# Count subarrays with equal number of 1’s and 0’s

• Difficulty Level : Hard
• Last Updated : 31 Aug, 2021

Given an array arr[] of size n containing 0 and 1 only. The problem is to count the subarrays having an equal number of 0’s and 1’s.

Examples:

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```Input : arr[] = {1, 0, 0, 1, 0, 1, 1}
Output : 8
The index range for the 8 sub-arrays are:
(0, 1), (2, 3), (0, 3), (3, 4), (4, 5)
(2, 5), (0, 5), (1, 6)```

The problem is closely related to the Largest subarray with an equal number of 0’s and 1’s.
Approach: Following are the steps:

1. Consider all 0’s in arr[] as -1.
2. Create a hash table that holds the count of each sum[i] value, where sum[i] = sum(arr+..+arr[i]), for i = 0 to n-1.
3. Now start calculating the cumulative sum and then we get an incremental count of 1 for that sum represented as an index in the hash table. Arrays of each pair of positions with the same value in the cumulative sum constitute a continuous range with an equal number of 1’s and 0’s.
4. Now traverse the hash table and get the frequency of each element in the hash table. Let frequency be denoted as freq. For each freq > 1 we can choose any two pairs of indices of a sub-array by (freq * (freq – 1)) / 2 number of ways. Do the same for all freq and sum up the result will be the number of all possible sub-arrays containing the equal number of 1’s and 0’s.
5. Also, add freq of the sum of 0 to the hash table for the final result.

Explanation:
Considering all 0’s as -1, if sum[i] == sum[j], where sum[i] = sum(arr+..+arr[i]) and sum[j] = sum(arr+..+arr[j]) and ‘i’ is less than ‘j’, then sum(arr[i+1]+..+arr[j]) must be 0. It can only be 0 if arr(i+1, .., j) contains an equal number of 1’s and 0’s.

## C++

 `// C++ implementation to count subarrays with``// equal number of 1's and 0's``#include ` `using` `namespace` `std;` `// function to count subarrays with``// equal number of 1's and 0's``int` `countSubarrWithEqualZeroAndOne(``int` `arr[], ``int` `n)``{``    ``// 'um' implemented as hash table to store``    ``// frequency of values obtained through``    ``// cumulative sum``    ``unordered_map<``int``, ``int``> um;``    ``int` `curr_sum = 0;` `    ``// Traverse original array and compute cumulative``    ``// sum and increase count by 1 for this sum``    ``// in 'um'. Adds '-1' when arr[i] == 0``    ``for` `(``int` `i = 0; i < n; i++) {``        ``curr_sum += (arr[i] == 0) ? -1 : arr[i];``        ``um[curr_sum]++;``    ``}` `    ``int` `count = 0;``    ``// traverse the hash table 'um'``    ``for` `(``auto` `itr = um.begin(); itr != um.end(); itr++) {` `        ``// If there are more than one prefix subarrays``        ``// with a particular sum``        ``if` `(itr->second > 1)``            ``count += ((itr->second * (itr->second - 1)) / 2);``    ``}` `    ``// add the subarrays starting from 1st element and``    ``// have equal number of 1's and 0's``    ``if` `(um.find(0) != um.end())``        ``count += um;` `    ``// required count of subarrays``    ``return` `count;``}` `// Driver program to test above``int` `main()``{``    ``int` `arr[] = { 1, 0, 0, 1, 0, 1, 1 };``    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr);``    ``cout << ``"Count = "``         ``<< countSubarrWithEqualZeroAndOne(arr, n);``    ``return` `0;``}`

