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"boundTopicId": 722683,
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"title": "Queries on Number of Points Inside a Circle",
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"titleSlug": "queries-on-number-of-points-inside-a-circle",
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"content": "<p>You are given an array <code>points</code> where <code>points[i] = [x<sub>i</sub>, y<sub>i</sub>]</code> is the coordinates of the <code>i<sup>th</sup></code> point on a 2D plane. Multiple points can have the <strong>same</strong> coordinates.</p>\n\n<p>You are also given an array <code>queries</code> where <code>queries[j] = [x<sub>j</sub>, y<sub>j</sub>, r<sub>j</sub>]</code> describes a circle centered at <code>(x<sub>j</sub>, y<sub>j</sub>)</code> with a radius of <code>r<sub>j</sub></code>.</p>\n\n<p>For each query <code>queries[j]</code>, compute the number of points <strong>inside</strong> the <code>j<sup>th</sup></code> circle. Points <strong>on the border</strong> of the circle are considered <strong>inside</strong>.</p>\n\n<p>Return <em>an array </em><code>answer</code><em>, where </em><code>answer[j]</code><em> is the answer to the </em><code>j<sup>th</sup></code><em> query</em>.</p>\n\n<p> </p>\n<p><strong class=\"example\">Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/03/25/chrome_2021-03-25_22-34-16.png\" style=\"width: 500px; height: 418px;\" />\n<pre>\n<strong>Input:</strong> points = [[1,3],[3,3],[5,3],[2,2]], queries = [[2,3,1],[4,3,1],[1,1,2]]\n<strong>Output:</strong> [3,2,2]\n<b>Explanation: </b>The points and circles are shown above.\nqueries[0] is the green circle, queries[1] is the red circle, and queries[2] is the blue circle.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/03/25/chrome_2021-03-25_22-42-07.png\" style=\"width: 500px; height: 390px;\" />\n<pre>\n<strong>Input:</strong> points = [[1,1],[2,2],[3,3],[4,4],[5,5]], queries = [[1,2,2],[2,2,2],[4,3,2],[4,3,3]]\n<strong>Output:</strong> [2,3,2,4]\n<b>Explanation: </b>The points and circles are shown above.\nqueries[0] is green, queries[1] is red, queries[2] is blue, and queries[3] is purple.\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 <= points.length <= 500</code></li>\n\t<li><code>points[i].length == 2</code></li>\n\t<li><code>0 <= x<sub>i</sub>, y<sub>i</sub> <= 500</code></li>\n\t<li><code>1 <= queries.length <= 500</code></li>\n\t<li><code>queries[j].length == 3</code></li>\n\t<li><code>0 <= x<sub>j</sub>, y<sub>j</sub> <= 500</code></li>\n\t<li><code>1 <= r<sub>j</sub> <= 500</code></li>\n\t<li>All coordinates are integers.</li>\n</ul>\n\n<p> </p>\n<p><strong>Follow up:</strong> Could you find the answer for each query in better complexity than <code>O(n)</code>?</p>\n",
