Given an array of positive and negative numbers, the task is to find if there is a subarray (of size at least one) with 0 sum.
Examples:
Input: {4, 2, -3, 1, 6}
Output: true
Explanation:
There is a subarray with zero sum from index 1 to 3.
Input: {4, 2, 0, 1, 6}
Output: true
Explanation: The third element is zero. A single element is also a sub-array.
Input: {-3, 2, 3, 1, 6}
Output: false
Subarray with 0 sum using Nested loop:
Generate every subarray and calcuate the sum of each subarray. Check if subarray sum is 0 then return true. Otherwise, if no such subarray found then return false.
Below is the implementation of the above approach:
C++
// C++ program to find if
// there is a zero sum subarray
#include <iostream>
using namespace std;
bool subArrayExists(int arr[], int n)
{
for (int i = 0; i < n; i++) {
// starting point of the sub arrray and
// sum is initialized with first element of subarray
// a[i]
int sum = arr[i];
if (sum == 0)
return true;
for (int j = i + 1; j < n; j++) {
// we are finding the sum till jth index
// starting from ith index
sum += arr[j];
if (sum == 0)
return true;
}
}
return false;
}
// Driver's code
int main()
{
int arr[] = { -3, 2, 3, 1, 6 };
int N = sizeof(arr) / sizeof(arr[0]);
// Function call
if (subArrayExists(arr, N))
cout << "Found a subarray with 0 sum";
else
cout << "No Such Sub Array Exists!";
return 0;
}
// This code is contributed by Tapesh(tapeshdua420)
// Java program to find if
// there is a zero sum subarray
import java.util.Arrays;
public class Main {
public static boolean subArrayExists(int arr[], int n)
{
for (int i = 0; i < n; i++) {
int sum = arr[i];
if (sum == 0)
return true;
for (int j = i + 1; j < n; j++) {
sum += arr[j];
if (sum == 0)
return true;
}
}
return false;
}
// Driver's code
public static void main(String[] args)
{
int arr[] = { -3, 2, 3, 1, 6 };
int N = arr.length;
// Function call
if (subArrayExists(arr, N))
System.out.println("Found a subarray with 0 sum");
else
System.out.println("No Such Sub Array Exists!");
}
}
// This code is contributed by Utkarsh Kumar
def subArrayExists(arr, n):
for i in range(n):
# Starting point of the subarray and
# sum is initialized with the first element of subarray
sum = arr[i]
if sum == 0:
return True
for j in range(i + 1, n):
# We are finding the sum till the jth index
# starting from the ith index
sum += arr[j]
if sum == 0:
return True
return False
# Driver's code
if __name__ == "__main__":
arr = [-3, 2, 3, 1, 6]
N = len(arr)
# Function call
if subArrayExists(arr, N):
print("Found a subarray with 0 sum")
else:
print("No Such Sub Array Exists!")
// C# program to find if
// there is a zero sum subarray
using System;
public class GFG {
public static bool subArrayExists(int[] arr, int n)
{
for (int i = 0; i < n; i++) {
int sum = arr[i];
if (sum == 0)
return true;
for (int j = i + 1; j < n; j++) {
sum += arr[j];
if (sum == 0)
return true;
}
}
return false;
}
// Driver's code
public static void Main()
{
int[] arr = { -3, 2, 3, 1, 6 };
int N = arr.Length;
// Function call
if (subArrayExists(arr, N))
Console.WriteLine("Found a subarray with 0 sum");
else
Console.WriteLine("No Such Sub Array Exists!");
}
}
// This code is contributed by Pushpesh Raj
function subArrayExists(arr) {
const n = arr.length;
for (let i = 0; i < n; i++) {
// Starting point of the subarray, and the sum is initialized with the first element of the subarray.
let sum = arr[i];
if (sum === 0)
return true;
for (let j = i + 1; j < n; j++) {
// We are finding the sum until the jth index starting from the ith index.
sum += arr[j];
if (sum === 0)
return true;
}
}
return false;
}
const arr = [-3, 2, 3, 1, 6];
// Function call
if (subArrayExists(arr))
console.log("Found a subarray with 0 sum");
else
console.log("No such subarray exists!");
OutputNo Such Sub Array Exists!
Time Complexity: O(N2)
Auxiliary Space: O(1)
Subarray with 0 sum using Hashing:
The idea is to iterate through the array and for every element arr[i], calculate the sum of elements from 0 to i (this can simply be done as sum += arr[i]). If the current sum has been seen before, then there must be a zero-sum subarray. Hashing is used to store the sum values so that sum can be stored quickly and find out whether the current sum is seen before or not.
Follow the given steps to solve the problem:
- Declare a variable sum, to store the sum of prefix elements
- Traverse the array and at each index, add the element into the sum and check if this sum exists earlier. If the sum exists, then return true
- Also, insert every prefix sum into a map, so that later on it can be found whether the current sum is seen before or not
- At the end return false, as no such subarray is found
Illustration:
arr[] = {1, 4, -2, -2, 5, -4, 3}
Consider all prefix sums, one can notice that there is a subarray with 0 sum when :
- Either a prefix sum repeats
- Or, prefix sum becomes 0.
