How do you solve Minimum Value to Get Positive Step by Step Sum on LeetCode?

Minimum Value to Get Positive Step by Step Sum (LeetCode #1413) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(1) space complexity. Key insight: The minimum startValue is determined by the lowest point reached in the cumulative sum.

What is the time complexity of Minimum Value to Get Positive Step by Step Sum?

The optimal solution for Minimum Value to Get Positive Step by Step Sum runs in O(n) time and uses O(1) space. This solution runs in O(n) time because we only traverse the array nums once, and it uses O(1) space since we only maintain a few integer variables.

What is the brute force solution for Minimum Value to Get Positive Step by Step Sum?

The brute force approach for Minimum Value to Get Positive Step by Step Sum is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves trying different values for startValue and checking if the step-by-step sum remains positive throughout the iteration. This is simple but inefficient as it checks each possible startValue until it finds a valid one. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Minimum Value to Get Positive Step by Step Sum?

Minimum Value to Get Positive Step by Step Sum uses the following concepts: Array, Prefix Sum. The recommended patterns to study are: Prefix Sum, Cumulative Sum.

What are the interview tips for Minimum Value to Get Positive Step by Step Sum?

Always clarify the problem statement and constraints before jumping into coding. Think about edge cases, such as arrays with all negative numbers. Explain your thought process clearly while coding, as it helps the interviewer understand your approach.

What are common mistakes when solving Minimum Value to Get Positive Step by Step Sum?

Failing to consider the case where the cumulative sum becomes negative. Not initializing the prefix sum correctly or misunderstanding its role.

#1413

Minimum Value to Get Positive Step by Step Sum

Easy

ArrayPrefix SumPrefix SumCumulative Sum

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)

The optimal solution focuses on calculating the minimum prefix sum of the cumulative sums of nums. This allows us to determine the minimum startValue directly by ensuring the cumulative sum never drops below 1.

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Algorithm

4 steps

1Step 1: Initialize a variable total to 0 and minPrefixSum to 0.
2Step 2: Iterate through each number in nums, updating total by adding the current number.
3Step 3: Update minPrefixSum to be the minimum of itself and total.
4Step 4: If minPrefixSum is less than 1, return 1 - minPrefixSum as the required startValue; otherwise, return 1.

solution.py7 lines

1def minStartValue(nums):
2    total = 0
3    minPrefixSum = 0
4    for num in nums:
5        total += num
6        minPrefixSum = min(minPrefixSum, total)
7    return 1 - minPrefixSum if minPrefixSum < 1 else 1

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Complexity note: This solution runs in O(n) time because we only traverse the array nums once, and it uses O(1) space since we only maintain a few integer variables.

1The minimum startValue is determined by the lowest point reached in the cumulative sum.
2If the cumulative sum is always above 1, the minimum startValue is simply 1.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.