Apply Operations to Make Sum of Array Greater Than or Equal to k Python/Java solution

In Python or Java, iterate over possible values of x (the largest element after increments). For each x, compute operations = (x - 1) + (ceil(k / x) - 1) and track the minimum. The implementation uses simple loops and integer arithmetic.

What is the best approach for Apply Operations to Make Sum of Array Greater Than or Equal to k?

The optimal approach is a greedy math strategy that balances increments and copy operations. First increase one element to a value x using x-1 increments, then copy that value until the total sum reaches k. The cost becomes (x - 1) + (ceil(k / x) - 1). Enumerating x around sqrt(k) finds the minimum efficiently.

Is Apply Operations to Make Sum of Array Greater Than or Equal to k asked at Google/Amazon/Meta?

This style of problem appears in interviews at large tech companies because it tests mathematical reasoning and greedy optimization. Variants involving operation cost balancing and array growth are common in Google, Amazon, and Meta coding interviews.

What data structure is used in Apply Operations to Make Sum of Array Greater Than or Equal to k?

No complex data structure is required. The optimal solution relies mainly on mathematical reasoning and simple enumeration. Only a few integer variables are needed to compute increments, copies, and the resulting sum.

What is the time complexity of Apply Operations to Make Sum of Array Greater Than or Equal to k?

The optimized greedy solution runs in O(sqrt(k)) time and O(1) space because only a small range of candidate values for the maximum element needs to be tested. A naive dynamic programming simulation can take up to O(k^2) time and O(k) space.

Description Hints 2 Solution Video 22:21

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

Q: Is Apply Operations to Make Sum of Array Greater Than or Equal to k easy or hard?

The problem is rated Medium because the operations themselves are simple but the optimal solution requires a mathematical observation. Many first attempts simulate operations or use DP, while the intended solution uses a greedy enumeration formula.

Q: How to solve Apply Operations to Make Sum of Array Greater Than or Equal to k in O(n)?

The problem is typically solved in O(sqrt(k)) rather than O(n). The idea is to enumerate the target value x of the largest element, compute increments needed (x-1), and then calculate copies needed ceil(k/x)-1. The minimum total operations across all candidates gives the answer.

Medium44.2% acceptance2 companies

You are given a positive integer k. Initially, you have an array nums = [1].

You can perform any of the following operations on the array any number of times (possibly zero):

Choose any element in the array and increase its value by 1.
Duplicate any element in the array and add it to the end of the array.

Return the minimum number of operations required to make the sum of elements of the final array greater than or equal to k.

Example 1:

Input: k = 11

Output: 5

Explanation:

We can do the following operations on the array nums = [1]:

Increase the element by 1 three times. The resulting array is nums = [4].
Duplicate the element two times. The resulting array is nums = [4,4,4].

The sum of the final array is 4 + 4 + 4 = 12 which is greater than or equal to k = 11.
The total number of operations performed is 3 + 2 = 5.

Example 2:

Input: k = 1

Output: 0

Explanation:

The sum of the original array is already greater than or equal to 1, so no operations are needed.

Constraints:

1 <= k <= 10⁵

Asked at 2 companies

Zscaler Turing

Topics

Hints open one at a time

Hint 1

It is optimal to make all the increase operations first and all the duplicate operations last.

Hint 2

Iterate over all possible number of increase operations that can be done and find the corresponding number of duplicate operations.

22:21

Still stuck?Read 3 approaches, or watch a walkthrough.

Open solution

LanguageLoading editor…

1class Solution:
2    def minOperations(self, k: int) -> int:
3        

Starter codePython 3Spaces: 4

Examples

Case 1Case 2

Input

Your code is saved on this device.Solution