Prefix sums for above array are: 1, 5, 3, 1, 6, 2, 5
Since prefix sum 1 repeats, we have a subarray with 0 sum.
Below is the Implementation of the above approach:
C++
// C++ program to find if
// there is a zero sum subarray
#include <bits/stdc++.h>
using namespace std;
bool subArrayExists(int arr[], int N)
{
unordered_set<int> sumSet;
// Traverse through array
// and store prefix sums
int sum = 0;
for (int i = 0; i < N; i++) {
sum += arr[i];
// If prefix sum is 0 or
// it is already present
if (sum == 0 || sumSet.find(sum) != sumSet.end())
return true;
sumSet.insert(sum);
}
return false;
}
// Driver's code
int main()
{
int arr[] = {-3, 2, 3, 1, 6};
int N = sizeof(arr) / sizeof(arr[0]);
// Function call
if (subArrayExists(arr, N))
cout << "Found a subarray with 0 sum";
else
cout << "No Such Sub Array Exists!";
return 0;
}
// Java program to find
// if there is a zero sum subarray
import java.util.HashSet;
import java.util.Set;
class ZeroSumSubarray {
// Returns true if arr[]
// has a subarray with sero sum
static Boolean subArrayExists(int arr[])
{
// Creates an empty hashset hs
Set<Integer> hs = new HashSet<Integer>();
// Initialize sum of elements
int sum = 0;
// Traverse through the given array
for (int i = 0; i < arr.length; i++) {
// Add current element to sum
sum += arr[i];
// Return true in following cases
// a) Current element is 0
// b) sum of elements from 0 to i is 0
// c) sum is already present in hash set
if (arr[i] == 0 || sum == 0 || hs.contains(sum))
return true;
// Add sum to hash set
hs.add(sum);
}
// We reach here only when there is
// no subarray with 0 sum
return false;
}
// Driver's code
public static void main(String arg[])
{
int arr[] = {-3, 2, 3, 1, 6};
// Function call
if (subArrayExists(arr))
System.out.println(
"Found a subarray with 0 sum");
else
System.out.println("No Such Sub Array Exists!");
}
}
# python3 program to find if
# there is a zero sum subarray
def subArrayExists(arr, N):
# traverse through array
# and store prefix sums
n_sum = 0
s = set()
for i in range(N):
n_sum += arr[i]
# If prefix sum is 0 or
# it is already present
if n_sum == 0 or n_sum in s:
return True
s.add(n_sum)
return False
# Driver's code
if __name__ == '__main__':
arr = [-3, 2, 3, 1, 6]
N = len(arr)
# Function call
if subArrayExists(arr, N) == True:
print("Found a subarray with 0 sum")
else:
print("No Such sub array exits!")
# This code is contributed by Shrikant13
// C# program to find if there
// is a zero sum subarray
using System;
using System.Collections.Generic;
class GFG {
// Returns true if arr[] has
// a subarray with sero sum
static bool SubArrayExists(int[] arr)
{
// Creates an empty HashSet hM
HashSet<int> hs = new HashSet<int>();
// Initialize sum of elements
int sum = 0;
// Traverse through the given array
for (int i = 0; i < arr.Length; i++) {
// Add current element to sum
sum += arr[i];
// Return true in following cases
// a) Current element is 0
// b) sum of elements from 0 to i is 0
// c) sum is already present in hash set
if (arr[i] == 0 || sum == 0 || hs.Contains(sum))
return true;
// Add sum to hash set
hs.Add(sum);
}
// Reach here only when there is
// no subarray with 0 sum
return false;
}
// Driver's code
public static void Main()
{
int[] arr = {-3, 2, 3, 1, 6};
// Function call
if (SubArrayExists(arr))
Console.WriteLine(
"Found a subarray with 0 sum");
else
Console.WriteLine("No Such Sub Array Exists!");
}
}
// A Javascript program to
// find if there is a zero sum subarray
const subArrayExists = (arr) => {
const sumSet = new Set();
// Traverse through array
// and store prefix sums
let sum = 0;
for (let i = 0 ; i < arr.length ; i++)
{
sum += arr[i];
// If prefix sum is 0
// or it is already present
if (sum === 0 || sumSet.has(sum))
return true;
sumSet.add(sum);
}
return false;
}
// Driver code
const arr = [-3, 2, 3, 1, 6];
if (subArrayExists(arr))
console.log("Found a subarray with 0 sum");
else
console.log("No Such Sub Array Exists!");
OutputNo Such Sub Array Exists!
Time Complexity: O(N) under the assumption that a good hashing function is used, that allows insertion and retrieval operations in O(1) time.
