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; } |
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Java
// 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. |
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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.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 |
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C#
// 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 |
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PHP
<?php // PHP implementation to find the // smallest sum contiguous subarray // function to find the smallest // sum contiguous subarray function smallestSumSubarr($arr, $n) { // to store the minimum // value that is ending // up to the current index $min_ending_here = 999999; // to store the minimum value // encountered so far $min_so_far = 999999; // traverse the array elements for($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 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 ?> |
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Output:
Smallest sum: -6
Time Complexity: O(n)
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