You are given a 0-indexed integer array nums of length n.
\n
\nThe numbers from 0 to n - 1 are divided into three groups numbered from 1 to 3, where number i belongs to group nums[i]. Notice that some groups may be empty.
\n
\nYou are allowed to perform this operation any number of times:
x and change its group. More formally, change nums[x] to any number from 1 to 3.A new array res is constructed using the following procedure:
1, 2, and 3 to res in this order.Array nums is called a beautiful array if the constructed array res is sorted in non-decreasing order.
Return the minimum number of operations to make nums a beautiful array.
\n
Example 1:
\n\n\nInput: nums = [2,1,3,2,1]\nOutput: 3\nExplanation: 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\n\n
Example 2:
\n\n\nInput: nums = [1,3,2,1,3,3]\nOutput: 2\nExplanation: 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\n\n
Example 3:
\n\n\nInput: nums = [2,2,2,2,3,3]\nOutput: 0\nExplanation: 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\n\n
\n
Constraints:
\n\n1 <= nums.length <= 1001 <= nums[i] <= 3给你一个下标从 0 开始长度为 n 的整数数组 nums 。
\n
\n从 0 到 n - 1 的数字被分为编号从 1 到 3 的三个组，数字 i 属于组 nums[i] 。注意，有的组可能是 空的 。
\n
\n你可以执行以下操作任意次：
x 并改变它的组。更正式的，你可以将 nums[x] 改为数字 1 到 3 中的任意一个。你将按照以下过程构建一个新的数组 res ：
1 ，2 和 3 中的元素 依次 连接以得到 res 。如果得到的 res 是 非递减顺序的，那么我们称数组 nums 是 美丽数组 。
请你返回将 nums 变为 美丽数组 需要的最少步数。
\n\n
示例 1：
\n\n\n输入：nums = [2,1,3,2,1]\n输出：3\n解释：以下三步操作是最优方案：\n1. 将 nums[0] 变为 1 。\n2. 将 nums[2] 变为 1 。\n3. 将 nums[3] 变为 1 。\n执行以上操作后，将每组中的数字排序，组 1 为 [0,1,2,3,4] ，组 2 和组 3 都为空。所以 res 等于 [0,1,2,3,4] ，它是非递减顺序的。\n三步操作是最少需要的步数。\n\n\n
示例 2：
\n\n\n输入：nums = [1,3,2,1,3,3]\n输出：2\n解释：以下两步操作是最优方案：\n1. 将 nums[1] 变为 1 。\n2. 将 nums[2] 变为 1 。\n执行以上操作后，将每组中的数字排序，组 1 为 [0,1,2,3] ，组 2 为空，组 3 为 [4,5] 。所以 res 等于 [0,1,2,3,4,5] ，它是非递减顺序的。\n两步操作是最少需要的步数。\n\n\n
示例 3：
\n\n\n输入：nums = [2,2,2,2,3,3]\n输出：0\n解释：不需要执行任何操作。\n组 1 为空，组 2 为 [0,1,2,3] ，组 3 为 [4,5] 。所以 res 等于 [0,1,2,3,4,5] ，它是非递减顺序的。\n\n\n
\n\n
提示：
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collections<\\/a>\\u3002\\u5982\\u679c\\u60a8\\u9700\\u8981\\u4f7f\\u7528\\u5176\\u4ed6\\u5e93\\u51fd\\u6570\\uff0c\\u8bf7\\u81ea\\u884c\\u5bfc\\u5165\\u3002<\\/p>\\r\\n\\r\\n \\u6ce8\\u610f Python 2.7 \\u5c06\\u57282020\\u5e74\\u540e\\u4e0d\\u518d\\u7ef4\\u62a4<\\/a>\\u3002 \\u5982\\u60f3\\u4f7f\\u7528\\u6700\\u65b0\\u7248\\u7684Python\\uff0c\\u8bf7\\u9009\\u62e9Python 3\\u3002<\\/p>\"],\"c\":[\"C\",\" \\u7248\\u672c\\uff1a \\u7f16\\u8bd1\\u65f6\\uff0c\\u5c06\\u4f1a\\u91c7\\u7528 \\u4e3a\\u4e86\\u4f7f\\u7528\\u65b9\\u4fbf\\uff0c\\u5927\\u90e8\\u5206\\u6807\\u51c6\\u5e93\\u7684\\u5934\\u6587\\u4ef6\\u5df2\\u7ecf\\u88ab\\u81ea\\u52a8\\u5bfc\\u5165\\u3002<\\/p>\\r\\n\\r\\n \\u5982\\u60f3\\u4f7f\\u7528\\u54c8\\u5e0c\\u8868\\u8fd0\\u7b97, \\u60a8\\u53ef\\u4ee5\\u4f7f\\u7528 uthash<\\/a>\\u3002 \\\"uthash.h\\\"\\u5df2\\u7ecf\\u9ed8\\u8ba4\\u88ab\\u5bfc\\u5165\\u3002\\u8bf7\\u770b\\u5982\\u4e0b\\u793a\\u4f8b:<\\/p>\\r\\n\\r\\n 1. 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\\u6a21\\u5757\\u4e2d\\u63d0\\u4f9b\\uff1ahttps:\\/\\/www.rubydoc.info\\/github\\/kanwei\\/algorithms\\/Algorithms<\\/p>\"],\"swift\":[\"Swift\",\" \\u7248\\u672c\\uff1a \\u6211\\u4eec\\u901a\\u5e38\\u4fdd\\u8bc1\\u66f4\\u65b0\\u5230 Apple\\u653e\\u51fa\\u7684\\u6700\\u65b0\\u7248Swift<\\/a>\\u3002\\u5982\\u679c\\u60a8\\u53d1\\u73b0Swift\\u4e0d\\u662f\\u6700\\u65b0\\u7248\\u7684\\uff0c\\u8bf7\\u8054\\u7cfb\\u6211\\u4eec\\uff01\\u6211\\u4eec\\u5c06\\u5c3d\\u5feb\\u66f4\\u65b0\\u3002<\\/p>\"],\"golang\":[\"Go\",\" \\u7248\\u672c\\uff1a \\u652f\\u6301 https:\\/\\/godoc.org\\/github.com\\/emirpasic\\/gods@v1.18.1<\\/a> \\u7b2c\\u4e09\\u65b9\\u5e93\\u3002<\\/p>\"],\"python3\":[\"Python3\",\" \\u7248\\u672c\\uff1a \\u4e3a\\u4e86\\u65b9\\u4fbf\\u8d77\\u89c1\\uff0c\\u5927\\u90e8\\u5206\\u5e38\\u7528\\u5e93\\u5df2\\u7ecf\\u88ab\\u81ea\\u52a8 \\u5bfc\\u5165\\uff0c\\u5982array<\\/a>, bisect<\\/a>, collections<\\/a>\\u3002 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