mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
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187 lines
19 KiB
JSON
187 lines
19 KiB
JSON
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"title": "Maximize Grid Happiness",
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"content": "<p>You are given four integers, <code>m</code>, <code>n</code>, <code>introvertsCount</code>, and <code>extrovertsCount</code>. You have an <code>m x n</code> grid, and there are two types of people: introverts and extroverts. There are <code>introvertsCount</code> introverts and <code>extrovertsCount</code> extroverts.</p>\n\n<p>You should decide how many people you want to live in the grid and assign each of them one grid cell. Note that you <strong>do not</strong> have to have all the people living in the grid.</p>\n\n<p>The <strong>happiness</strong> of each person is calculated as follows:</p>\n\n<ul>\n\t<li>Introverts <strong>start</strong> with <code>120</code> happiness and <strong>lose</strong> <code>30</code> happiness for each neighbor (introvert or extrovert).</li>\n\t<li>Extroverts <strong>start</strong> with <code>40</code> happiness and <strong>gain</strong> <code>20</code> happiness for each neighbor (introvert or extrovert).</li>\n</ul>\n\n<p>Neighbors live in the directly adjacent cells north, east, south, and west of a person's cell.</p>\n\n<p>The <strong>grid happiness</strong> is the <strong>sum</strong> of each person's happiness. Return<em> the <strong>maximum possible grid happiness</strong>.</em></p>\n\n<p> </p>\n<p><strong class=\"example\">Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2020/11/05/grid_happiness.png\" style=\"width: 261px; height: 121px;\" />\n<pre>\n<strong>Input:</strong> m = 2, n = 3, introvertsCount = 1, extrovertsCount = 2\n<strong>Output:</strong> 240\n<strong>Explanation:</strong> Assume the grid is 1-indexed with coordinates (row, column).\nWe can put the introvert in cell (1,1) and put the extroverts in cells (1,3) and (2,3).\n- Introvert at (1,1) happiness: 120 (starting happiness) - (0 * 30) (0 neighbors) = 120\n- Extrovert at (1,3) happiness: 40 (starting happiness) + (1 * 20) (1 neighbor) = 60\n- Extrovert at (2,3) happiness: 40 (starting happiness) + (1 * 20) (1 neighbor) = 60\nThe grid happiness is 120 + 60 + 60 = 240.\nThe above figure shows the grid in this example with each person's happiness. The introvert stays in the light green cell while the extroverts live on the light purple cells.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> m = 3, n = 1, introvertsCount = 2, extrovertsCount = 1\n<strong>Output:</strong> 260\n<strong>Explanation:</strong> Place the two introverts in (1,1) and (3,1) and the extrovert at (2,1).\n- Introvert at (1,1) happiness: 120 (starting happiness) - (1 * 30) (1 neighbor) = 90\n- Extrovert at (2,1) happiness: 40 (starting happiness) + (2 * 20) (2 neighbors) = 80\n- Introvert at (3,1) happiness: 120 (starting happiness) - (1 * 30) (1 neighbor) = 90\nThe grid happiness is 90 + 80 + 90 = 260.\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> m = 2, n = 2, introvertsCount = 4, extrovertsCount = 0\n<strong>Output:</strong> 240\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 <= m, n <= 5</code></li>\n\t<li><code>0 <= introvertsCount, extrovertsCount <= min(m * n, 6)</code></li>\n</ul>\n",
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"For each cell, it has 3 options, either it is empty, or contains an introvert, or an extrovert.",
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"You can do DP where you maintain the state of the previous row, the number of remaining introverts and extroverts, the current row and column, and try the 3 options for each cell.",
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