You are given a 0-indexed integer array nums having length n, and an integer k.
You can perform the following increment operation any number of times (including zero):
\n\ni in the range [0, n - 1], and increase nums[i] by 1.An array is considered beautiful if, for any subarray with a size of 3 or more, its maximum element is greater than or equal to k.
Return an integer denoting the minimum number of increment operations needed to make nums beautiful.
A subarray is a contiguous non-empty sequence of elements within an array.
\n\n\n
Example 1:
\n\n\nInput: nums = [2,3,0,0,2], k = 4\nOutput: 3\nExplanation: We can perform the following increment operations to make nums beautiful:\nChoose index i = 1 and increase nums[1] by 1 -> [2,4,0,0,2].\nChoose index i = 4 and increase nums[4] by 1 -> [2,4,0,0,3].\nChoose index i = 4 and increase nums[4] by 1 -> [2,4,0,0,4].\nThe subarrays with a size of 3 or more are: [2,4,0], [4,0,0], [0,0,4], [2,4,0,0], [4,0,0,4], [2,4,0,0,4].\nIn all the subarrays, the maximum element is equal to k = 4, so nums is now beautiful.\nIt can be shown that nums cannot be made beautiful with fewer than 3 increment operations.\nHence, the answer is 3.\n\n\n
Example 2:
\n\n\nInput: nums = [0,1,3,3], k = 5\nOutput: 2\nExplanation: We can perform the following increment operations to make nums beautiful:\nChoose index i = 2 and increase nums[2] by 1 -> [0,1,4,3].\nChoose index i = 2 and increase nums[2] by 1 -> [0,1,5,3].\nThe subarrays with a size of 3 or more are: [0,1,5], [1,5,3], [0,1,5,3].\nIn all the subarrays, the maximum element is equal to k = 5, so nums is now beautiful.\nIt can be shown that nums cannot be made beautiful with fewer than 2 increment operations.\nHence, the answer is 2.\n\n\n
Example 3:
\n\n\nInput: nums = [1,1,2], k = 1\nOutput: 0\nExplanation: The only subarray with a size of 3 or more in this example is [1,1,2].\nThe maximum element, 2, is already greater than k = 1, so we don't need any increment operation.\nHence, the answer is 0.\n\n\n
\n
Constraints:
\n\n3 <= n == nums.length <= 1050 <= nums[i] <= 1090 <= k <= 109给你一个下标从 0 开始、长度为 n 的整数数组 nums ，和一个整数 k 。
你可以执行下述 递增 运算 任意 次（可以是 0 次）：
\n\n[0, n - 1] 中选择一个下标 i ，并将 nums[i] 的值加 1 。如果数组中任何长度 大于或等于 3 的子数组，其 最大 元素都大于或等于 k ，则认为数组是一个 美丽数组 。
以整数形式返回使数组变为 美丽数组 需要执行的 最小 递增运算数。
\n\n子数组是数组中的一个连续 非空 元素序列。
\n\n\n\n
示例 1：
\n\n\n输入：nums = [2,3,0,0,2], k = 4\n输出：3\n解释：可以执行下述递增运算，使 nums 变为美丽数组：\n选择下标 i = 1 ，并且将 nums[1] 的值加 1 -> [2,4,0,0,2] 。\n选择下标 i = 4 ，并且将 nums[4] 的值加 1 -> [2,4,0,0,3] 。\n选择下标 i = 4 ，并且将 nums[4] 的值加 1 -> [2,4,0,0,4] 。\n长度大于或等于 3 的子数组为 [2,4,0], [4,0,0], [0,0,4], [2,4,0,0], [4,0,0,4], [2,4,0,0,4] 。\n在所有子数组中，最大元素都等于 k = 4 ，所以 nums 现在是美丽数组。\n可以证明无法用少于 3 次递增运算使 nums 变为美丽数组。\n因此，答案为 3 。\n\n\n
示例 2：
\n\n\n输入：nums = [0,1,3,3], k = 5\n输出：2\n解释：可以执行下述递增运算，使 nums 变为美丽数组：\n选择下标 i = 2 ，并且将 nums[2] 的值加 1 -> [0,1,4,3] 。\n选择下标 i = 2 ，并且将 nums[2] 的值加 1 -> [0,1,5,3] 。\n长度大于或等于 3 的子数组为 [0,1,5]、[1,5,3]、[0,1,5,3] 。\n在所有子数组中，最大元素都等于 k = 5 ，所以 nums 现在是美丽数组。\n可以证明无法用少于 2 次递增运算使 nums 变为美丽数组。 \n因此，答案为 2 。\n\n\n
示例 3：
\n\n\n输入：nums = [1,1,2], k = 1\n输出：0\n解释：在这个示例中，只有一个长度大于或等于 3 的子数组 [1,1,2] 。\n其最大元素 2 已经大于 k = 1 ，所以无需执行任何增量运算。\n因此，答案为 0 。\n\n\n
\n\n
提示：
\n\n3 <= n == nums.length <= 1050 <= nums[i] <= 1090 <= k <= 1093 consecutive values in the array that is greater than or equal to k.",
"The problem can be solved using dynamic programming.",
"Let dp[i] be the minimum number of increment operations required to make the subarray consisting of the first i values beautiful, while also having the value at nums[i] >= k.",
"dp[0] = max(0, k - nums[0]), dp[1] = max(0, k - nums[1]), and dp[2] = max(0, k - nums[2]).",
"dp[i] = max(0, k - nums[i]) + min(dp[i - 1], dp[i - 2], dp[i - 3]) for i in the range [3, n - 1].",
"The answer to the problem is min(dp[n - 1], dp[n - 2], dp[n - 3])."
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