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"content": "<p>You are given an array <code>points</code> where <code>points[i] = [x<sub>i</sub>, y<sub>i</sub>]</code> is the coordinates of the <code>i<sup>th</sup></code> point on a 2D plane. Multiple points can have the <strong>same</strong> coordinates.</p>\n\n<p>You are also given an array <code>queries</code> where <code>queries[j] = [x<sub>j</sub>, y<sub>j</sub>, r<sub>j</sub>]</code> describes a circle centered at <code>(x<sub>j</sub>, y<sub>j</sub>)</code> with a radius of <code>r<sub>j</sub></code>.</p>\n\n<p>For each query <code>queries[j]</code>, compute the number of points <strong>inside</strong> the <code>j<sup>th</sup></code> circle. Points <strong>on the border</strong> of the circle are considered <strong>inside</strong>.</p>\n\n<p>Return <em>an array </em><code>answer</code><em>, where </em><code>answer[j]</code><em> is the answer to the </em><code>j<sup>th</sup></code><em> query</em>.</p>\n\n<p> </p>\n<p><strong class=\"example\">Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/03/25/chrome_2021-03-25_22-34-16.png\" style=\"width: 500px; height: 418px;\" />\n<pre>\n<strong>Input:</strong> points = [[1,3],[3,3],[5,3],[2,2]], queries = [[2,3,1],[4,3,1],[1,1,2]]\n<strong>Output:</strong> [3,2,2]\n<b>Explanation: </b>The points and circles are shown above.\nqueries[0] is the green circle, queries[1] is the red circle, and queries[2] is the blue circle.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/03/25/chrome_2021-03-25_22-42-07.png\" style=\"width: 500px; height: 390px;\" />\n<pre>\n<strong>Input:</strong> points = [[1,1],[2,2],[3,3],[4,4],[5,5]], queries = [[1,2,2],[2,2,2],[4,3,2],[4,3,3]]\n<strong>Output:</strong> [2,3,2,4]\n<b>Explanation: </b>The points and circles are shown above.\nqueries[0] is green, queries[1] is red, queries[2] is blue, and queries[3] is purple.\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 <= points.length <= 500</code></li>\n\t<li><code>points[i].length == 2</code></li>\n\t<li><code>0 <= x<sub>i</sub>, y<sub>i</sub> <= 500</code></li>\n\t<li><code>1 <= queries.length <= 500</code></li>\n\t<li><code>queries[j].length == 3</code></li>\n\t<li><code>0 <= x<sub>j</sub>, y<sub>j</sub> <= 500</code></li>\n\t<li><code>1 <= r<sub>j</sub> <= 500</code></li>\n\t<li>All coordinates are integers.</li>\n</ul>\n\n<p> </p>\n<p><strong>Follow up:</strong> Could you find the answer for each query in better complexity than <code>O(n)</code>?</p>\n",
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"translatedTitle": "统计一个圆中点的数目",
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"translatedContent": "<p>给你一个数组 <code>points</code> ，其中 <code>points[i] = [x<sub>i</sub>, y<sub>i</sub>]</code> ，表示第 <code>i</code> 个点在二维平面上的坐标。多个点可能会有 <strong>相同</strong> 的坐标。</p>\n\n<p>同时给你一个数组 <code>queries</code> ，其中 <code>queries[j] = [x<sub>j</sub>, y<sub>j</sub>, r<sub>j</sub>]</code> ，表示一个圆心在 <code>(x<sub>j</sub>, y<sub>j</sub>)</code> 且半径为 <code>r<sub>j</sub></code><sub> </sub>的圆。</p>\n\n<p>对于每一个查询 <code>queries[j]</code> ，计算在第 <code>j</code> 个圆 <strong>内</strong> 点的数目。如果一个点在圆的 <strong>边界上</strong> ，我们同样认为它在圆 <strong>内</strong> 。</p>\n\n<p>请你返回一个数组<em> </em><code>answer</code> ，其中<em> </em><code>answer[j]</code>是第 <code>j</code> 个查询的答案。</p>\n\n<p> </p>\n\n<p><strong>示例 1：</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/03/25/chrome_2021-03-25_22-34-16.png\" style=\"width: 500px; height: 418px;\">\n<pre><b>输入：</b>points = [[1,3],[3,3],[5,3],[2,2]], queries = [[2,3,1],[4,3,1],[1,1,2]]\n<b>输出：</b>[3,2,2]\n<b>解释：</b>所有的点和圆如上图所示。