Merge Operations to Reach Minimum Bound (Medium) — Practice with Code Visualizer

You are given an integer array nums and a positive integer k representing a minimum bound threshold.

Your objective is to transform the array such that every element is at least k. To accomplish this, you may perform a special merge operation any number of times. Each merge operation works as follows:

Select the two smallest elements x and y from the current array.
Remove both x and y from the array.
Insert a new element computed as min(x, y) * 2 + max(x, y) back into the array.

Important Notes:

A merge operation can only be performed when the array contains at least two elements.
The new combined element is calculated by taking twice the smaller value plus the larger value.
The position where the new element is inserted does not affect the solution since only element values matter.

Your task is to determine the minimum number of merge operations required so that all elements in the array become greater than or equal to k.

It is guaranteed that an answer always exists—that is, through some sequence of operations, you can always make every element satisfy the bound condition.

Initially, nums = [2,11,10,1,3]. The smallest elements are 1 and 2. • First merge: Remove 1 and 2, insert min(1,2)2 + max(1,2) = 12 + 2 = 4. Array becomes [4,11,10,3]. • Second merge: Remove 3 and 4, insert min(3,4)2 + max(3,4) = 32 + 4 = 10. Array becomes [10,11,10]. All elements are now ≥ 10, so the answer is 2 operations.

We need all elements to reach at least 20. • After 1st merge: [2,4,9,3] (merged 1 and 1 into 3) • After 2nd merge: [7,4,9] (merged 2 and 3 into 7) • After 3rd merge: [15,9] (merged 4 and 7 into 15) • After 4th merge: [33] (merged 9 and 15 into 33) With 33 ≥ 20, the answer is 4 operations.

All elements (10, 20, 30) are already greater than or equal to k = 5. No merge operations are needed.