## Java

 `// Java implementation to count subarrays with``// equal number of 1's and 0's``import` `java.util.*;` `class` `GFG``{` `// function to count subarrays with``// equal number of 1's and 0's``static` `int` `countSubarrWithEqualZeroAndOne(``int` `arr[], ``int` `n)``{``    ``// 'um' implemented as hash table to store``    ``// frequency of values obtained through``    ``// cumulative sum``    ``Map um = ``new` `HashMap<>();``    ``int` `curr_sum = ``0``;` `    ``// Traverse original array and compute cumulative``    ``// sum and increase count by 1 for this sum``    ``// in 'um'. Adds '-1' when arr[i] == 0``    ``for` `(``int` `i = ``0``; i < n; i++) {``        ``curr_sum += (arr[i] == ``0``) ? -``1` `: arr[i];``        ``um.put(curr_sum, um.get(curr_sum)==``null``?``1``:um.get(curr_sum)+``1``);``    ``}` `    ``int` `count = ``0``;``    ` `    ``// traverse the hash table 'um'``    ``for` `(Map.Entry itr : um.entrySet())``    ``{` `        ``// If there are more than one prefix subarrays``        ``// with a particular sum``        ``if` `(itr.getValue() > ``1``)``            ``count += ((itr.getValue()* (itr.getValue()- ``1``)) / ``2``);``    ``}` `    ``// add the subarrays starting from 1st element and``    ``// have equal number of 1's and 0's``    ``if` `(um.containsKey(``0``))``        ``count += um.get(``0``);` `    ``// required count of subarrays``    ``return` `count;``}` `// Driver program to test above``public` `static` `void` `main(String[] args)``{``    ``int` `arr[] = { ``1``, ``0``, ``0``, ``1``, ``0``, ``1``, ``1` `};``    ``int` `n = arr.length;``    ``System.out.println(``"Count = "``        ``+ countSubarrWithEqualZeroAndOne(arr, n));``}``}` `// This code is contributed by Rajput-Ji`

## Python3

 `# Python3 implementation to count``# subarrays with equal number``# of 1's and 0's` `# function to count subarrays with``# equal number of 1's and 0's``def` `countSubarrWithEqualZeroAndOne (arr, n):` `    ``# 'um' implemented as hash table``    ``# to store frequency of values``    ``# obtained through cumulative sum``    ``um ``=` `dict``()``    ``curr_sum ``=` `0``    ` `    ``# Traverse original array and compute``    ``# cumulative sum and increase count``    ``# by 1 for this sum in 'um'.``    ``# Adds '-1' when arr[i] == 0``    ``for` `i ``in` `range``(n):``        ``curr_sum ``+``=` `(``-``1` `if` `(arr[i] ``=``=` `0``) ``else` `arr[i])``        ``if` `um.get(curr_sum):``            ``um[curr_sum]``+``=``1``        ``else``:``            ``um[curr_sum]``=``1``    ` `    ``count ``=` `0``    ` `    ``# traverse the hash table 'um'``    ``for` `itr ``in` `um:``        ` `        ``# If there are more than one``        ``# prefix subarrays with a``        ``# particular sum``        ``if` `um[itr] > ``1``:``            ``count ``+``=` `((um[itr] ``*` `int``(um[itr] ``-` `1``)) ``/` `2``)``    ` `    ``# add the subarrays starting from``    ``# 1st element and have equal``    ``# number of 1's and 0's``    ``if` `um.get(``0``):``        ``count ``+``=` `um[``0``]``    ` `    ``# required count of subarrays``    ``return` `int``(count)``    ` `# Driver code to test above``arr ``=` `[ ``1``, ``0``, ``0``, ``1``, ``0``, ``1``, ``1` `]``n ``=` `len``(arr)``print``(``"Count ="``,``    ``countSubarrWithEqualZeroAndOne(arr, n))` `# This code is contributed by "Sharad_Bhardwaj".`

