Longest Subarray having sum of elements atmost ‘k’
Given an array of integers, our goal is to find the length of largest subarray having sum of its elements atmost ‘k’ where k>0.
Examples:
Input : arr[] = {1, 2, 1, 0, 1, 1, 0},
k = 4
Output : 5
Explanation:
{1, 2, 1} => sum = 4, length = 3
{1, 2, 1, 0}, {2, 1, 0, 1} => sum = 4, length = 4
{1, 0, 1, 1, 0} =>5 sum = 3, length = 5
Method 1 (Brute Force)
Find all the subarrays whose sum is less than or equal to k and return the one with largest length.
Time Complexity : O(n^2)
Method 2 (Efficient):
An efficient approach is to use sliding window technique.
- Traverse the array and check if on adding the current element its sum is less than or equal to k.
- If it’s less than k then add it to sum and increase the count.
-
- Else
- Remove the first element of subarray and decrease the count.
- Again check if on adding the current element its sum is less than or equal to k.
- If it’s less than k then add it to sum and increase the count.
- Keep track of Maximum count.
.
C++
// A C++ program to find longest subarray with // sum of elements at-least k. #include <bits/stdc++.h> using namespace std; // function to find the length of largest subarray // having sum atmost k. int atMostSum(int arr[], int n, int k) { int sum = 0; int cnt = 0, maxcnt = 0; for (int i = 0; i < n; i++) { // If adding current element doesn't // cross limit add it to current window if ((sum + arr[i]) <= k) { sum += arr[i]; cnt++; } // Else, remove first element of current // window and add the current element else if(sum!=0) { sum = sum - arr[i - cnt] + arr[i]; } // keep track of max length. maxcnt = max(cnt, maxcnt); } return maxcnt; } // Driver function int main() { int arr[] = {1, 2, 1, 0, 1, 1, 0}; int n = sizeof(arr) / sizeof(arr[0]); int k = 4; cout << atMostSum(arr, n, k); return 0; } |
chevron_right
filter_none
Java
// Java program to find longest subarray with // sum of elements at-least k. import java.util.*; class GFG { // function to find the length of largest // subarray having sum atmost k. public static int atMostSum(int arr[], int n, int k) { int sum = 0; int cnt = 0, maxcnt = 0; for (int i = 0; i < n; i++) { // If adding current element doesn't // cross limit add it to current window if ((sum + arr[i]) <= k) { sum += arr[i]; cnt++; } // Else, remove first element of current // window. else if(sum!=0) { sum = sum - arr[i - cnt] + arr[i]; } // keep track of max length. maxcnt = Math.max(cnt, maxcnt); } return maxcnt; } /* Driver program to test above function */ public static void main(String[] args) { int arr[] = { 1, 2, 1, 0, 1, 1, 0 }; int n = arr.length; int k = 4; System.out.print(atMostSum(arr, n, k)); } } // This code is contributed by Arnav Kr. Mandal. |
chevron_right
filter_none
Python3
# Python3 program to find longest subarray # with sum of elements at-least k. # function to find the length of largest # subarray having sum atmost k. def atMostSum(arr, n, k): _sum = 0 cnt = 0 maxcnt = 0 for i in range(n): # If adding current element doesn't # Cross limit add it to current window if ((_sum + arr[i]) <= k): _sum += arr[i] cnt += 1 # Else, remove first element of current # window and add the current element elif(sum != 0): _sum = _sum - arr[i - cnt] + arr[i] # keep track of max length. maxcnt = max(cnt, maxcnt) return maxcnt # Driver function arr = [1, 2, 1, 0, 1, 1, 0] n = len(arr) k = 4print(atMostSum(arr, n, k)) # This code is contributed by "Abhishek Sharma 44" |
chevron_right
filter_none
C#
// C# program to find longest subarray // with sum of elements at-least k. using System; class GFG { // function to find the length of largest // subarray having sum atmost k. public static int atMostSum(int []arr, int n, int k) { int sum = 0; int cnt = 0, maxcnt = 0; for (int i = 0; i < n; i++) { // If adding current element doesn't // cross limit add it to current window if ((sum + arr[i]) <= k) { sum += arr[i]; cnt++; } // Else, remove first element // of current window. else if(sum!=0) { sum = sum - arr[i - cnt] + arr[i]; } // keep track of max length. maxcnt = Math.Max(cnt, maxcnt); } return maxcnt; } // Driver Code public static void Main() { int []arr = {1, 2, 1, 0, 1, 1, 0}; int n = arr.Length; int k = 4; Console.Write(atMostSum(arr, n, k)); } } // This code is contributed by Nitin Mittal |
chevron_right
filter_none
PHP
<?php // A PHP program to find longest // subarray with sum of elements // at-least k. // function to find the length // of largest subarray having // sum atmost k. function atMostSum(&$arr, $n, $k) { $sum = 0; $cnt = 0; $maxcnt = 0; for($i = 0; $i < $n; $i++) { // If adding current element // doesn't cross limit add // it to current window if (($sum + $arr[$i]) <= $k) { $sum += $arr[$i] ; $cnt += 1 ; } // Else, remove first element // of current window and add // the current element else if($sum != 0) $sum = $sum - $arr[$i - $cnt] + $arr[$i]; // keep track of max length. $maxcnt = max($cnt, $maxcnt); } return $maxcnt; } // Driver Code $arr = array(1, 2, 1, 0, 1, 1, 0); $n = sizeof($arr); $k = 4; print(atMostSum($arr, $n, $k)); // This code is contributed // by ChitraNayal ?> |
chevron_right
filter_none
Output:
5
Time Complexity : O(n)
This article is contributed by Kshitiz gupta. 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.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.