Auxiliary Space: O(N) Here extra space is required for hashing
Similar Reads
Basics & Prerequisites
Data Structures
Array Data StructureIn this article, we introduce array, implementation in different popular languages, its basic operations and commonly seen problems / interview questions. An array stores items (in case of C/C++ and Java Primitive Arrays) or their references (in case of Python, JS, Java Non-Primitive) at contiguous
3 min read
String in Data StructureA string is a sequence of characters. The following facts make string an interesting data structure.Small set of elements. Unlike normal array, strings typically have smaller set of items. For example, lowercase English alphabet has only 26 characters. ASCII has only 256 characters.Strings are immut
2 min read
Hashing in Data StructureHashing is a technique used in data structures that efficiently stores and retrieves data in a way that allows for quick access. Hashing involves mapping data to a specific index in a hash table (an array of items) using a hash function. It enables fast retrieval of information based on its key. The
2 min read
Linked List Data StructureA linked list is a fundamental data structure in computer science. It mainly allows efficient insertion and deletion operations compared to arrays. Like arrays, it is also used to implement other data structures like stack, queue and deque. Here’s the comparison of Linked List vs Arrays Linked List:
2 min read
Stack Data StructureA Stack is a linear data structure that follows a particular order in which the operations are performed. The order may be LIFO(Last In First Out) or FILO(First In Last Out). LIFO implies that the element that is inserted last, comes out first and FILO implies that the element that is inserted first
2 min read
Queue Data StructureA Queue Data Structure is a fundamental concept in computer science used for storing and managing data in a specific order. It follows the principle of "First in, First out" (FIFO), where the first element added to the queue is the first one to be removed. It is used as a buffer in computer systems
2 min read
Tree Data StructureTree Data Structure is a non-linear data structure in which a collection of elements known as nodes are connected to each other via edges such that there exists exactly one path between any two nodes. Types of TreeBinary Tree : Every node has at most two childrenTernary Tree : Every node has at most
4 min read
Graph Data StructureGraph Data Structure is a collection of nodes connected by edges. It's used to represent relationships between different entities. If you are looking for topic-wise list of problems on different topics like DFS, BFS, Topological Sort, Shortest Path, etc., please refer to Graph Algorithms. Basics of
3 min read
Trie Data StructureThe Trie data structure is a tree-like structure used for storing a dynamic set of strings. It allows for efficient retrieval and storage of keys, making it highly effective in handling large datasets. Trie supports operations such as insertion, search, deletion of keys, and prefix searches. In this
15+ min read
Algorithms
Searching AlgorithmsSearching algorithms are essential tools in computer science used to locate specific items within a collection of data. In this tutorial, we are mainly going to focus upon searching in an array. When we search an item in an array, there are two most common algorithms used based on the type of input
2 min read
Sorting AlgorithmsA Sorting Algorithm is used to rearrange a given array or list of elements in an order. For example, a given array [10, 20, 5, 2] becomes [2, 5, 10, 20] after sorting in increasing order and becomes [20, 10, 5, 2] after sorting in decreasing order. There exist different sorting algorithms for differ
3 min read
Introduction to RecursionThe process in which a function calls itself directly or indirectly is called recursion and the corresponding function is called a recursive function. A recursive algorithm takes one step toward solution and then recursively call itself to further move. The algorithm stops once we reach the solution
14 min read
Greedy AlgorithmsGreedy algorithms are a class of algorithms that make locally optimal choices at each step with the hope of finding a global optimum solution. At every step of the algorithm, we make a choice that looks the best at the moment. To make the choice, we sometimes sort the array so that we can always get
3 min read
Graph AlgorithmsGraph is a non-linear data structure like tree data structure. The limitation of tree is, it can only represent hierarchical data. For situations where nodes or vertices are randomly connected with each other other, we use Graph. Example situations where we use graph data structure are, a social net
3 min read
Dynamic Programming or DPDynamic Programming is an algorithmic technique with the following properties.It is mainly an optimization over plain recursion. Wherever we see a recursive solution that has repeated calls for the same inputs, we can optimize it using Dynamic Programming. The idea is to simply store the results of
3 min read
Bitwise AlgorithmsBitwise algorithms in Data Structures and Algorithms (DSA) involve manipulating individual bits of binary representations of numbers to perform operations efficiently. These algorithms utilize bitwise operators like AND, OR, XOR, NOT, Left Shift, and Right Shift.BasicsIntroduction to Bitwise Algorit
4 min read
Advanced
Segment TreeSegment Tree is a data structure that allows efficient querying and updating of intervals or segments of an array. It is particularly useful for problems involving range queries, such as finding the sum, minimum, maximum, or any other operation over a specific range of elements in an array. The tree
3 min read
Pattern SearchingPattern searching algorithms are essential tools in computer science and data processing. These algorithms are designed to efficiently find a particular pattern within a larger set of data. Patten SearchingImportant Pattern Searching Algorithms:Naive String Matching : A Simple Algorithm that works i
2 min read
GeometryGeometry is a branch of mathematics that studies the properties, measurements, and relationships of points, lines, angles, surfaces, and solids. From basic lines and angles to complex structures, it helps us understand the world around us.Geometry for Students and BeginnersThis section covers key br
2 min read
Interview Preparation
Practice Problem