## C#

 `// C# implementation to count subarrays``// with equal number of 1's and 0's``using` `System;``using` `System.Collections.Generic;` `class` `GFG``{` `// function to count subarrays with``// equal number of 1's and 0's``static` `int` `countSubarrWithEqualZeroAndOne(``int` `[]arr,``                                          ``int` `n)``{``    ``// 'um' implemented as hash table to store``    ``// frequency of values obtained through``    ``// cumulative sum``    ``Dictionary<``int``,``               ``int``> mp = ``new` `Dictionary<``int``,``                                        ``int``>();``    ``int` `curr_sum = 0;` `    ``// Traverse original array and compute cumulative``    ``// sum and increase count by 1 for this sum``    ``// in 'um'. Adds '-1' when arr[i] == 0``    ``for` `(``int` `i = 0; i < n; i++)``    ``{``        ``curr_sum += (arr[i] == 0) ? -1 : arr[i];``        ``if``(mp.ContainsKey(curr_sum))``        ``{``            ``var` `v = mp[curr_sum];``            ``mp.Remove(curr_sum);``            ``mp.Add(curr_sum, ++v);``        ``}``        ``else``            ``mp.Add(curr_sum, 1);``    ``}` `    ``int` `count = 0;``    ` `    ``// traverse the hash table 'um'``    ``foreach``(KeyValuePair<``int``, ``int``> itr ``in` `mp)``    ``{` `        ``// If there are more than one prefix subarrays``        ``// with a particular sum``        ``if` `(itr.Value > 1)``            ``count += ((itr.Value* (itr.Value - 1)) / 2);``    ``}` `    ``// add the subarrays starting from 1st element``    ``// and have equal number of 1's and 0's``    ``if` `(mp.ContainsKey(0))``        ``count += mp;` `    ``// required count of subarrays``    ``return` `count;``}` `// Driver program to test above``public` `static` `void` `Main(String[] args)``{``    ``int` `[]arr = { 1, 0, 0, 1, 0, 1, 1 };``    ``int` `n = arr.Length;``    ``Console.WriteLine(``"Count = "` `+``            ``countSubarrWithEqualZeroAndOne(arr, n));``}``}` `// This code is contributed by PrinciRaj1992`

## Javascript

 ``

Output:

`Count = 8`

Time Complexity: O(n).
Auxiliary Space: O(n).

Another approach:

## C++

 `#include ` `using` `namespace` `std;` `int` `countSubarrWithEqualZeroAndOne(``int` `arr[], ``int` `n)``{``    ``map<``int``, ``int``> mp;``    ``int` `sum = 0;``    ``int` `count = 0;``    ``for` `(``int` `i = 0; i < n; i++) {``        ``// Replacing 0's in array with -1``        ``if` `(arr[i] == 0)``            ``arr[i] = -1;` `        ``sum += arr[i];` `        ``// If sum = 0, it implies number of 0's and 1's are``        ``// equal from arr..arr[i]``        ``if` `(sum == 0)``            ``count++;` `          ``//if mp[sum] exists then add "frequency-1" to count``        ``if` `(mp[sum])``            ``count += mp[sum];``      ` `          ``//if frequency of "sum" is zero then we initialize that frequency to 1``          ``//if its not 0, we increment it``        ``if` `(mp[sum] == 0)``            ``mp[sum] = 1;``        ``else``            ``mp[sum]++;``    ``}``    ``return` `count;``}` `int` `main()``{``    ``int` `arr[] = { 1, 0, 0, 1, 0, 1, 1 };` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr);` `    ``cout << ``"count="``         ``<< countSubarrWithEqualZeroAndOne(arr, n);``}`

