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"question": {
"questionId": "3344",
"questionFrontendId": "3102",
"categoryTitle": "Algorithms",
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"title": "Minimize Manhattan Distances",
"titleSlug": "minimize-manhattan-distances",
"content": "<p>You are given a array <code>points</code> representing integer coordinates of some points on a 2D plane, where <code>points[i] = [x<sub>i</sub>, y<sub>i</sub>]</code>.</p>\n\n<p>The distance between two points is defined as their <span data-keyword=\"manhattan-distance\">Manhattan distance</span>.</p>\n\n<p>Return <em>the <strong>minimum</strong> possible value for <strong>maximum</strong> distance between any two points by removing exactly one point</em>.</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\">points = [[3,10],[5,15],[10,2],[4,4]]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">12</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>The maximum distance after removing each point is the following:</p>\n\n<ul>\n\t<li>After removing the 0<sup>th</sup> point the maximum distance is between points (5, 15) and (10, 2), which is <code>|5 - 10| + |15 - 2| = 18</code>.</li>\n\t<li>After removing the 1<sup>st</sup> point the maximum distance is between points (3, 10) and (10, 2), which is <code>|3 - 10| + |10 - 2| = 15</code>.</li>\n\t<li>After removing the 2<sup>nd</sup> point the maximum distance is between points (5, 15) and (4, 4), which is <code>|5 - 4| + |15 - 4| = 12</code>.</li>\n\t<li>After removing the 3<sup>rd</sup> point the maximum distance is between points (5, 15) and (10, 2), which is <code>|5 - 10| + |15 - 2| = 18</code>.</li>\n</ul>\n\n<p>12 is the minimum possible maximum distance between any two points after removing exactly one point.</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\">points = [[1,1],[1,1],[1,1]]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">0</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>Removing any of the points results in the maximum distance between any two points of 0.</p>\n</div>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>3 &lt;= points.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>points[i].length == 2</code></li>\n\t<li><code>1 &lt;= points[i][0], points[i][1] &lt;= 10<sup>8</sup></code></li>\n</ul>\n",
"translatedTitle": "最小化曼哈顿距离",
"translatedContent": "<p>给你一个下标从 <strong>0</strong> 开始的数组 <code>points</code> ,它表示二维平面上一些点的整数坐标,其中 <code>points[i] = [x<sub>i</sub>, y<sub>i</sub>]</code> 。</p>\n\n<p>两点之间的距离定义为它们的<span data-keyword=\"manhattan-distance\">曼哈顿距离</span>。</p>\n\n<p>请你恰好移除一个点,返回移除后任意两点之间的 <strong>最大 </strong>距离可能的 <strong>最小 </strong>值。</p>\n\n<p>&nbsp;</p>\n\n<p><strong class=\"example\">示例 1</strong></p>\n\n<pre>\n<strong>输入:</strong>points = [[3,10],[5,15],[10,2],[4,4]]\n<strong>输出:</strong>12\n<strong>解释:</strong>移除每个点后的最大距离如下所示:\n- 移除第 0 个点后,最大距离在点 (5, 15) 和 (10, 2) 之间,为 |5 - 10| + |15 - 2| = 18 。\n- 移除第 1 个点后,最大距离在点 (3, 10) 和 (10, 2) 之间,为 |3 - 10| + |10 - 2| = 15 。\n- 移除第 2 个点后,最大距离在点 (5, 15) 和 (4, 4) 之间,为 |5 - 4| + |15 - 4| = 12 。\n- 移除第 3 个点后,最大距离在点 (5, 15) 和 (10, 2) 之间的,为 |5 - 10| + |15 - 2| = 18 。\n在恰好移除一个点后任意两点之间的最大距离可能的最小值是 12 。\n</pre>\n\n<p><strong class=\"example\">示例 2</strong></p>\n\n<pre>\n<strong>输入:</strong>points = [[1,1],[1,1],[1,1]]\n<strong>输出:</strong>0\n<strong>解释:</strong>移除任一点后,任意两点之间的最大距离都是 0 。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示:</strong></p>\n\n<ul>\n\t<li><code>3 &lt;= points.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>points[i].length == 2</code></li>\n\t<li><code>1 &lt;= points[i][0], points[i][1] &lt;= 10<sup>8</sup></code></li>\n</ul>\n",
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"Notice that the Manhattan distance between two points <code>[x<sub>i</sub>, y<sub>i</sub>]</code> and <code>[x<sub>j</sub>, y<sub>j</sub>] is <code> max({x<sub>i</sub> - x<sub>j</sub> + y<sub>i</sub> - y<sub>j</sub>, x<sub>i</sub> - x<sub>j</sub> - y<sub>i</sub> + y<sub>j</sub>, - x<sub>i</sub> + x<sub>j</sub> + y<sub>i</sub> - y<sub>j</sub>, - x<sub>i</sub> + x<sub>j</sub> - y<sub>i</sub> + y<sub>j</sub>})</code></code>.",
"If you replace points as <code>[x<sub>i</sub> - y<sub>i</sub>, x<sub>i</sub> + y<sub>i</sub>]</code> then the Manhattan distance is <code>max(max(x<sub>i</sub>) - min(x<sub>i</sub>), max(y<sub>i</sub>) - min(y<sub>i</sub>))</code> over all <code>i</code>.",
"After those observations, the problem just becomes a simulation. Create multiset of points <code>[x<sub>i</sub> - y<sub>i</sub>, x<sub>i</sub> + y<sub>i</sub>]</code>, you can iterate on a point you might remove and get the maximum Manhattan distance over all other points."
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