Leetcode #1413: Minimum Value to Get Positive Step by Step Sum
In this guide, we solve Leetcode #1413 Minimum Value to Get Positive Step by Step Sum in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
Given an array of integers nums, you start with an initial positive value startValue. In each iteration, you calculate the step by step sum of startValue plus elements in nums (from left to right).
Quick Facts
- Difficulty: Easy
- Premium: No
- Tags: Array, Prefix Sum
Intuition
Range queries become simple once we precompute cumulative sums.
We can transform subarray conditions into prefix comparisons.
Approach
Compute prefix sums and use a map to find matching prefixes.
This avoids nested loops while keeping the logic clear.
Steps:
- Compute prefix sums.
- Use a map to find valid ranges.
- Update the answer.
Example
Input: nums = [-3,2,-3,4,2]
Output: 5
Explanation: If you choose startValue = 4, in the third iteration your step by step sum is less than 1.
step by step sum
startValue = 4 | startValue = 5 | nums
(4 -3 ) = 1 | (5 -3 ) = 2 | -3
(1 +2 ) = 3 | (2 +2 ) = 4 | 2
(3 -3 ) = 0 | (4 -3 ) = 1 | -3
(0 +4 ) = 4 | (1 +4 ) = 5 | 4
(4 +2 ) = 6 | (5 +2 ) = 7 | 2
Python Solution
class Solution:
def minStartValue(self, nums: List[int]) -> int:
s, t = 0, inf
for num in nums:
s += num
t = min(t, s)
return max(1, 1 - t)
Complexity
The time complexity is O(n). The space complexity is O(n).
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.