Longest Subarray With Sum K
Last Updated :
11 Jan, 2025
Given an array arr[] of size n containing integers, the task is to find the length of the longest subarray having sum equal to the given value k.
Note: If there is no subarray with sum equal to k, return 0.
Examples:
Input: arr[] = [10, 5, 2, 7, 1, -10], k = 15
Output: 6
Explanation: Subarrays with sum = 15 are [5, 2, 7, 1], [10, 5] and [10, 5, 2, 7, 1, -10]. The length of the longest subarray with a sum of 15 is 6.
Input: arr[] = [-5, 8, -14, 2, 4, 12], k = -5
Output: 5
Explanation: Only subarray with sum = 15 is [-5, 8, -14, 2, 4] of length 5.
Input: arr[] = [10, -10, 20, 30], k = 5
Output: 0
Explanation: No subarray with sum = 5 is present in arr[].
[Naive Approach] Using Nested Loop - O(n^2) Time and O(1) Space
The idea is to check the sum of all the subarrays and return the length of the longest subarray having the sum k.
C++
// C++ program to find the length of the longest
// subarray having sum k using nested loop
#include <iostream>
#include <vector>
using namespace std;
// Function to find longest sub-array having sum k
int longestSubarray(vector<int>& arr, int k) {
int res = 0;
for (int i = 0; i < arr.size(); i++) {
// Sum of subarray from i to j
int sum = 0;
for (int j = i; j < arr.size(); j++) {
sum += arr[j];
// If subarray sum is equal to k
if (sum == k) {
// find subarray length and update result
int subLen = j - i + 1;
res = max(res, subLen);
}
}
}
return res;
}
int main() {
vector<int> arr = {10, 5, 2, 7, 1, -10};
int k = 15;
cout << longestSubarray(arr, k) << endl;
return 0;
}
// C program to find the length of the longest
// subarray having sum k using nested loop
#include <stdio.h>
// Function to find longest sub-array having sum k
int longestSubarray(int arr[], int n, int k) {
int res = 0;
for (int i = 0; i < n; i++) {
// Sum of subarray from i to j
int sum = 0;
for (int j = i; j < n; j++) {
sum += arr[j];
// If subarray sum is equal to k
if (sum == k) {
// Find subarray length and update result
int subLen = j - i + 1;
res = (res > subLen) ? res : subLen;
}
}
}
return res;
}
int main() {
int arr[] = {10, 5, 2, 7, 1, -10};
int k = 15;
int n = sizeof(arr) / sizeof(arr[0]);
printf("%d\n", longestSubarray(arr, n, k));
return 0;
}
// Java program to find the length of the longest
// subarray having sum k using nested loop
class GfG {
// Function to find longest sub-array having sum k
static int longestSubarray(int[] arr, int k) {
int res = 0;
for (int i = 0; i < arr.length; i++) {
// Sum of subarray from i to j
int sum = 0;
for (int j = i; j < arr.length; j++) {
sum += arr[j];
// If subarray sum is equal to k
if (sum == k) {
// find subarray length and update result
int subLen = j - i + 1;
res = Math.max(res, subLen);
}
}
}
return res;
}
public static void main(String[] args) {
int[] arr = {10, 5, 2, 7, 1, -10};
int k = 15;
System.out.println(longestSubarray(arr, k));
}
}
# Python program to find the length of the longest
# subarray having sum k using nested loop
# Function to find longest sub-array having sum k
def longestSubarray(arr, k):
res = 0
for i in range(len(arr)):
# Sum of subarray from i to j
sum = 0
for j in range(i, len(arr)):
sum += arr[j]
# If subarray sum is equal to k
if sum == k:
# find subarray length and update result
subLen = j - i + 1
res = max(res, subLen)
return res
if __name__ == "__main__":
arr = [10, 5, 2, 7, 1, -10]
k = 15
print(longestSubarray(arr, k))
// C# program to find the length of the longest
// subarray having sum k using nested loop
using System;
class GfG {
// Function to find longest sub-array having sum k
static int longestSubarray(int[] arr, int k) {
int res = 0;
for (int i = 0; i < arr.Length; i++) {
// Sum of subarray from i to j
int sum = 0;
for (int j = i; j < arr.Length; j++) {
sum += arr[j];
// If subarray sum is equal to k
if (sum == k) {
// find subarray length and update result
int subLen = j - i + 1;
res = Math.Max(res, subLen);
}
}
}
return res;
}
static void Main() {
int[] arr = {10, 5, 2, 7, 1, -10};
int k = 15;
Console.WriteLine(longestSubarray(arr, k));
}
}
// JavaScript program to find the length of the longest
// subarray having sum k using nested loop
// Function to find longest sub-array having sum k
function longestSubarray(arr, k) {
let res = 0;
for (let i = 0; i < arr.length; i++) {
// Sum of subarray from i to j
let sum = 0;
for (let j = i; j < arr.length; j++) {
sum += arr[j];
// If subarray sum is equal to k
if (sum === k) {
// find subarray length and update result
let subLen = j - i + 1;
res = Math.max(res, subLen);
}
}
}
return res;
}
// Driver Code
const arr = [10, 5, 2, 7, 1, -10];
const k = 15;
console.log(longestSubarray(arr, k));
[Expected Approach] Using Hash Map and Prefix Sum - O(n) Time and O(n) Space
If you take a closer look at this problem, this is mainly an extension of Longest Subarray with 0 sum.
