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"title": "K Highest Ranked Items Within a Price Range",
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"content": "<p>You are given a <strong>0-indexed</strong> 2D integer array <code>grid</code> of size <code>m x n</code> that represents a map of the items in a shop. The integers in the grid represent the following:</p>\n\n<ul>\n\t<li><code>0</code> represents a wall that you cannot pass through.</li>\n\t<li><code>1</code> represents an empty cell that you can freely move to and from.</li>\n\t<li>All other positive integers represent the price of an item in that cell. You may also freely move to and from these item cells.</li>\n</ul>\n\n<p>It takes <code>1</code> step to travel between adjacent grid cells.</p>\n\n<p>You are also given integer arrays <code>pricing</code> and <code>start</code> where <code>pricing = [low, high]</code> and <code>start = [row, col]</code> indicates that you start at the position <code>(row, col)</code> and are interested only in items with a price in the range of <code>[low, high]</code> (<strong>inclusive</strong>). You are further given an integer <code>k</code>.</p>\n\n<p>You are interested in the <strong>positions</strong> of the <code>k</code> <strong>highest-ranked</strong> items whose prices are <strong>within</strong> the given price range. The rank is determined by the <strong>first</strong> of these criteria that is different:</p>\n\n<ol>\n\t<li>Distance, defined as the length of the shortest path from the <code>start</code> (<strong>shorter</strong> distance has a higher rank).</li>\n\t<li>Price (<strong>lower</strong> price has a higher rank, but it must be <strong>in the price range</strong>).</li>\n\t<li>The row number (<strong>smaller</strong> row number has a higher rank).</li>\n\t<li>The column number (<strong>smaller</strong> column number has a higher rank).</li>\n</ol>\n\n<p>Return <em>the </em><code>k</code><em> highest-ranked items within the price range <strong>sorted</strong> by their rank (highest to lowest)</em>. If there are fewer than <code>k</code> reachable items within the price range, return <em><strong>all</strong> of them</em>.</p>\n\n<p>&nbsp;</p>\n<p><strong>Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/12/16/example1drawio.png\" style=\"width: 200px; height: 151px;\" />\n<pre>\n<strong>Input:</strong> grid = [[1,2,0,1],[1,3,0,1],[0,2,5,1]], pricing = [2,5], start = [0,0], k = 3\n<strong>Output:</strong> [[0,1],[1,1],[2,1]]\n<strong>Explanation:</strong> You start at (0,0).\nWith a price range of [2,5], we can take items from (0,1), (1,1), (2,1) and (2,2).\nThe ranks of these items are:\n- (0,1) with distance 1\n- (1,1) with distance 2\n- (2,1) with distance 3\n- (2,2) with distance 4\nThus, the 3 highest ranked items in the price range are (0,1), (1,1), and (2,1).\n</pre>\n\n<p><strong>Example 2:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/12/16/example2drawio1.png\" style=\"width: 200px; height: 151px;\" />\n<pre>\n<strong>Input:</strong> grid = [[1,2,0,1],[1,3,3,1],[0,2,5,1]], pricing = [2,3], start = [2,3], k = 2\n<strong>Output:</strong> [[2,1],[1,2]]\n<strong>Explanation:</strong> You start at (2,3).\nWith a price range of [2,3], we can take items from (0,1), (1,1), (1,2) and (2,1).\nThe ranks of these items are:\n- (2,1) with distance 2, price 2\n- (1,2) with distance 2, price 3\n- (1,1) with distance 3\n- (0,1) with distance 4\nThus, the 2 highest ranked items in the price range are (2,1) and (1,2).\n</pre>\n\n<p><strong>Example 3:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/12/30/example3.png\" style=\"width: 149px; height: 150px;\" />\n<pre>\n<strong>Input:</strong> grid = [[1,1,1],[0,0,1],[2,3,4]], pricing = [2,3], start = [0,0], k = 3\n<strong>Output:</strong> [[2,1],[2,0]]\n<strong>Explanation:</strong> You start at (0,0).\nWith a price range of [2,3], we can take items from (2,0) and (2,1). \nThe ranks of these items are: \n- (2,1) with distance 5\n- (2,0) with distance 6\nThus, the 2 highest ranked items in the price range are (2,1) and (2,0). \nNote that k = 3 but there are only 2 reachable items within the price range.