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leetcode-problemset/leetcode/originData/minimum-score-by-changing-two-elements.json

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"title": "Minimum Score by Changing Two Elements",
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"content": "<p>You are given a <strong>0-indexed</strong> integer array <code>nums</code>.</p>\n\n<ul>\n\t<li>The <strong>low</strong> score of <code><font face=\"monospace\">nums</font></code> is the minimum value of <code>|nums[i]&nbsp;- nums[j]|</code> over all <code>0 &lt;= i &lt; j &lt; nums.length</code>.</li>\n\t<li>The <strong>high</strong> score of&nbsp;<code><font face=\"monospace\">nums</font></code> is the maximum value of <code>|nums[i]&nbsp;- nums[j]|</code> over all <code>0 &lt;= i &lt; j &lt; nums.length</code>.</li>\n\t<li>The <strong>score</strong> of <code>nums</code> is the sum of the <strong>high</strong> and <strong>low</strong> scores of nums.</li>\n</ul>\n\n<p>To minimize the score of <code>nums</code>, we can change the value of <strong>at most two</strong> elements of <code>nums</code>.</p>\n\n<p>Return <em>the <strong>minimum</strong> possible <strong>score</strong> after changing&nbsp;the value of <strong>at most two</strong> elements o</em>f <code>nums</code>.</p>\n\n<p>Note that <code>|x|</code> denotes the absolute value of <code>x</code>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [1,4,3]\n<strong>Output:</strong> 0\n<strong>Explanation:</strong> Change value of nums[1] and nums[2] to 1 so that nums becomes [1,1,1]. Now, the value of <code>|nums[i] - nums[j]|</code> is always equal to 0, so we return 0 + 0 = 0.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [1,4,7,8,5]\n<strong>Output:</strong> 3\n<strong>Explanation:</strong> Change nums[0] and nums[1] to be 6. Now nums becomes [6,6,7,8,5].\nOur low score is achieved when i = 0 and j = 1, in which case |<code>nums[i] - nums[j]</code>| = |6 - 6| = 0.\nOur high score is achieved when i = 3 and j = 4, in which case |<code>nums[i] - nums[j]</code>| = |8 - 5| = 3.\nThe sum of our high and low score is 3, which we can prove to be minimal.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>3 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 10<sup>9</sup></code></li>\n</ul>\n",
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"Changing the minimum or maximum values will only minimize the score.",
"Think about what all possible pairs of minimum and maximum values can be changed to form the minimum score."
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