leetcode-problemset/leetcode-cn/originData/maximum-good-people-based-on-statements.json

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            "questionId": "2272",
            "questionFrontendId": "2151",
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            "title": "Maximum Good People Based on Statements",
            "titleSlug": "maximum-good-people-based-on-statements",
            "content": "<p>There are two types of persons:</p>\n\n<ul>\n\t<li>The <strong>good person</strong>: The person who always tells the truth.</li>\n\t<li>The <strong>bad person</strong>: The person who might tell the truth and might lie.</li>\n</ul>\n\n<p>You are given a <strong>0-indexed</strong> 2D integer array <code>statements</code> of size <code>n x n</code> that represents the statements made by <code>n</code> people about each other. More specifically, <code>statements[i][j]</code> could be one of the following:</p>\n\n<ul>\n\t<li><code>0</code> which represents a statement made by person <code>i</code> that person <code>j</code> is a <strong>bad</strong> person.</li>\n\t<li><code>1</code> which represents a statement made by person <code>i</code> that person <code>j</code> is a <strong>good</strong> person.</li>\n\t<li><code>2</code> represents that <strong>no statement</strong> is made by person <code>i</code> about person <code>j</code>.</li>\n</ul>\n\n<p>Additionally, no person ever makes a statement about themselves. Formally, we have that <code>statements[i][i] = 2</code> for all <code>0 &lt;= i &lt; n</code>.</p>\n\n<p>Return <em>the <strong>maximum</strong> number of people who can be <strong>good</strong> based on the statements made by the </em><code>n</code><em> people</em>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/01/15/logic1.jpg\" style=\"width: 600px; height: 262px;\" />\n<pre>\n<strong>Input:</strong> statements = [[2,1,2],[1,2,2],[2,0,2]]\n<strong>Output:</strong> 2\n<strong>Explanation:</strong> Each person makes a single statement.\n- Person 0 states that person 1 is good.\n- Person 1 states that person 0 is good.\n- Person 2 states that person 1 is bad.\nLet&#39;s take person 2 as the key.\n- Assuming that person 2 is a good person:\n    - Based on the statement made by person 2, person 1 is a bad person.\n    - Now we know for sure that person 1 is bad and person 2 is good.\n    - Based on the statement made by person 1, and since person 1 is bad, they could be:\n        - telling the truth. There will be a contradiction in this case and this assumption is invalid.\n        - lying. In this case, person 0 is also a bad person and lied in their statement.\n    - <strong>Following that person 2 is a good person, there will be only one good person in the group</strong>.\n- Assuming that person 2 is a bad person:\n    - Based on the statement made by person 2, and since person 2 is bad, they could be:\n        - telling the truth. Following this scenario, person 0 and 1 are both bad as explained before.\n            - <strong>Following that person 2 is bad but told the truth, there will be no good persons in the group</strong>.\n        - lying. In this case person 1 is a good person.\n            - Since person 1 is a good person, person 0 is also a good person.\n            - <strong>Following that person 2 is bad and lied, there will be two good persons in the group</strong>.\nWe can see that at most 2 persons are good in the best case, so we return 2.\nNote that there is more than one way to arrive at this conclusion.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/01/15/logic2.jpg\" style=\"width: 600px; height: 262px;\" />\n<pre>\n<strong>Input:</strong> statements = [[2,0],[0,2]]\n<strong>Output:</strong> 1\n<strong>Explanation:</strong> Each person makes a single statement.\n- Person 0 states that person 1 is bad.\n- Person 1 states that person 0 is bad.\nLet&#39;s take person 0 as the key.