mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
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175 lines
18 KiB
JSON
175 lines
18 KiB
JSON
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"title": "Sorting Three Groups",
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"content": "<p>You are given a <strong>0-indexed</strong> integer array <code>nums</code> of length <code>n</code>.<br />\n<br />\nThe numbers from <code>0</code> to <code>n - 1</code> are divided into three groups numbered from <code>1</code> to <code>3</code>, where number <code>i</code> belongs to group <code>nums[i]</code>. Notice that some groups may be <strong>empty</strong>.<br />\n<br />\nYou are allowed to perform this operation any number of times:</p>\n\n<ul>\n\t<li>Pick number <code>x</code> and change its group. More formally, change <code>nums[x]</code> to any number from <code>1</code> to <code>3</code>.</li>\n</ul>\n\n<p>A new array <code>res</code> is constructed using the following procedure:</p>\n\n<ol>\n\t<li>Sort the numbers in each group independently.</li>\n\t<li>Append the elements of groups <code>1</code>, <code>2</code>, and <code>3</code> to <code>res</code> <strong>in this order</strong>.</li>\n</ol>\n\n<p>Array <code>nums</code> is called a <strong>beautiful array</strong> if the constructed array <code>res</code> is sorted in <strong>non-decreasing</strong> order.</p>\n\n<p>Return <em>the <strong>minimum</strong> number of operations to make </em><code>nums</code><em> a <strong>beautiful array</strong></em>.</p>\n\n<p> </p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [2,1,3,2,1]\n<strong>Output:</strong> 3\n<strong>Explanation:</strong> It's optimal to perform three operations:\n1. change nums[0] to 1.\n2. change nums[2] to 1.\n3. change nums[3] to 1.\nAfter performing the operations and sorting the numbers in each group, group 1 becomes equal to [0,1,2,3,4] and group 2 and group 3 become empty. Hence, res is equal to [0,1,2,3,4] which is sorted in non-decreasing order.\nIt can be proven that there is no valid sequence of less than three operations.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [1,3,2,1,3,3]\n<strong>Output:</strong> 2\n<strong>Explanation:</strong> It's optimal to perform two operations:\n1. change nums[1] to 1.\n2. change nums[2] to 1.\nAfter performing the operations and sorting the numbers in each group, group 1 becomes equal to [0,1,2,3], group 2 becomes empty, and group 3 becomes equal to [4,5]. Hence, res is equal to [0,1,2,3,4,5] which is sorted in non-decreasing order.\nIt can be proven that there is no valid sequence of less than two operations.\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [2,2,2,2,3,3]\n<strong>Output:</strong> 0\n<strong>Explanation:</strong> It's optimal to not perform operations.\nAfter sorting the numbers in each group, group 1 becomes empty, group 2 becomes equal to [0,1,2,3] and group 3 becomes equal to [4,5]. Hence, res is equal to [0,1,2,3,4,5] which is sorted in non-decreasing order.\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 <= nums.length <= 100</code></li>\n\t<li><code>1 <= nums[i] <= 3</code></li>\n</ul>\n",
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"The problem asks to change the array nums to make it sorted (i.e., all the 1s are on the left of 2s, and all the 2s are on the left of 3s.).",
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"We can try all the possibilities to make nums indices range in [0, i) to 0 and [i, j) to 1 and [j, n) to 2. Note the ranges are left-close and right-open; each might be empty. Namely, 0 <= i <= j <= n.",
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"Count the changes we need for each possibility by comparing the expected and original values at each index position."
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