410. Split Array Largest Sum

2023, Jan 16 2 mins read

1. 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.
A subarray is a contiguous part of the array.

2. Example

Example 1

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.

Example 2

Input: nums = [1,2,3,4,5], k = 2
Output: 9
Explanation: There are four ways to split nums into two subarrays.
The best way is to split it into [1,2,3] and [4,5], where the largest sum among the two subarrays is only 9.

3. Constraints

1 <= nums.length <= 1000
0 <= nums[i] <= 10$^{6}$
1 <= k <= min(50, nums.length)

4. Solutions

Binary Search & Greedy

n = nums.size()
Time complexity: O(nlog(sum(nums) - max(nums)))
Space complexity: O(1)

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class Solution {
private:
    int check(const vector<int> &nums, int sum_limit, int k) {
        // greedy
        // this problem asks for contiguous subarray, otherwise it will be much complex
        int max_sum = 0;
        for (int i = 0, sum = 0; i < nums.size(); ++i) {
            sum += nums[i];
            if (sum > sum_limit) {
                --k;
                sum = nums[i];
            }

            max_sum = max(max_sum, sum);
        }

        return k >= 1 ? max_sum : -1;
    }

public:
    int splitArray(const vector<int> &nums, int k) {
        int max_num = 0, nums_sum = 0;
        for (int num : nums) {
            max_num = max(max_num, num);
            nums_sum += num;
        }

        int result = 0;
        for (int left = max_num, right = nums_sum; left <= right;) {
            int mid = (left + right) / 2;

            int check_result = check(nums, mid, k);
            // be careful of this (), the order of ":" > ","
            check_result == -1 ? left = mid + 1 : (right = mid - 1, result = check_result);
        }

        return result;
    }
};