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

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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++ implementation to find the smallest sum // contiguous subarray #include    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 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);     cout << "Smallest sum: "          << smallestSumSubarr(arr, n);     return 0;      }

 // Java implementation to find the smallest sum // contiguous subarray class GFG {            // function to find the smallest sum contiguous     // subarray     static int smallestSumSubarr(int arr[], int n)     {                    // to store the minimum value that is          // ending up to the current index         int min_ending_here = 2147483647;                    // to store the minimum value encountered         // so far         int min_so_far = 2147483647;                    // 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 = Math.min(min_so_far,                                    min_ending_here);                  }                    // required smallest sum contiguous          // subarray value         return min_so_far;     }            // Driver method     public static void main(String[] args)     {                    int arr[] = {3, -4, 2, -3, -1, 7, -5};         int n = arr.length;                    System.out.print("Smallest sum: "                 + smallestSumSubarr(arr, n));     } }    // This code is contributed by Anant Agarwal.

 # 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.maxsize            # to store the minimum value encountered so far     min_so_far = sys.maxsize            # 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

 // C# implementation to find the  // smallest sum contiguous subarray using System;    class GFG {        // function to find the smallest sum      // contiguous subarray     static int smallestSumSubarr(int[] arr, int n)     {         // to store the minimum value that is         // ending up to the current index         int min_ending_here = 2147483647;            // to store the minimum value encountered         // so far         int min_so_far = 2147483647;            // 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 = Math.Min(min_so_far,                                 min_ending_here);         }            // required smallest sum contiguous         // subarray value         return min_so_far;     }        // Driver method     public static void Main()     {            int[] arr = { 3, -4, 2, -3, -1, 7, -5 };         int n = arr.Length;            Console.Write("Smallest sum: " +              smallestSumSubarr(arr, n));     } }    // This code is contributed by Sam007

 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 = array(3, -4, 2, -3, -1, 7, -5);     \$n = count(\$arr) ;     echo "Smallest sum: "          .smallestSumSubarr(\$arr, \$n);    // This code is contributed by Sam007 ?>

Output:
Smallest sum: -6

Time Complexity: O(n)

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Improved By : Sam007, Nikhil.01a

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