leetcode-problemset/leetcode-cn/originData/count-pairs-of-points-with-distance-k.json

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        "question": {
            "questionId": "2953",
            "questionFrontendId": "2857",
            "categoryTitle": "Algorithms",
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            "title": "Count Pairs of Points With Distance k",
            "titleSlug": "count-pairs-of-points-with-distance-k",
            "content": "<p>You are given a <strong>2D</strong> integer array <code>coordinates</code> and an integer <code>k</code>, where <code>coordinates[i] = [x<sub>i</sub>, y<sub>i</sub>]</code> are the coordinates of the <code>i<sup>th</sup></code> point in a 2D plane.</p>\n\n<p>We define the <strong>distance</strong> between two points <code>(x<sub>1</sub>, y<sub>1</sub>)</code> and <code>(x<sub>2</sub>, y<sub>2</sub>)</code> as <code>(x1 XOR x2) + (y1 XOR y2)</code> where <code>XOR</code> is the bitwise <code>XOR</code> operation.</p>\n\n<p>Return <em>the number of pairs </em><code>(i, j)</code><em> such that </em><code>i &lt; j</code><em> and the distance between points </em><code>i</code><em> and </em><code>j</code><em> is equal to </em><code>k</code>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> coordinates = [[1,2],[4,2],[1,3],[5,2]], k = 5\n<strong>Output:</strong> 2\n<strong>Explanation:</strong> We can choose the following pairs:\n- (0,1): Because we have (1 XOR 4) + (2 XOR 2) = 5.\n- (2,3): Because we have (1 XOR 5) + (3 XOR 2) = 5.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> coordinates = [[1,3],[1,3],[1,3],[1,3],[1,3]], k = 0\n<strong>Output:</strong> 10\n<strong>Explanation:</strong> Any two chosen pairs will have a distance of 0. There are 10 ways to choose two pairs.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>2 &lt;= coordinates.length &lt;= 50000</code></li>\n\t<li><code>0 &lt;= x<sub>i</sub>, y<sub>i</sub> &lt;= 10<sup>6</sup></code></li>\n\t<li><code>0 &lt;= k &lt;= 100</code></li>\n</ul>\n",
            "translatedTitle": "统计距离为 k 的点对",
            "translatedContent": "<p>给你一个 <strong>二维</strong>&nbsp;整数数组&nbsp;<code>coordinates</code>&nbsp;和一个整数&nbsp;<code>k</code>&nbsp;，其中&nbsp;<code>coordinates[i] = [x<sub>i</sub>, y<sub>i</sub>]</code>&nbsp;是第 <code>i</code>&nbsp;个点在二维平面里的坐标。</p>\n\n<p>我们定义两个点&nbsp;<code>(x<sub>1</sub>, y<sub>1</sub>)</code>&nbsp;和&nbsp;<code>(x<sub>2</sub>, y<sub>2</sub>)</code>&nbsp;的 <strong>距离</strong>&nbsp;为&nbsp;<code>(x1 XOR x2) + (y1 XOR y2)</code> ，<code>XOR</code>&nbsp;指的是按位异或运算。</p>\n\n<p>请你返回满足<em>&nbsp;</em><code>i &lt; j</code><em>&nbsp;</em>且点<em>&nbsp;</em><code>i</code><em> </em>和点<em>&nbsp;</em><code>j</code>之间距离为<em>&nbsp;</em><code>k</code>&nbsp;的点对数目。</p>\n\n<p>&nbsp;</p>\n\n<p><strong class=\"example\">示例 1：</strong></p>\n\n<pre>\n<b>输入：</b>coordinates = [[1,2],[4,2],[1,3],[5,2]], k = 5\n<b>输出：</b>2\n<b>解释：</b>以下点对距离为 k ：\n- (0, 1)：(1 XOR 4) + (2 XOR 2) = 5 。\n- (2, 3)：(1 XOR 5) + (3 XOR 2) = 5 。\n</pre>\n\n<p><strong class=\"example\">示例 2：</strong></p>\n\n<pre>\n<b>输入：</b>coordinates = [[1,3],[1,3],[1,3],[1,3],[1,3]], k = 0\n<b>输出：</b>10\n<b>解释：</b>任何两个点之间的距离都为 0 ，所以总共有 10 组点对。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>2 &lt;= coordinates.length &lt;= 50000</code></li>\n\t<li><code>0 &lt;= x<sub>i</sub>, y<sub>i</sub> &lt;= 10<sup>6</sup></code></li>\n\t<li><code>0 &lt;= k &lt;= 100</code></li>\n</ul>\n",
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            "hints": [
                "<div class=\"_1l1MA\">Suppose that <code>x = x<sub>1</sub> XOR x<sub>2</sub></code> and y = y<sub>1</sub> XOR y<sub>2</sub> then we can get <code>x<sub>2</sub> = x XOR x<sub>1</sub></code> and <code>y<sub>2</sub> = y XOR y<sub>1</sub></code>.</div>",
                "<div class=\"_1l1MA\">We are supposed to have k = x + y so we can get <code>x<sub>2</sub> = x XOR x<sub>1</sub></code> and <code>y<sub>2</sub> = (k - x) XOR y<sub>1</sub></code>.</div>",
                "<div class=\"_1l1MA\">We can iterate over all possible values of <code>x</code> and count the number of points <code>(x<sub>1</sub>, x<sub>2</sub>)</code> and <code>(x<sub>2</sub>, y<sub>2</sub>)</code>.</div>"
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