## Java

 `import` `java.util.HashMap;``import` `java.util.Map;` `// Java implementation to count subarrays with``// equal number of 1's and 0's``public` `class` `Main {` `    ``// Function that returns count of sub arrays``    ``// with equal numbers of 1's and 0's``    ``static` `int` `countSubarrWithEqualZeroAndOne(``int``[] arr,``                                              ``int` `n)``    ``{``        ``Map myMap = ``new` `HashMap<>();``        ``int` `sum = ``0``;``        ``int` `count = ``0``;``        ``for` `(``int` `i = ``0``; i < n; i++) {``            ``// Replacing 0's in array with -1``            ``if` `(arr[i] == ``0``)``                ``arr[i] = -``1``;` `            ``sum += arr[i];` `            ``// If sum = 0, it implies number of 0's and 1's``            ``// are equal from arr..arr[i]``            ``if` `(sum == ``0``)``                ``count++;` `            ``if` `(myMap.containsKey(sum))``                ``count += myMap.get(sum);` `            ``if` `(!myMap.containsKey(sum))``                ``myMap.put(sum, ``1``);``            ``else``                ``myMap.put(sum, myMap.get(sum) + ``1``);``        ``}``        ``return` `count;``    ``}` `    ``// main function``    ``public` `static` `void` `main(String[] args)``    ``{``        ``int` `arr[] = { ``1``, ``0``, ``0``, ``1``, ``0``, ``1``, ``1` `};``        ``int` `n = arr.length;``        ``System.out.println(``            ``"Count = "``            ``+ countSubarrWithEqualZeroAndOne(arr, n));``    ``}``}`

## Python3

 `# Python3 implementation to count subarrays``# with equal number of 1's and 0's`  `def` `countSubarrWithEqualZeroAndOne(arr, n):``    ``mp ``=` `dict``()``    ``Sum` `=` `0``    ``count ``=` `0` `    ``for` `i ``in` `range``(n):` `        ``# Replacing 0's in array with -1``        ``if` `(arr[i] ``=``=` `0``):``            ``arr[i] ``=` `-``1` `        ``Sum` `+``=` `arr[i]` `        ``# If Sum = 0, it implies number of``        ``# 0's and 1's are equal from arr..arr[i]``        ``if` `(``Sum` `=``=` `0``):``            ``count ``+``=` `1` `        ``if` `(``Sum` `in` `mp.keys()):``            ``count ``+``=` `mp[``Sum``]` `        ``mp[``Sum``] ``=` `mp.get(``Sum``, ``0``) ``+` `1` `    ``return` `count`  `# Driver Code``arr ``=` `[``1``, ``0``, ``0``, ``1``, ``0``, ``1``, ``1``]` `n ``=` `len``(arr)` `print``(``"count ="``,``      ``countSubarrWithEqualZeroAndOne(arr, n))` `# This code is contributed by mohit kumar`

## C#

 `// C# implementation to count subarrays with``// equal number of 1's and 0's``using` `System;``using` `System.Collections.Generic;` `class` `GFG {` `    ``// Function that returns count of sub arrays``    ``// with equal numbers of 1's and 0's``    ``static` `int` `countSubarrWithEqualZeroAndOne(``int``[] arr,``                                              ``int` `n)``    ``{``        ``Dictionary<``int``, ``int``> myMap``            ``= ``new` `Dictionary<``int``, ``int``>();``        ``int` `sum = 0;``        ``int` `count = 0;``        ``for` `(``int` `i = 0; i < n; i++) {``            ``// Replacing 0's in array with -1``            ``if` `(arr[i] == 0)``                ``arr[i] = -1;` `            ``sum += arr[i];` `            ``// If sum = 0, it implies number of 0's and 1's``            ``// are equal from arr..arr[i]``            ``if` `(sum == 0)``                ``count++;` `            ``if` `(myMap.ContainsKey(sum))``                ``count += myMap[sum];` `            ``if` `(!myMap.ContainsKey(sum))``                ``myMap.Add(sum, 1);``            ``else` `{``                ``var` `v = myMap[sum] + 1;``                ``myMap.Remove(sum);``                ``myMap.Add(sum, v);``            ``}``        ``}``        ``return` `count;``    ``}` `    ``// Driver code``    ``public` `static` `void` `Main(String[] args)``    ``{``        ``int``[] arr = { 1, 0, 0, 1, 0, 1, 1 };``        ``int` `n = arr.Length;``        ``Console.WriteLine(``            ``"Count = "``            ``+ countSubarrWithEqualZeroAndOne(arr, n));``    ``}``}` `// This code is contributed by 29AjayKumar`

## Javascript

 ``

Output:

`Count = 8`

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