Minimum Deletions To Make Array Divisible - Leetcode Solution

Problem Statement:

Given an integer array nums, find the minimum number of operations required to make all elements of nums divisible by some integer k.

An operation is to remove an element from the array.

Return the minimum number of operations to make all elements divisible by k.

Solution:

First, we need to understand what the problem is asking us to do. We have an array, and we need to make all the elements of the array divisible by a number k. We can do this by removing some elements from the array.

To solve this problem, we need to find the sum of all the elements in the array and then divide it by k. Let's take an example to understand this:

Example:

Input: nums = [3, 7, 2, 1, 4, 8, 5], k=3

Step 1:

We find the sum of the array by looping through all the elements in the array and adding them up:

sum=3+7+2+1+4+8+5=30

Step 2:

We divide the sum by k to get the remainder:

remainder = sum % k = 30 % 3 = 0

If the remainder is 0, then all the elements in the array are already divisible by k, so we don't need to remove any elements. In this case, we return 0.

Step 3:

If the remainder is not 0, we need to find the minimum number of elements we can remove to make the sum of the array divisible by k. We can do this by taking the remainder and subtracting it from k. This gives us the minimum number of elements we need to remove.

min_deletions = k - remainder = 3 - 0 = 3

In this case, we can remove any three elements from the array to make the sum of the remaining elements divisible by k. There are multiple ways to remove three elements, but one possible solution is to remove 7, 5, and 2. The remaining elements are [3, 1, 4, 8], and the sum of these elements is 16, which is divisible by 3.

Complexity Analysis:

Time Complexity: O(n), where n is the number of elements in the input array.

Space Complexity: O(1), as we are using constant extra space.

Final Thoughts:

This problem can be solved using a simple mathematical formula. We calculate the sum of all the elements in the array and divide it by k. If the remainder is not 0, we need to remove some elements from the array to make the remaining elements divisible by k.

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