2919 - Minimum Increment Operations to Make Array Beautiful\.

Medium

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 ):

• Choose an index i 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.

Example 1:

Input: nums = 2,3,0,0,2, k = 4

Output: 3

Explanation: We can perform the following increment operations to make nums beautiful:

Choose index i = 1 and increase nums1 by 1 ->2,4,0,0,2.

Choose index i = 4 and increase nums4 by 1 ->2,4,0,0,3.

Choose index i = 4 and increase nums4 by 1 ->2,4,0,0,4.

The 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.

In all the subarrays, the maximum element is equal to k = 4, so nums is now beautiful.

It can be shown that nums cannot be made beautiful with fewer than 3 increment operations.

Hence, the answer is 3.

Example 2:

Input: nums = 0,1,3,3, k = 5

Output: 2

Explanation: We can perform the following increment operations to make nums beautiful:

Choose index i = 2 and increase nums2 by 1 ->0,1,4,3.

Choose index i = 2 and increase nums2 by 1 ->0,1,5,3.

The subarrays with a size of 3 or more are: 0,1,5, 1,5,3, 0,1,5,3.

In all the subarrays, the maximum element is equal to k = 5, so nums is now beautiful.

It can be shown that nums cannot be made beautiful with fewer than 2 increment operations.

Hence, the answer is 2.

Example 3:

Input: nums = 1,1,2, k = 1

Output: 0

Explanation: The only subarray with a size of 3 or more in this example is 1,1,2. The maximum element, 2, is already greater than k = 1, so we don't need any increment operation. Hence, the answer is 0.

Constraints:

• <code>3 <= n == nums.length <= 10⁵</code>

• <code>0 <= numsi<= 10⁹</code>

• <code>0 <= k <= 10⁹</code>