Split Array Largest Sum

Problem Description

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.

Key Insights

• The problem requires dividing an array into k contiguous subarrays.
• The goal is to minimize the maximum sum among these k subarrays.
• Binary search can be used to find the minimum possible largest sum.
• The feasible range for the binary search includes the maximum element in nums (minimum possible largest sum) and the sum of all elements in nums (maximum possible largest sum).
• A greedy approach can check if a mid-value can be the largest sum by trying to form subarrays without exceeding that sum.

Space and Time Complexity

Time Complexity: O(n log S), where n is the number of elements in nums and S is the sum of all elements in nums.
Space Complexity: O(1), since we are using a constant amount of extra space.

Solution

To solve the problem, we use a binary search approach combined with a greedy algorithm. The binary search is performed on the possible values of the largest sum, while the greedy check determines if a given largest sum can be achieved with k subarrays.

1. Binary Search Setup: Initialize the lower bound (left) as the maximum element in nums, and the upper bound (right) as the sum of all elements in nums.
2. Greedy Check: For a mid-value between left and right, iterate through nums to count how many subarrays can be formed without exceeding the mid-value.
3. Adjust Search Bounds: If the count of subarrays is less than or equal to k, it means we can potentially lower the largest sum, so adjust the upper bound. Otherwise, increase the lower bound.

Code Solutions