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

The optimal solution for Apply Operations to Make Sum of Array Greater Than or Equal to k runs in O(n) time and uses O(1) space. The time complexity is O(n) because we may need to increment the sum up to k. The space complexity is O(1) as we only use a few variables.

What is the brute force solution for Apply Operations to Make Sum of Array Greater Than or Equal to k?

The brute force approach for Apply Operations to Make Sum of Array Greater Than or Equal to k is Brute Force, with O(n²) time complexity and O(1) space complexity. In the brute force approach, we will try every possible combination of increase and duplicate operations to find the minimum number of operations needed to achieve a sum greater than or equal to k. This method is straightforward but inefficient. The optimal Optimal Solution approach improves this to O(n).

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

Apply Operations to Make Sum of Array Greater Than or Equal to k uses the following concepts: Math, Greedy, Enumeration. The recommended patterns to study are: Greedy, Enumeration.

What are the interview tips for Apply Operations to Make Sum of Array Greater Than or Equal to k?

Always clarify the problem constraints and initial conditions before jumping into coding. Think about edge cases, such as when k is very small or equal to 1. Explain your thought process clearly while coding to demonstrate your understanding.

What are common mistakes when solving Apply Operations to Make Sum of Array Greater Than or Equal to k?

Failing to account for the initial sum of 1 when calculating operations. Overcomplicating the problem by not recognizing that increases should be prioritized.

#3091

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

Medium

MathGreedyEnumerationGreedyEnumeration

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(1)

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Intuition

Time O(n)Space O(1)

In the optimal solution, we focus on maximizing the effect of each increase operation before duplicating elements. By calculating how many increases we need first, we can minimize the number of duplicates required to reach or exceed k.

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Algorithm

4 steps

1Step 1: Initialize the current sum as 1 and operations as 0.
2Step 2: While the current sum is less than k, increment the current sum by 1 and increment the operations count.
3Step 3: After reaching or exceeding k, calculate how many duplicates are needed based on the current sum.
4Step 4: Return the total operations count.

solution.py8 lines

1def minOperations(k):
2    current_sum = 1
3    operations = 0
4    while current_sum < k:
5        current_sum += 1
6        operations += 1
7    duplicates_needed = (k - current_sum + current_sum - 1) // current_sum
8    return operations + duplicates_needed

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Complexity note: The time complexity is O(n) because we may need to increment the sum up to k. The space complexity is O(1) as we only use a few variables.

1Maximizing the sum through increases first minimizes the number of duplicates needed.
2Understanding the relationship between increases and duplicates is key to optimizing the solution.

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