Leetcode #410: Split Array Largest Sum
In this guide, we solve Leetcode #410 Split Array Largest 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 integer array nums and an integer k, split nums into k non-empty subarrays such that the largest sum of any subarray is minimized. Return the minimized largest sum of the split.
Quick Facts
- Difficulty: Hard
- Premium: No
- Tags: Greedy, Array, Binary Search, Dynamic Programming, Prefix Sum
Intuition
The problem structure suggests a monotonic decision, which makes binary search a natural fit.
By halving the search space each step, we reach the answer efficiently.
Approach
Search either directly on a sorted array or on the answer space using a check function.
Each check is fast, and the logarithmic search keeps the overall runtime low.
Steps:
- Define the search bounds.
- Check the mid point condition.
- Narrow the bounds until convergence.
Example
Input: nums = [7,2,5,10,8], k = 2
Output: 18
Explanation: There are four ways to split nums into two subarrays.
The best way is to split it into [7,2,5] and [10,8], where the largest sum among the two subarrays is only 18.
Python Solution
class Solution:
def splitArray(self, nums: List[int], k: int) -> int:
def check(mx):
s, cnt = inf, 0
for x in nums:
s += x
if s > mx:
s = x
cnt += 1
return cnt <= k
left, right = max(nums), sum(nums)
return left + bisect_left(range(left, right + 1), True, key=check)
Complexity
The time complexity is , and the space complexity is . The space complexity is .
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.