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Leetcode Split Array Largest Sum problem solution

YASH PAL, 31 July 2024

In this Leetcode Split Array Largest Sum problem solution, You are 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.

Leetcode Split Array Largest Sum problem solution

Problem solution in Python.

class Solution:
    def splitArray(self, nums: List[int], m: int) -> int:
        dp = [[float("inf") for _ in range(len(nums))] for _ in range(m)]
        dp[0][0] = nums[0]
        for j in range(1, len(nums)):
            dp[0][j] = dp[0][j-1] + nums[j]
        
        for i in range(1,m):
            for j in range(i, len(nums)):
                dp[i][j] = min([max(dp[i-1][k],dp[0][j]-dp[0][k]) for k in range(i-1, j)])
        return dp[-1][-1]

Problem solution in Java.

class Solution {
    public int splitArray(int[] nums, int m) {
        int low = IntStream.of(nums).max().orElse(0);
        int high = IntStream.of(nums).sum();
        while (low < high) {
            int mid = low + (high - low) / 2;
            if (split(nums, mid) > m) {
                low = mid + 1;
            } else {
                high = mid;
            }
        }
        return low;
    }
    
    private int split(int[] nums, int sum) {
        int ret = 1;
        int currentSum = 0;
        for (int i = 0; i < nums.length; i++) {
            if (currentSum + nums[i] > sum) {
                ret++;
                currentSum = 0;
            }
            currentSum += nums[i];
        }
        return ret;
    }
}

Problem solution in C++.

bool can_split(vector<int> &nums,int m,long long int sum)
    {
        long long int cnt=1,cnt_sum=0;
        for (int i = 0; i <nums.size() ; ++i) {
            cnt_sum+=nums[i];
            if(cnt_sum>sum)
            {
                cnt_sum=nums[i];
                ++cnt;
                if (cnt>m) return false;
            }
        }
        return true;
    }
    int splitArray(vector<int>& nums, int m) 
    {
        long long left=*max_element(nums.begin(),nums.end());
        long long right=accumulate(nums.begin(),nums.end(),0ll);
        while(left<right)
        {
            long long mid=(left+right)>>1;
            if(can_split(nums,m,mid)) right=mid;
            else left=mid+1;
        }
        return left;
        
    }

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