Find the largest subarray with 0 sum
Given an array of integers, find length of the largest subarray with sum equals to 0.
Examples:
Input: arr[] = {15, 2, 2, 8, 1, 7, 10, 23}; Output: 5 The largest subarray with 0 sum is 2, 2, 8, 1, 7 Input: arr[] = {1, 2, 3} Output: 0 There is no subarray with 0 sum Input: arr[] = {1, 0, 3} Output: 1
A simple solution is to consider all subarrays one by one and check the sum of every subarray. We can run two loops: the outer loop picks a starting point i and the inner loop tries all subarrays starting from i. Time complexity of this method is O(n^{2}).
Below are implementations of this solution.
 C/C++

/* A simple C++ program to find largest subarray with 0 sum */
#include<bits/stdc++.h>
using
namespace
std;
// Returns length of the largest subarray with 0 sum
int
maxLen(
int
arr[],
int
n)
{
int
max_len = 0;
// Initialize result
// Pick a starting point
for
(
int
i = 0; i < n; i++)
{
// Initialize currr_sum for every starting point
int
curr_sum = 0;
// try all subarrays starting with 'i'
for
(
int
j = i; j < n; j++)
{
curr_sum += arr[j];
// If curr_sum becomes 0, then update max_len
// if required
if
(curr_sum == 0)
max_len = max(max_len, ji+1);
}
}
return
max_len;
}
// Driver program to test above function
int
main()
{
int
arr[] = {15, 2, 2, 8, 1, 7, 10, 23};
int
n =
sizeof
(arr)/
sizeof
(arr[0]);
cout <<
"Length of the longest 0 sum subarray is "
<< maxLen(arr, n);
return
0;
}
Output:
Length of the longest 0 sum subarray is 5
We can Use Hashing to solve this problem in O(n) time. The idea is to iterate through the array and for every element arr[i], calculate sum of elements form 0 to i (this can simply be done as sum += arr[i]). If the current sum has been seen before, then there is a zero sum array. Hashing is used to store the sum values, so that we can quickly store sum and find out whether the current sum is seen before or not.
Following are implementations of the above approach.
 Java

// A Java program to find maximum length subarray with 0 sum
import
java.util.HashMap;
class
MaxLenZeroSumSub {
// Returns length of the maximum length subarray with 0 sum
static
int
maxLen(
int
arr[])
{
// Creates an empty hashMap hM
HashMap<Integer, Integer> hM =
new
HashMap<Integer, Integer>();
int
sum =
0
;
// Initialize sum of elements
int
max_len =
0
;
// Initialize result
// Traverse through the given array
for
(
int
i =
0
; i < arr.length; i++)
{
// Add current element to sum
sum += arr[i];
if
(arr[i] ==
0
&& max_len ==
0
)
max_len =
1
;
if
(sum ==
0
)
max_len = i+
1
;
// Look this sum in hash table
Integer prev_i = hM.get(sum);
// If this sum is seen before, then update max_len
// if required
if
(prev_i !=
null
)
max_len = Math.max(max_len, iprev_i);
else
// Else put this sum in hash table
hM.put(sum, i);
}
return
max_len;
}
// Drive method
public
static
void
main(String arg[])
{
int
arr[] = {
15
, 
2
,
2
, 
8
,
1
,
7
,
10
,
23
};
System.out.println(
"Length of the longest 0 sum subarray is "
+ maxLen(arr));
}
}
Output:
Length of the longest 0 sum subarray is 5
Time Complexity of this solution can be considered as O(n) under the assumption that we have good hashing function that allows insertion and retrieval operations in O(1) time.
Disclaimer: This does not belong to TechCodeBit, its an article taken from the below
source and credits.
source and credits:http://www.geeksforgeeks.org/findthelargestsubarraywith0sum/
We have built the accelerating growthoriented website for budding engineers and aspiring job holders of technology companies such as Google, Facebook, and Amazon
If you would like to study our free courses you can join us at
http://www.techcodebit.com. #techcodebit #google #microsoft #facebook #interview portal #jobplacements
#technicalguide