 1：</strong></p>\n\n<pre>\n<b>输入：</b>n = 3, m = 2\n<b>输出：</b>3\n<b>解释：</b>以下数对满足题目要求：(1,2) ，(3,2) ，(2,1) 。\n</pre>\n\n<p><strong class=\"example\">示例 2：</strong></p>\n\n<pre>\n<b>输入：</b>n = 1, m = 1\n<b>输出：</b>0\n<b>解释：</b>没有数对满足题目要求。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= n, m &lt;= 10<sup>5</sup></code></li>\n</ul>\n",
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