The idea is based on the fact that if Sj - Si = k (where Si and Sj are prefix sums till index i and j respectively, and i < j), then the subarray between i+1 to j has sum equal to k.
For example, arr[] = [5, 2, -3, 4, 7] and k = 3. The value of S3 - S0= 3, it means the subarray from index 1 to 3 has sum equals to 3.
So we mainly compute prefix sums in the array and store these prefix sums in a hash table. And check if current prefix sum - k is already present. If current prefix sum - k is present in the hash table and is mapped to index j, then subarray from j to current index has sum equal to k.
Below are the main points to consider in your implementation.
- If we have the whole prefix having sum equal to k, we should prefer it as it would be the longest possible till that point.
- If there are multiple occurrences of a prefixSum, we must store index of the earliest occurrence of prefixSum because we need to find the longest subarray.
C++
// C++ program to find longest sub-array having sum k
// using Hash Map and Prefix Sum
#include <iostream>
#include <unordered_map>
#include <vector>
using namespace std;
// Function to find longest sub-array having sum k
int longestSubarray(vector<int>& arr, int k) {
unordered_map<int, int> mp;
int res = 0;
int prefSum = 0;
for (int i = 0; i < arr.size(); ++i) {
prefSum += arr[i];
// Check if the entire prefix sums to k
if (prefSum == k)
res = i + 1;
// If prefixSum - k exists in the map then there exist such
// subarray from (index of previous prefix + 1) to i.
else if (mp.find(prefSum - k) != mp.end())
res = max(res, i - mp[prefSum - k]);
// Store only first occurrence index of prefSum
if (mp.find(prefSum) == mp.end())
mp[prefSum] = i;
}
return res;
}
int main() {
vector<int> arr = {10, 5, 2, 7, 1, -10};
int k = 15;
cout << longestSubarray(arr, k) << endl;
}
// Java program to find longest sub-array having sum k
// using Hash Map and Prefix Sum
import java.util.HashMap;
import java.util.Map;
class GfG {
// Function to find longest sub-array having sum k
static int longestSubarray(int[] arr, int k) {
Map<Integer, Integer> mp = new HashMap<>();
int res = 0;
int prefSum = 0;
for (int i = 0; i < arr.length; ++i) {
prefSum += arr[i];
// Check if the entire prefix sums to k
if (prefSum == k)
res = i + 1;
// If prefixSum - k exists in the map then there exist such
// subarray from (index of previous prefix + 1) to i.
else if (mp.containsKey(prefSum - k))
res = Math.max(res, i - mp.get(prefSum - k));
// Store only first occurrence index of prefSum
if (!mp.containsKey(prefSum))
mp.put(prefSum, i);
}
return res;
}
public static void main(String[] args) {
int[] arr = {10, 5, 2, 7, 1, -10};
int k = 15;
System.out.println(longestSubarray(arr, k));
}
}
# Python program to find longest sub-array having sum k
# using Hash Map and Prefix Sum
# Function to find longest sub-array having sum k
def longestSubarray(arr, k):
mp = {}
res = 0
prefSum = 0
for i in range(len(arr)):
prefSum += arr[i]
# Check if the entire prefix sums to k
if prefSum == k:
res = i + 1
# If prefixSum - k exists in the map then there exist such
# subarray from (index of previous prefix + 1) to i.
elif (prefSum - k) in mp:
res = max(res, i - mp[prefSum - k])
# Store only first occurrence index of prefSum
if prefSum not in mp:
mp[prefSum] = i
return res
if __name__ == "__main__":
arr = [10, 5, 2, 7, 1, -10]
k = 15
print(longestSubarray(arr, k))
// C# program to find longest sub-array having sum k
// using Hash Map and Prefix Sum
using System;
using System.Collections.Generic;
class GfG {
// Function to find longest sub-array having sum k
static int longestSubarray(int[] arr, int k) {
Dictionary<int, int> mp = new Dictionary<int, int>();
int res = 0;
int prefSum = 0;
for (int i = 0; i < arr.Length; ++i) {
prefSum += arr[i];
// Check if the entire prefix sums to k
if (prefSum == k)
res = i + 1;
// If prefixSum - k exists in the map then there exist such
// subarray from (index of previous prefix + 1) to i.
else if (mp.ContainsKey(prefSum - k))
res = Math.Max(res, i - mp[prefSum - k]);
// Store only first occurrence index of prefSum
if (!mp.ContainsKey(prefSum))
mp[prefSum] = i;
}
return res;
}
static void Main() {
int[] arr = {10, 5, 2, 7, 1, -10};
int k = 15;
Console.WriteLine(longestSubarray(arr, k));
}
}
// JavaScript program to find longest sub-array having sum k
// using Hash Map and Prefix Sum
// Function to find longest sub-array having sum k
function longestSubarray(arr, k) {
let mp = new Map();
let res = 0;
let prefSum = 0;
for (let i = 0; i < arr.length; ++i) {
prefSum += arr[i];
// Check if the entire prefix sums to k
if (prefSum === k)
res = i + 1;
// If prefixSum - k exists in the map then there exist such
// subarray from (index of previous prefix + 1) to i.
else if (mp.has(prefSum - k))
res = Math.max(res, i - mp.get(prefSum - k));
// Store only first occurrence index of prefSum
if (!mp.has(prefSum))
mp.set(prefSum, i);
}
return res;
}
// Driver Code
const arr = [10, 5, 2, 7, 1, -10];
const k = 15;
console.log(longestSubarray(arr, k));
Related Problem
Largest subarray with equal number of 0s and 1s
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