README_EN.md

410. Split Array Largest Sum

中文文档

Description

Given an array nums which consists of non-negative integers and an integer m, you can split the array into m non-empty continuous subarrays.

Write an algorithm to minimize the largest sum among these m subarrays.

 

Example 1:

Input: nums = [7,2,5,10,8], m = 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], m = 2
Output: 9

Example 3:

Input: nums = [1,4,4], m = 3
Output: 4

 

Constraints:

• 1 <= nums.length <= 1000
• 0 <= nums[i] <= 106
• 1 <= m <= min(50, nums.length)

Solutions

Binary search.

Python3

class Solution:
    def splitArray(self, nums: List[int], m: int) -> int:
        def check(x):
            s, cnt = 0, 1
            for num in nums:
                if s + num > x:
                    cnt += 1
                    s = num
                else:
                    s += num
            return cnt <= m

        left, right = max(nums), sum(nums)
        while left < right:
            mid = (left + right) >> 1
            if check(mid):
                right = mid
            else:
                left = mid + 1
        return left

Java

class Solution {
    public int splitArray(int[] nums, int m) {
        int mx = -1;
        for (int num : nums) {
            mx = Math.max(mx, num);
        }
        int left = mx, right = (int) 1e9;
        while (left < right) {
            int mid = (left + right) >> 1;
            if (check(nums, m, mid)) {
                right = mid;
            } else {
                left = mid + 1;
            }
        }
        return left;
    }

    private boolean check(int[] nums, int m, int x) {
        int s = 0, cnt = 1;
        for (int num : nums) {
            if (s + num > x) {
                ++cnt;
                s = num;
            } else {
                s += num;
            }
        }
        return cnt <= m;
    }
}

C++

class Solution {
public:
    int splitArray(vector<int>& nums, int m) {
        int left = *max_element(nums.begin(), nums.end()), right = (int) 1e9;
        while (left < right) {
            int mid = left + right >> 1;
            if (check(nums, m, mid)) right = mid;
            else left = mid + 1;
        }
        return left;
    }

    bool check(vector<int>& nums, int m, int x) {
        int s = 0, cnt = 1;
        for (int num : nums) {
            if (s + num > x) {
                ++cnt;
                s = num;
            } else {
                s += num;
            }
        }
        return cnt <= m;
    }
};

Go

func splitArray(nums []int, m int) int {
	mx := -1
	for _, num := range nums {
		mx = max(mx, num)
	}
	left, right := mx, int(1e9)
	for left < right {
		mid := (left + right) >> 1
		if check(nums, m, mid) {
			right = mid
		} else {
			left = mid + 1
		}
	}
	return left
}

func check(nums []int, m, x int) bool {
	s, cnt := 0, 1
	for _, num := range nums {
		if s+num > x {
			cnt++
			s = num
		} else {
			s += num
		}
	}
	return cnt <= m
}

func max(a, b int) int {
	if a > b {
		return a
	}
	return b
}

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