leetcode-problemset/leetcode-cn/originData/select-cells-in-grid-with-maximum-score.json

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        "question": {
            "questionId": "3563",
            "questionFrontendId": "3276",
            "categoryTitle": "Algorithms",
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            "title": "Select Cells in Grid With Maximum Score",
            "titleSlug": "select-cells-in-grid-with-maximum-score",
            "content": "<p>You are given a 2D matrix <code>grid</code> consisting of positive integers.</p>\n\n<p>You have to select <em>one or more</em> cells from the matrix such that the following conditions are satisfied:</p>\n\n<ul>\n\t<li>No two selected cells are in the <strong>same</strong> row of the matrix.</li>\n\t<li>The values in the set of selected cells are <strong>unique</strong>.</li>\n</ul>\n\n<p>Your score will be the <strong>sum</strong> of the values of the selected cells.</p>\n\n<p>Return the <strong>maximum</strong> score you can achieve.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">grid = [[1,2,3],[4,3,2],[1,1,1]]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">8</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2024/07/29/grid1drawio.png\" /></p>\n\n<p>We can select the cells with values 1, 3, and 4 that are colored above.</p>\n</div>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">grid = [[8,7,6],[8,3,2]]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">15</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2024/07/29/grid8_8drawio.png\" style=\"width: 170px; height: 114px;\" /></p>\n\n<p>We can select the cells with values 7 and 8 that are colored above.</p>\n</div>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= grid.length, grid[i].length &lt;= 10</code></li>\n\t<li><code>1 &lt;= grid[i][j] &lt;= 100</code></li>\n</ul>\n",
            "translatedTitle": "选择矩阵中单元格的最大得分",
            "translatedContent": "<p>给你一个由正整数构成的二维矩阵 <code>grid</code>。</p>\n\n<p>你需要从矩阵中选择<strong> 一个或多个 </strong>单元格，选中的单元格应满足以下条件：</p>\n\n<ul>\n\t<li>所选单元格中的任意两个单元格都不会处于矩阵的 <strong>同一行</strong>。</li>\n\t<li>所选单元格的值 <strong>互不相同</strong>。</li>\n</ul>\n\n<p>你的得分为所选单元格值的<strong>总和</strong>。</p>\n\n<p>返回你能获得的<strong> 最大 </strong>得分。</p>\n\n<p>&nbsp;</p>\n\n<p><strong class=\"example\">示例 1：</strong></p>\n\n<div class=\"example-block\">\n<p><strong>输入：</strong> <span class=\"example-io\">grid = [[1,2,3],[4,3,2],[1,1,1]]</span></p>\n\n<p><strong>输出：</strong> <span class=\"example-io\">8</span></p>\n\n<p><strong>解释：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2024/07/29/grid1drawio.png\" /></p>\n\n<p>选择上图中用彩色标记的单元格，对应的值分别为 1、3 和 4 。</p>\n</div>\n\n<p><strong class=\"example\">示例 2：</strong></p>\n\n<div class=\"example-block\">\n<p><strong>输入：</strong> <span class=\"example-io\">grid = [[8,7,6],[8,3,2]]</span></p>\n\n<p><strong>输出：</strong> <span class=\"example-io\">15</span></p>\n\n<p><strong>解释：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2024/07/29/grid8_8drawio.png\" style=\"width: 170px; height: 114px;\" /></p>\n\n<p>选择上图中用彩色标记的单元格，对应的值分别为 7 和 8 。</p>\n</div>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= grid.length, grid[i].length &lt;= 10</code></li>\n\t<li><code>1 &lt;= grid[i][j] &lt;= 100</code></li>\n</ul>\n",
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            "hints": [
                "Sort all the cells in the grid by their values and keep track of their original positions.",
                "Try dynamic programming with the following states: the current cell that we might select and a bitmask representing all the rows from which we have already selected a cell so far."
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