\n- Assuming that person 0 is a good person:\n    - Based on the statement made by person 0, person 1 is a bad person and was lying.\n    - <strong>Following that person 0 is a good person, there will be only one good person in the group</strong>.\n- Assuming that person 0 is a bad person:\n    - Based on the statement made by person 0, and since person 0 is bad, they could be:\n        - telling the truth. Following this scenario, person 0 and 1 are both bad.\n            - <strong>Following that person 0 is bad but told the truth, there will be no good persons in the group</strong>.\n        - lying. In this case person 1 is a good person.\n            - <strong>Following that person 0 is bad and lied, there will be only one good person in the group</strong>.\nWe can see that at most, one person is good in the best case, so we return 1.\nNote that there is more than one way to arrive at this conclusion.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>n == statements.length == statements[i].length</code></li>\n\t<li><code>2 &lt;= n &lt;= 15</code></li>\n\t<li><code>statements[i][j]</code> is either <code>0</code>, <code>1</code>, or <code>2</code>.</li>\n\t<li><code>statements[i][i] == 2</code></li>\n</ul>\n",
            "translatedTitle": "基于陈述统计最多好人数",
            "translatedContent": "<p>游戏中存在两种角色：</p>\n\n<ul>\n\t<li><strong>好人</strong>：该角色只说真话。</li>\n\t<li><strong>坏人</strong>：该角色可能说真话，也可能说假话。</li>\n</ul>\n\n<p>给你一个下标从 <strong>0</strong> 开始的二维整数数组 <code>statements</code> ，大小为 <code>n x n</code> ，表示 <code>n</code> 个玩家对彼此角色的陈述。具体来说，<code>statements[i][j]</code> 可以是下述值之一：</p>\n\n<ul>\n\t<li><code>0</code> 表示 <code>i</code> 的陈述认为 <code>j</code> 是 <strong>坏人</strong> 。</li>\n\t<li><code>1</code> 表示 <code>i</code> 的陈述认为 <code>j</code> 是 <strong>好人</strong> 。</li>\n\t<li><code>2</code> 表示 <code>i</code> 没有对 <code>j</code> 作出陈述。</li>\n</ul>\n\n<p>另外，玩家不会对自己进行陈述。形式上，对所有&nbsp;<code>0 &lt;= i &lt; n</code> ，都有 <code>statements[i][i] = 2</code> 。</p>\n\n<p>根据这 <code>n</code> 个玩家的陈述，返回可以认为是 <strong>好人</strong> 的 <strong>最大</strong> 数目。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/01/15/logic1.jpg\" style=\"width: 600px; height: 262px;\">\n<pre><strong>输入：</strong>statements = [[2,1,2],[1,2,2],[2,0,2]]\n<strong>输出：</strong>2\n<strong>解释：</strong>每个人都做一条陈述。\n- 0 认为 1 是好人。\n- 1 认为 0 是好人。\n- 2 认为 1 是坏人。\n以 2 为突破点。\n- 假设 2 是一个好人：\n    - 基于 2 的陈述，1 是坏人。\n    - 那么可以确认 1 是坏人，2 是好人。\n    - 基于 1 的陈述，由于 1 是坏人，那么他在陈述时可能：\n        - 说真话。在这种情况下会出现矛盾，所以假设无效。\n        - 说假话。在这种情况下，0 也是坏人并且在陈述时说假话。\n    - <strong>在认为 2 是好人的情况下，这组玩家中只有一个好人。</strong>\n- 假设 2 是一个坏人：\n    - 基于 2 的陈述，由于 2 是坏人，那么他在陈述时可能：\n        - 说真话。在这种情况下，0 和 1 都是坏人。\n            - <strong>在认为 2 是坏人但说真话的情况下，这组玩家中没有一个好人。</strong>\n        - 说假话。在这种情况下，1 是好人。\n            - 由于 1 是好人，0 也是好人。\n            - <strong>在认为 2 是坏人且说假话的情况下，这组玩家中有两个好人。</strong>\n在最佳情况下，至多有两个好人，所以返回 2 。\n注意，能得到此结论的方法不止一种。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/01/15/logic2.jpg\" style=\"width: 600px; height: 262px;\">\n<pre><strong>输入：</strong>statements = [[2,0],[0,2]]\n<strong>输出：</strong>1\n<strong>解释：</strong>每个人都做一条陈述。\n- 0 认为 1 是坏人。\n- 1 认为 0 是坏人。\n以 0 为突破点。\n- 假设 0 是一个好人：\n    - 基于与 0 的陈述，1 是坏人并说假话。\n    - <strong>在认为 0 是好人的情况下，这组玩家中只有一个好人。</strong>\n- 假设 0 是一个坏人：\n    - 基于 0 的陈述，由于 0 是坏人，那么他在陈述时可能：\n        - 说真话。在这种情况下，0 和 1 都是坏人。\n            - <strong>在认为 0 是坏人但说真话的情况下，这组玩家中没有一个好人。</strong>\n        - 说假话。在这种情况下，1 是好人。\n            - <strong>在认为 0 是坏人且说假话的情况下，这组玩家中只有一个好人。</strong>\n在最佳情况下，至多有一个好人，所以返回 1 。 \n注意，能得到此结论的方法不止一种。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>n == statements.length == statements[i].length</code></li>\n\t<li><code>2 &lt;= n &lt;= 15</code></li>\n\t<li><code>statements[i][j]</code> 的值为 <code>0</code>、<code>1</code> 或 <code>2</code></li>\n\t<li><code>statements[i][i] == 2</code></li>\n</ul>\n",
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