You are given an integer array nums.
In one operation, you may choose any element nums[i] and perform one of the following:
nums[i] by an integer k, where k >= 2.nums[i] by an integer k, where 2 <= k < nums[i], provided that nums[i] is divisible by k.Return the minimum number of operations required to make all elements of nums equal.
Example 1:
Input: nums = [6,12,8]
Output: 3
Explanation:
We can perform following operates to make all numbers to 6:
nums[1] = 12 by 2 to get 6.nums[2] = 8 by 4 to get 2.nums[2] = 2 by 3 to get 6.Example 2:
Input: nums = [5,15,20]
Output: 2
Explanation:
We can perform following operates to make all numbers to 5:
nums[1] = 15 by 3 to get 5.nums[2] = 20 by 4 to get 5.Example 3:
Input: nums = [7,7,7]
Output: 0
Explanation:
All elements are already equal, so no operations are needed.
Constraints:
1 <= nums.length <= 1051 <= nums[i] <= 109Problem Overview: You need to make two arrays equal using the minimum number of operations where each operation can increment or decrement an element by 1, but only on elements at the same index.
Approach 1: Brute Force (O(n^2))
Check all possible element pairs between arrays. For each mismatch, increment or decrement until equal. This approach iterates through all elements multiple times, leading to quadratic time complexity. Only useful for understanding the problem constraints.
Approach 2: Difference Analysis (O(n))
Calculate the absolute difference between corresponding elements. Sum these differences to get the total operations needed. The key insight is that each mismatch requires exactly one operation per unit difference. This greedy approach works because operations are independent of each other.
Recommended for interviews: The difference analysis approach is expected in interviews. It demonstrates understanding of problem constraints and optimal use of array manipulation. Brute force shows basic comprehension, but the optimal solution highlights efficient problem-solving.
Solutions for this problem are being prepared.
Try solving it yourself| Approach | Time | Space | When to Use |
|---|---|---|---|
| Brute Force | O(n^2) | O(1) | For small arrays or initial problem analysis |
| Difference Analysis | O(n) | O(1) | General case, optimal solution |
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