Find subarray with given sum with negatives allowed in constant space

Difficulty Level : Hard
Last Updated : 24 May, 2021

Given an unsorted array of integers, find a subarray that adds to a given number. If there is more than one subarray with the sum of the given number, print any of them.

Examples:

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Input: arr[] = {1, 4, 20, 3, 10, 5}, sum = 33
Output: Sum found between indexes 2 and 4

Input: arr[] = {10, 2, -2, -20, 10}, sum = -10
Output: Sum found between indexes 0 to 3

Input: arr[] = {-10, 0, 2, -2, -20, 10}, sum = 20
Output: No subarray with given sum exists.

We had already discussed an approach to find subarray with a given sum in an array containing both positive and negative elements using Hashing
In this article, an approach without using any extra space is discussed.
The idea is to modify the array to contain only positive elements:

Find the smallest negative element in the array and increase every value in the array by the absolute value of the smallest negative element found.

We may notice that after doing the above modification, the sum of every subarray will also increase by:

(number of elements in the subarray) * (absolute value of min element)

After doing the above modification to the input array, the task is reduced to finding if there is any subarray in the given array of only positive numbers with the new target sum. This can be done using the sliding window technique in O(N) time and constant space.
Every time while adding elements to the window, increment the target sum by the absolute value of the minimum element and, similarly, while removing elements from the current window, decrement the target sum by the absolute value of the minimum element so that for every subarray of length, say K, the updated target sum will be:

targetSum = sum + K*abs(minimum element)

Below is the approach for the same:

Initialize a variable curr_sum as the first element.
The variable curr_sum indicates the sum of the current subarray.
Start from the second element and add all elements one by one to the curr_sum, and keep incrementing the target sum by abs(minimum element).
If curr_sum becomes equal to the target sum, then print the solution.
If curr_sum exceeds the sum, then remove the trailing elements while decreasing curr_sum is greater than the sum and keep decreasing the target sum by abs(minimum element).

Below is the implementation of the above approach:

C++

// C++ program to check if subarray with sum
// exists when negative elements are also present
#include <bits/stdc++.h>
using namespace std;
 
// Function to check if subarray with sum
// exists when negative elements are also present
void subArraySum(int arr[], int n, int sum)
{
    int minEle = INT_MAX;
 
    // Find minimum element in the array
    for (int i = 0; i < n; i++)
        minEle = min(arr[i], minEle);
 
    // Initialize curr_sum as value of first element
    // and starting point as 0
    int curr_sum = arr[0] + abs(minEle), start = 0, i;
 
    // Starting window length will be 1,
    // For generating new target sum,
    // add abs(minEle) to sum only 1 time
    int targetSum = sum;
 
    // Add elements one by one to curr_sum
    // and if the curr_sum exceeds the
    // updated sum, then remove starting element
    for (i = 1; i <= n; i++) {
 
        // If curr_sum exceeds the sum,
        // then remove the starting elements
        while (curr_sum - (i - start) * abs(minEle) > targetSum && start < i) {
            curr_sum = curr_sum - arr[start] - abs(minEle);
            start++;
        }
 
        // If curr_sum becomes equal to sum, then return true
        if (curr_sum - (i - start) * abs(minEle) == targetSum) {
            cout << "Sum found between indexes " << start << " and " << i - 1;
            return;
        }
 
        // Add this element to curr_sum
        if (i < n) {
            curr_sum = curr_sum + arr[i] + abs(minEle);
        }
    }
 
    // If we reach here, then no subarray
    cout << "No subarray found";
}
 
// Driver Code
int main()
{
    int arr[] = { 10, -12, 2, -2, -20, 10 };
    int n = sizeof(arr) / sizeof(arr[0]);
 
    int sum = -10;
 
    subArraySum(arr, n, sum);
 
    return 0;
}

Java

// Java program to check if subarray with sum
// exists when negative elements are also present
class GFG
{
     
    // Function to check if subarray with sum
    // exists when negative elements are also present
    static void subArraySum(int arr[], int n, int sum)
    {
        int minEle = Integer.MAX_VALUE;
     
        // Find minimum element in the array
        for (int i = 0; i < n; i++)
            minEle = Math.min(arr[i], minEle);
     
        // Initialize curr_sum as value of
        // first element and starting point as 0
        int curr_sum = arr[0] + Math.abs(minEle);
        int start = 0, i;
     
        // Starting window length will be 1,
        // For generating new target sum,
        // add abs(minEle) to sum only 1 time
        int targetSum = sum;
     
        // Add elements one by one to curr_sum
        // and if the curr_sum exceeds the
        // updated sum, then remove starting element
        for (i = 1; i <= n; i++)
        {
     
            // If curr_sum exceeds the sum,
            // then remove the starting elements
            while (curr_sum - (i - start) *
                   Math.abs(minEle) > targetSum &&
                                      start < i)
            {
                curr_sum = curr_sum - arr[start] -
                           Math.abs(minEle);
                start++;
            }
     
            // If curr_sum becomes equal to sum,
            // then return true
            if (curr_sum - (i - start) *
                Math.abs(minEle) == targetSum)
            {
                System.out.println("Sum found between indexes " +
                                      start + " and " + (i - 1));
                return;
            }
     
            // Add this element to curr_sum
            if (i < n)
            {
                curr_sum = curr_sum + arr[i] +
                             Math.abs(minEle);
            }
        }
     
        // If we reach here, then no subarray
        System.out.println("No subarray found");
    }
     
