Smallest sum contiguous subarray

Given an array containing n integers. The problem is to find the sum of the elements of the contiguous subarray having the smallest(minimum) sum.

Examples:

Input : arr[] = {3, -4, 2, -3, -1, 7, -5}
Output : -6
Subarray is {-4, 2, -3, -1} = -6

Input : arr = {2, 6, 8, 1, 4}
Output : 1

Naive Approach: Consider all the contiguous subarrays of diiferent sizes and find their sum. The subarray having the smallest(minimum) sum is the required answer.

Efficient Approach: It is a variation to the problem of finding the largest sum contiguous subarray based on the idea of Kadane’s algorithm.

Algorithm:

smallestSumSubarr(arr, n)
    Initialize min_ending_here = INT_MAX
    Initialize min_so_far = INT_MAX
    
    for i = 0 to n-1
        if min_ending_here > 0
            min_ending_here = arr[i]        
        else
            min_ending_here += arr[i]
        min_so_far = min(min_so_far, min_ending_here)

    return min_so_far

C++

// C++ implementation to find the smallest sum
// contiguous subarray
#include <bits/stdc++.h>

using namespace std;

// function to find the smallest sum contiguous subarray
int smallestSumSubarr(int arr[], int n)
{
	// to store the minimum value that is ending
	// up to the current index
	int min_ending_here = INT_MAX;
	
	// to store the minimum value encountered so far
	int min_so_far = INT_MAX;
	
	// traverse the array elements
	for (int i=0; i<n; i++)
	{
		// if min_ending_here > 0, then it could not possibly
		// contribute to the minimum sum further
		if (min_ending_here > 0)
			min_ending_here = arr[i];
		
		// else add the value arr[i] to min_ending_here	
		else
			min_ending_here += arr[i];
		
		// update min_so_far
		min_so_far = min(min_so_far, min_ending_here);			
	}
	
	// required smallest sum contiguous subarray value
	return min_so_far;
}


// Driver program to test above
int main()
{
	int arr[] = {3, -4, 2, -3, -1, 7, -5};
	int n = sizeof(arr) / sizeof(arr[0]);
	cout << "Smallest sum: "
	     << smallestSumSubarr(arr, n);
	return 0;     
} 

Python

# Python program to find the smallest sum
# contiguous subarray
import sys

# function to find the smallest sum 
# contiguous subarray
def smallestSumSubarr(arr, n):
    # to store the minimum value that is ending
    # up to the current index
    min_ending_here = sys.maxint
    
    # to store the minimum value encountered so far
    min_so_far = sys.maxint
    
    # traverse the array elements
    for i in range(n):
        # if min_ending_here > 0, then it could not possibly
        # contribute to the minimum sum further
        if (min_ending_here > 0):
            min_ending_here = arr[i]
        
        # else add the value arr[i] to min_ending_here 
        else:
            min_ending_here += arr[i]
         
        # update min_so_far
        min_so_far = min(min_so_far, min_ending_here)
    
    # required smallest sum contiguous subarray value
    return min_so_far
    
# Driver code
arr = [3, -4, 2, -3, -1, 7, -5]
n = len(arr)
print "Smallest sum: ", smallestSumSubarr(arr, n)

# This code is contributed by Sachin Bisht


Output:

Smallest sum: -6

Time Complexity: O(n)

This article is contributed by Ayush Jauhari. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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