Given an array of N elements, the task is to minimize the maximum difference of adjacent elements by inserting at most K elements in the array.
Input: arr = [2, 6, 8] K = 1
After insertion of 4 in between 2 and 6, the array becomes [2, 4, 6, 8]. In this case the maximum difference between any adjacent element is 2, which is the minimum that can be.
Input: arr = [3, 12] K = 2
After insertion of 6 and 9 in between 3 and 12, the array becomes [3, 6, 9, 12]. In this case the maximum difference between any adjacent element is 3, which is the minimum that can be.
Approach: In order to solve this problem, we are using the following Binary Search based approach:
- Find the maximum difference between any two adjacent element in the array and store it in a variable, say worst.
- Search from best(1 initially) to worst and for every mid value find the number of insertions required.
- Whenever the number of insertions is greater than K for a particular value of mid, search between [mid + 1, worst], that is the higher half. Otherwise search between [best, mid-1], that is the lower half to check if the maximum difference can be further minimized with at most K insertions.
- The final worst value after termination of the loop gives the answer.
Below code is the implementation of the above approach:
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