Minimum operations to make GCD multiple of k
Detailed guide and Python implementation for the 'Minimum operations to make GCD multiple of k' problem.
Problem Statement
Write a function min_operations_gcd_k(arr, k) that returns the minimum number of operations to make the Greatest Common Divisor (GCD) of all elements in the array a multiple of k. In one operation, you can either increment or decrement any element of the array by 1.
- •1 <= len(arr) <= 10^5
- •1 <= k <= 10^4
- •1 <= arr[i] <= 10^9
Examples
min_operations_gcd_k([4, 5, 6], 5)
2
Increment 4 to 5 (1 op) and decrement 6 to 5 (1 op). The array becomes [5, 5, 5] whose GCD is 5, which is a multiple of 5.
min_operations_gcd_k([2, 3], 3)
1
Increment 2 to 3 (1 op). The array becomes [3, 3] whose GCD is 3, which is a multiple of 3.
Need a Hint?
Edge Cases to Watch
- Empty input structures
- Single element inputs
- Large numerical bounds
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