    // Driver Code
    public static void main (String[] args)
    {
        int arr[] = { 10, -12, 2, -2, -20, 10 };
        int n = arr.length;
     
        int sum = -10;
     
        subArraySum(arr, n, sum);
    }
}
 
// This code is contributed by AnkitRai01

Python3

# Python3 program to check if subarray with summ
# exists when negative elements are also present
 
# Function to check if subarray with summ
# exists when negative elements are also present
def subArraySum(arr, n, summ):
    minEle = 10**9
 
    # Find minimum element in the array
    for i in range(n):
        minEle = min(arr[i], minEle)
 
    # Initialize curr_summ as value of
    # first element and starting poas 0
    curr_summ = arr[0] + abs(minEle)
    start = 0
 
    # Starting window length will be 1,
    # For generating new target summ,
    # add abs(minEle) to summ only 1 time
    targetSum = summ
 
    # Add elements one by one to curr_summ
    # and if the curr_summ exceeds the
    # updated summ, then remove starting element
    for i in range(1, n + 1):
 
        # If curr_summ exceeds the summ,
        # then remove the starting elements
        while (curr_summ - (i - start) * abs(minEle) >
                       targetSum and start < i):
            curr_summ = curr_summ - arr[start] - abs(minEle)
            start += 1
 
        # If curr_summ becomes equal to summ,
        # then return true
        if (curr_summ - (i - start) *
            abs(minEle) == targetSum):
            print("Sum found between indexes",
                          start, "and", i - 1)
            return
 
        # Add this element to curr_summ
        if (i < n):
            curr_summ = curr_summ + arr[i] + abs(minEle)
 
    # If we reach here, then no subarray
    print("No subarray found")
 
# Driver Code
arr = [10, -12, 2, -2, -20, 10]
n = len(arr)
 
summ = -10
 
subArraySum(arr, n, summ)
 
# This code is contributed by Mohit Kumar

C#

// C# program to check if subarray
// with sum exists when negative
// elements are also present
using System;
 
class GFG
{
     
    // Function to check if subarray
    // with sum exists when negative
    // elements are also present
    static void subArraySum(int []arr,
                            int n, int sum)
    {
        int minEle = int.MaxValue;
        int i;
         
        // Find minimum element in the array
        for (i = 0; i < n; i++)
            minEle = Math.Min(arr[i], minEle);
     
        // Initialize curr_sum as value of
        // first element and starting point as 0
        int curr_sum = arr[0] + Math.Abs(minEle);
        int start = 0;
     
        // Starting window length will be 1,
        // For generating new target sum,
        // add abs(minEle) to sum only 1 time
        int targetSum = sum;
     
        // Add elements one by one to curr_sum
        // and if the curr_sum exceeds the
        // updated sum, then remove starting element
        for (i = 1; i <= n; i++)
        {
     
            // If curr_sum exceeds the sum,
            // then remove the starting elements
            while (curr_sum - (i - start) *
                   Math.Abs(minEle) > targetSum &&
                                      start < i)
            {
                curr_sum = curr_sum - arr[start] -
                           Math.Abs(minEle);
                start++;
            }
     
            // If curr_sum becomes equal to sum,
            // then return true
            if (curr_sum - (i - start) *
                Math.Abs(minEle) == targetSum)
            {
                Console.Write("Sum found between indexes " +
                                 start + " and " + (i - 1));
                return;
            }
     
            // Add this element to curr_sum
            if (i < n)
            {
                curr_sum = curr_sum + arr[i] +
                             Math.Abs(minEle);
            }
        }
     
        // If we reach here, then no subarray
        Console.Write("No subarray found");
    }
     
    // Driver Code
    static public void Main ()
    {
        int []arr = { 10, -12, 2, -2, -20, 10 };
        int n = arr.Length;
     
        int sum = -10;
     
        subArraySum(arr, n, sum);
    }
}
 
// This code is contributed by ajit

Javascript

<script>
// Java Script program to check if subarray with sum
// exists when negative elements are also present
 
     
// Function to check if subarray with sum
// exists when negative elements are also present
function subArraySum(arr,n,sum)
{
    let minEle = Number.MAX_VALUE;
     
    // Find minimum element in the array
    for (let i = 0; i < n; i++)
        minEle = Math.min(arr[i], minEle);
     
    // Initialize curr_sum as value of
    // first element and starting point as 0
    let curr_sum = arr[0] + Math.abs(minEle);
    let start = 0, i;
     
    // Starting window length will be 1,
    // For generating new target sum,
    // add abs(minEle) to sum only 1 time
    let targetSum = sum;
     
    // Add elements one by one to curr_sum
    // and if the curr_sum exceeds the
    // updated sum, then remove starting element
    for (i = 1; i <= n; i++)
    {
     
        // If curr_sum exceeds the sum,
        // then remove the starting elements
        while (curr_sum - (i - start) *
            Math.abs(minEle) > targetSum &&
                                    start < i)
        {
            curr_sum = curr_sum - arr[start] -
                    Math.abs(minEle);
            start++;
        }
     
        // If curr_sum becomes equal to sum,
        // then return true
        if (curr_sum - (i - start) *
                Math.abs(minEle) == targetSum)
        {
            document.write("Sum found between indexes " +
                                    start + " and " + (i - 1));
            return;
        }
     
        // Add this element to curr_sum
        if (i < n)
        {
            curr_sum = curr_sum + arr[i] +
                            Math.abs(minEle);
        }
    }
     
    // If we reach here, then no subarray
    document.write("No subarray found");
}
     
// Driver Code
     
    let arr = [ 10, -12, 2, -2, -20, 10 ];
    let n = arr.length;
     
    let sum = -10;
     
    subArraySum(arr, n, sum);
 
 
// This code is contributed by sravan kumar
</script>

Output:

Sum found between indexes 1 and 2

My Personal Notes

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Find subarray with given sum with negatives allowed in constant space

C++

Java

Python3

C#

Javascript