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LeetCode 3091: Apply Operations to Make Sum of Array Greater Than or Equal to k Solution

Master LeetCode problem 3091 (Apply Operations to Make Sum of Array Greater Than or Equal to k), a medium challenge, with our optimized solutions in Java, C++, and Python. Explore detailed explanations, test your code in our interactive editor, and prepare for coding interviews.

3091. Apply Operations to Make Sum of Array Greater Than or Equal to k

Medium
MathGreedyEnumeration

Problem Explanation

Explanation:

To solve this problem, we need to find the minimum number of operations required to make the sum of elements of the array greater than or equal to k. We start with an array containing only the number 1 and perform two types of operations: increase an element by 1 or duplicate an element.

The key observation is that duplicating an element will exponentially increase the sum of the array. To minimize the number of operations, we should always duplicate the largest element in the array.

  1. Initialize the sum as 1 and the count of operations as 0.
  2. While the sum is less than k, if duplicating the largest element will make the sum >= k, duplicate the largest element. Otherwise, increment the largest element in the array by 1.
  3. Repeat step 2 until the sum becomes greater than or equal to k.
  4. Return the count of operations as the answer.

Time complexity: O(log(k)) - as we are duplicating the largest element in each step until the sum reaches k. Space complexity: O(1) - as we are not using any extra space other than some variables.

:

Solution Code

class Solution {
    public int minOperations(int k) {
        int sum = 1;
        int operations = 0;
        
        while (sum < k) {
            if (sum + sum / 2 >= k) {
                sum += sum / 2;
            } else {
                sum++;
            }
            operations++;
        }
        
        return operations;
    }
}

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