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": "Count Number of Rectangles Containing Each Point",
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"content": "<p>You are given a 2D integer array <code>rectangles</code> where <code>rectangles[i] = [l<sub>i</sub>, h<sub>i</sub>]</code> indicates that <code>i<sup>th</sup></code> rectangle has a length of <code>l<sub>i</sub></code> and a height of <code>h<sub>i</sub></code>. You are also given a 2D integer array <code>points</code> where <code>points[j] = [x<sub>j</sub>, y<sub>j</sub>]</code> is a point with coordinates <code>(x<sub>j</sub>, y<sub>j</sub>)</code>.</p>\n\n<p>The <code>i<sup>th</sup></code> rectangle has its <strong>bottom-left corner</strong> point at the coordinates <code>(0, 0)</code> and its <strong>top-right corner</strong> point at <code>(l<sub>i</sub>, h<sub>i</sub>)</code>.</p>\n\n<p>Return<em> an integer array </em><code>count</code><em> of length </em><code>points.length</code><em> where </em><code>count[j]</code><em> is the number of rectangles that <strong>contain</strong> the </em><code>j<sup>th</sup></code><em> point.</em></p>\n\n<p>The <code>i<sup>th</sup></code> rectangle <strong>contains</strong> the <code>j<sup>th</sup></code> point if <code>0 <= x<sub>j</sub> <= l<sub>i</sub></code> and <code>0 <= y<sub>j</sub> <= h<sub>i</sub></code>. Note that points that lie on the <strong>edges</strong> of a rectangle are also considered to be contained by that rectangle.</p>\n\n<p> </p>\n<p><strong class=\"example\">Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/03/02/example1.png\" style=\"width: 300px; height: 509px;\" />\n<pre>\n<strong>Input:</strong> rectangles = [[1,2],[2,3],[2,5]], points = [[2,1],[1,4]]\n<strong>Output:</strong> [2,1]\n<strong>Explanation:</strong> \nThe first rectangle contains no points.\nThe second rectangle contains only the point (2, 1).\nThe third rectangle contains the points (2, 1) and (1, 4).\nThe number of rectangles that contain the point (2, 1) is 2.\nThe number of rectangles that contain the point (1, 4) is 1.\nTherefore, we return [2, 1].\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/03/02/example2.png\" style=\"width: 300px; height: 312px;\" />\n<pre>\n<strong>Input:</strong> rectangles = [[1,1],[2,2],[3,3]], points = [[1,3],[1,1]]\n<strong>Output:</strong> [1,3]\n<strong>Explanation:\n</strong>The first rectangle contains only the point (1, 1).\nThe second rectangle contains only the point (1, 1).\nThe third rectangle contains the points (1, 3) and (1, 1).\nThe number of rectangles that contain the point (1, 3) is 1.\nThe number of rectangles that contain the point (1, 1) is 3.\nTherefore, we return [1, 3].\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 <= rectangles.length, points.length <= 5 * 10<sup>4</sup></code></li>\n\t<li><code>rectangles[i].length == points[j].length == 2</code></li>\n\t<li><code>1 <= l<sub>i</sub>, x<sub>j</sub> <= 10<sup>9</sup></code></li>\n\t<li><code>1 <= h<sub>i</sub>, y<sub>j</sub> <= 100</code></li>\n\t<li>All the <code>rectangles</code> are <strong>unique</strong>.</li>\n\t<li>All the <code>points</code> are <strong>unique</strong>.</li>\n</ul>\n",
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"code": "class Solution {\n\n /**\n * @param Integer[][] $rectangles\n * @param Integer[][] $points\n * @return Integer[]\n */\n function countRectangles($rectangles, $points) {\n \n }\n}",
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"code": "# @param {Integer[][]} rectangles\n# @param {Integer[][]} points\n# @return {Integer[]}\ndef count_rectangles(rectangles, points)\n \nend",
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"The heights of the rectangles and the y-coordinates of the points are only at most 100, so for each point, we can iterate over the possible heights of the rectangles that contain a given point.",
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"For a given point and height, can we efficiently count how many rectangles with that height contain our point?",
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"Sort the rectangles at each height and use binary search."
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