\nqueries[0] 是绿色的圆，queries[1] 是红色的圆，queries[2] 是蓝色的圆。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/03/25/chrome_2021-03-25_22-42-07.png\" style=\"width: 500px; height: 390px;\">\n<pre><b>输入：</b>points = [[1,1],[2,2],[3,3],[4,4],[5,5]], queries = [[1,2,2],[2,2,2],[4,3,2],[4,3,3]]\n<b>输出：</b>[2,3,2,4]\n<b>解释：</b>所有的点和圆如上图所示。\nqueries[0] 是绿色的圆，queries[1] 是红色的圆，queries[2] 是蓝色的圆，queries[3] 是紫色的圆。\n</pre>\n\n<p> </p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 <= points.length <= 500</code></li>\n\t<li><code>points[i].length == 2</code></li>\n\t<li><code>0 <= x<sub>i</sub>, y<sub>i</sub> <= 500</code></li>\n\t<li><code>1 <= queries.length <= 500</code></li>\n\t<li><code>queries[j].length == 3</code></li>\n\t<li><code>0 <= x<sub>j</sub>, y<sub>j</sub> <= 500</code></li>\n\t<li><code>1 <= r<sub>j</sub> <= 500</code></li>\n\t<li>所有的坐标都是整数。</li>\n</ul>\n",
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"translatedContent": "<p>给你一个数组 <code>points</code> ，其中 <code>points[i] = [x<sub>i</sub>, y<sub>i</sub>]</code> ，表示第 <code>i</code> 个点在二维平面上的坐标。多个点可能会有 <strong>相同</strong> 的坐标。</p>\n\n<p>同时给你一个数组 <code>queries</code> ，其中 <code>queries[j] = [x<sub>j</sub>, y<sub>j</sub>, r<sub>j</sub>]</code> ，表示一个圆心在 <code>(x<sub>j</sub>, y<sub>j</sub>)</code> 且半径为 <code>r<sub>j</sub></code><sub> </sub>的圆。</p>\n\n<p>对于每一个查询 <code>queries[j]</code> ，计算在第 <code>j</code> 个圆 <strong>内</strong> 点的数目。如果一个点在圆的 <strong>边界上</strong> ，我们同样认为它在圆 <strong>内</strong> 。</p>\n\n<p>请你返回一个数组<em> </em><code>answer</code> ，其中<em> </em><code>answer[j]</code>是第 <code>j</code> 个查询的答案。</p>\n\n<p> </p>\n\n<p><strong>示例 1：</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/03/25/chrome_2021-03-25_22-34-16.png\" style=\"width: 500px; height: 418px;\">\n<pre><b>输入：</b>points = [[1,3],[3,3],[5,3],[2,2]], queries = [[2,3,1],[4,3,1],[1,1,2]]\n<b>输出：</b>[3,2,2]\n<b>解释：</b>所有的点和圆如上图所示。\nqueries[0] 是绿色的圆，queries[1] 是红色的圆，queries[2] 是蓝色的圆。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/03/25/chrome_2021-03-25_22-42-07.png\" style=\"width: 500px; height: 390px;\">\n<pre><b>输入：</b>points = [[1,1],[2,2],[3,3],[4,4],[5,5]], queries = [[1,2,2],[2,2,2],[4,3,2],[4,3,3]]\n<b>输出：</b>[2,3,2,4]\n<b>解释：</b>所有的点和圆如上图所示。\nqueries[0] 是绿色的圆，queries[1] 是红色的圆，queries[2] 是蓝色的圆，queries[3] 是紫色的圆。\n</pre>\n\n<p> </p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 <= points.length <= 500</code></li>\n\t<li><code>points[i].length == 2</code></li>\n\t<li><code>0 <= x<sub>i</sub>, y<sub>i</sub> <= 500</code></li>\n\t<li><code>1 <= queries.length <= 500</code></li>\n\t<li><code>queries[j].length == 3</code></li>\n\t<li><code>0 <= x<sub>j</sub>, y<sub>j</sub> <= 500</code></li>\n\t<li><code>1 <= r<sub>j</sub> <= 500</code></li>\n\t<li>所有的坐标都是整数。</li>\n</ul>\n",
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"isPaidOnly": false,
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"difficulty": "Medium",
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"likes": 79,
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