mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
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181 lines
19 KiB
JSON
181 lines
19 KiB
JSON
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"title": "Maximum Good People Based on Statements",
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"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 <= i < 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> </p>\n<p><strong>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'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>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'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> </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 <= n <= 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",
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"You should test every possible assignment of good and bad people, using a bitmask.",
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"In each bitmask, if the person i is good, then his statements should be consistent with the bitmask in order for the assignment to be valid.",
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"If the assignment is valid, count how many people are good and keep track of the maximum."
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