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>m == grid.length</code></li>\n\t<li><code>n == grid[i].length</code></li>\n\t<li><code>1 &lt;= m, n &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= m * n &lt;= 10<sup>5</sup></code></li>\n\t<li><code>0 &lt;= grid[i][j] &lt;= 10<sup>5</sup></code></li>\n\t<li><code>pricing.length == 2</code></li>\n\t<li><code>2 &lt;= low &lt;= high &lt;= 10<sup>5</sup></code></li>\n\t<li><code>start.length == 2</code></li>\n\t<li><code>0 &lt;= row &lt;= m - 1</code></li>\n\t<li><code>0 &lt;= col &lt;= n - 1</code></li>\n\t<li><code>grid[row][col] &gt; 0</code></li>\n\t<li><code>1 &lt;= k &lt;= m * n</code></li>\n</ul>\n",
"translatedTitle": "价格范围内最高排名的 K 样物品",
"translatedContent": "<p>给你一个下标从 <strong>0</strong>&nbsp;开始的二维整数数组&nbsp;<code>grid</code>&nbsp;,它的大小为&nbsp;<code>m x n</code>&nbsp;,表示一个商店中物品的分布图。数组中的整数含义为:</p>\n\n<ul>\n\t<li><code>0</code>&nbsp;表示无法穿越的一堵墙。</li>\n\t<li><code>1</code>&nbsp;表示可以自由通过的一个空格子。</li>\n\t<li>所有其他正整数表示该格子内的一样物品的价格。你可以自由经过这些格子。</li>\n</ul>\n\n<p>从一个格子走到上下左右相邻格子花费&nbsp;<code>1</code>&nbsp;步。</p>\n\n<p>同时给你一个整数数组&nbsp;<code>pricing</code> 和&nbsp;<code>start</code>&nbsp;,其中&nbsp;<code>pricing = [low, high]</code> 且&nbsp;<code>start = [row, col]</code>&nbsp;,表示你开始位置为&nbsp;<code>(row, col)</code>&nbsp;,同时你只对物品价格在<strong>&nbsp;闭区间</strong>&nbsp;<code>[low, high]</code>&nbsp;之内的物品感兴趣。同时给你一个整数&nbsp;<code>k</code>&nbsp;。</p>\n\n<p>你想知道给定范围 <strong>内</strong>&nbsp;且 <strong>排名最高</strong>&nbsp;的 <code>k</code>&nbsp;件物品的 <strong>位置</strong>&nbsp;。排名按照优先级从高到低的以下规则制定:</p>\n\n<ol>\n\t<li>距离:定义为从&nbsp;<code>start</code>&nbsp;到一件物品的最短路径需要的步数(<strong>较近</strong>&nbsp;距离的排名更高)。</li>\n\t<li>价格:<strong>较低</strong>&nbsp;价格的物品有更高优先级,但只考虑在给定范围之内的价格。</li>\n\t<li>行坐标:<strong>较小</strong>&nbsp;行坐标的有更高优先级。</li>\n\t<li>列坐标:<strong>较小</strong>&nbsp;列坐标的有更高优先级。</li>\n</ol>\n\n<p>请你返回给定价格内排名最高的 <code>k</code>&nbsp;件物品的坐标,将它们按照排名排序后返回。如果给定价格内少于 <code>k</code>&nbsp;件物品,那么请将它们的坐标&nbsp;<strong>全部</strong>&nbsp;返回。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/12/16/example1drawio.png\" style=\"width: 200px; height: 151px;\"></p>\n\n<pre><b>输入:</b>grid = [[1,2,0,1],[1,3,0,1],[0,2,5,1]], pricing = [2,5], start = [0,0], k = 3\n<b>输出:</b>[[0,1],[1,1],[2,1]]\n<b>解释:</b>起点为 (0,0) 。\n价格范围为 [2,5] ,我们可以选择的物品坐标为 (0,1)(1,1)(2,1) 和 (2,2) 。\n这些物品的排名为\n- (0,1) 距离为 1\n- (1,1) 距离为 2\n- (2,1) 距离为 3\n- (2,2) 距离为 4\n所以给定价格范围内排名最高的 3 件物品的坐标为 (0,1)(1,1) 和 (2,1) 。\n</pre>\n\n<p><strong>示例 2</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/12/16/example2drawio1.png\" style=\"width: 200px; height: 151px;\"></p>\n\n<pre><b>输入:</b>grid = [[1,2,0,1],[1,3,3,1],[0,2,5,1]], pricing = [2,3], start = [2,3], k = 2\n<b>输出:</b>[[2,1],[1,2]]\n<b>解释:</b>起点为 (2,3) 。\n价格范围为 [2,3] ,我们可以选择的物品坐标为 (0,1)(1,1)(1,2) 和 (2,1) 。\n这些物品的排名为 \n- (2,1) 距离为 2 ,价格为 2\n- (1,2) 距离为 2 ,价格为 3\n- (1,1) 距离为 3\n- (0,1) 距离为 4\n所以给定价格范围内排名最高的 2 件物品的坐标为 (2,1) 和 (1,2) 。\n</pre>\n\n<p><strong>示例 3</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/12/30/example3.png\" style=\"width: 149px; height: 150px;\"></p>\n\n<pre><b>输入:</b>grid = [[1,1,1],[0,0,1],[2,3,4]], pricing = [2,3], start = [0,0], k = 3\n<b>输出:</b>[[2,1],[2,0]]\n<b>解释:</b>起点为 (0,0) 。\n价格范围为 [2,3] ,我们可以选择的物品坐标为 (2,0) 和 (2,1) 。\n这些物品的排名为\n- (2,1) 距离为 5\n- (2,0) 距离为 6\n所以给定价格范围内排名最高的 2 件物品的坐标为 (2,1) 和 (2,0) 。\n注意k = 3 但给定价格范围内只有 2 件物品。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示:</strong></p>\n\n<ul>\n\t<li><code>m == grid.length</code></li>\n\t<li><code>n == grid[i].length</code></li>\n\t<li><code>1 &lt;= m, n &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= m * n &lt;= 10<sup>5</sup></code></li>\n\t<li><code>0 &lt;= grid[i][j] &lt;= 10<sup>5</sup></code></li>\n\t<li><code>pricing.length == 2</code></li>\n\t<li><code>2 &lt;= low &lt;= high &lt;= 10<sup>5</sup></code></li>\n\t<li><code>start.length == 2</code></li>\n\t<li><code>0 &lt;= row &lt;= m - 1</code></li>\n\t<li><code>0 &lt;= col &lt;= n - 1</code></li>\n\t<li><code>grid[row][col] &gt; 0</code></li>\n\t<li><code>1 &lt;= k &lt;= m * n</code></li>\n</ul>\n",
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