Largest Sum Contiguous Subarray

Largest Sum Contiguous Subarray

In the Largest Sum Contiguous Subarray problem we have to find the subarray with maximum sum. It is a very famous problem which is asked in many interviews. In this article, we will provide a C++ solution with an explanation.

Largest Sum Contiguous Subarray Problem Discription

Largest Sum Contiguous Subarray Problem Description

We are given an array with n integers. Output the maximum possible subarray sum.


  • First line contains single integer n the size of subarray.
  • Second line contains n integers – the elements of subarray.


  • The required sum.

Largest Sum Contiguous Subarray Solution

Basic Approach –

The basic or naive approach is to use a nested loop and find sum for all sub arrays generated.

Time Complexity – O(n^2)

Space Complexity – O(n)

Optimized Approach

The optimized approach uses Kadane’s Algorithm. The idea of kadane’s algorithm is simple. We maintain two sums –

  • Current Sum – Csum
  • Max Sum – MxSum

We iterate over the array adding current element to the current sum. If at any point the current sum becomes negative we set it to zero.

Time Complexity – O(n)

Space Complexity – O(n)

LargestLargest Sum Contiguous Subarray Problem Explanation


#include <bits/stdc++.h>
using namespace std;
int kadaneAlgo(int arr[], int n)
    int cSum = 0mxSum = INT_MIN;

    // Finding the maximum element
    for (int i = 0i < ni++)
        mxSum = max(arr[i], mxSum);
    //Since the maximum element is negative
    if (mxSum <= 0)
        return mxSum;

    // Kadane’s Algorithm
    for (int i = 0i < ni++)
        cSum += arr[i];
        if (cSum < 0)
            cSum = 0;
        mxSum = max(mxSumcSum);
    return mxSum;
int main()
    int n;
    cin >> n;
    int arr[n];

    for (int i = 0i < ni++)
        cin >> arr[i];

    cout << kadaneAlgo(arrn<< endl;

    return 0;


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