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; } |
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. |
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 = 4 print (atMostSum(arr, n, k)) # This code is contributed by "Abhishek Sharma 44" |
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 |
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 ?> |
Output:
5
Time Complexity : O(n)
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