# Find number of subarrays with XOR value a power of 2

Given an integer array, arr[] of size N. The XOR value of any subarray of arr[] is defined as the xor of all the integers in that subarray. The task is to find the number of sub-arrays with XOR value a power of 2. (1, 2, 4, 8, 16, ….)

Examples:

```Input :  arr[] = {2, 6, 7, 5, 8}
Output : 6
Subarrays : {2, 6}, {2}, {6, 7},  {6, 7, 5}, {7, 5}, {8}

Input : arr[] = {2, 4, 8, 16}
Output : 4
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach :

1. Maintain a hashmap which stores all the prefix XOR values and their counts.
2. At any index i, we need to find the number of subarrays which end at i and have XOR value a power of 2. We need to find for all the power of 2, the number of subarrays possible. For example. : Suppose current XOR value till index i is X, we need to find the number of subarrays which result in 16 (say S), so we need the count of prefix XOR Y such that (X^Y) = S or Y = S^X. Y can be find using Hash Map.
3. Perform Step 2, for all the index, add the output.

Below is the implementation of the above approach:

## C++

 `// C++ Program to count number of subarrays  ` `// with Bitwise-XOR as power of 2 ` ` `  `#include ` `#define ll long long int ` `#define MAX 10 ` `using` `namespace` `std; ` ` `  `// Function to find number of subarrays ` `int` `findSubarray(``int` `array[], ``int` `n) ` `{ ` `    ``// Hash Map to store prefix XOR values ` `    ``unordered_map<``int``, ``int``> mp; ` ` `  `    ``// When no element is selected ` `    ``mp.insert({ 0, 1 }); ` ` `  `    ``int` `answer = 0; ` `    ``int` `preXor = 0; ` `    ``for` `(``int` `i = 0; i < n; i++) { ` `        ``int` `value = 1; ` `        ``preXor ^= array[i]; ` ` `  `        ``// Check for all the powers of 2,  ` `        ``// till a MAX value ` `        ``for` `(``int` `j = 1; j <= MAX; j++) { ` `            ``int` `Y = value ^ preXor; ` `            ``if` `(mp.find(Y) != mp.end()) { ` `                ``answer += mp[Y]; ` `            ``} ` `            ``value *= 2; ` `        ``} ` ` `  `        ``// Insert Current prefixxor in Hash Map ` `        ``if` `(mp.find(preXor) != mp.end()) { ` `            ``mp[preXor]++; ` `        ``} ` `        ``else` `{ ` `            ``mp.insert({ preXor, 1 }); ` `        ``} ` `    ``} ` ` `  `    ``return` `answer; ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` `    ``int` `array[] = { 2, 6, 7, 5, 8 }; ` `     `  `    ``int` `n = ``sizeof``(array) / ``sizeof``(array); ` `     `  `    ``cout << findSubarray(array, n) << endl; ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java Program to count number of subarrays  ` `// with Bitwise-XOR as power of 2 ` `import` `java.util.*; ` ` `  `class` `GFG ` `{ ` ` `  `static` `int` `MAX = ``10``; ` ` `  `// Function to find number of subarrays ` `static` `int` `findSubarray(``int` `array[], ``int` `n) ` `{ ` `    ``// Hash Map to store prefix XOR values ` `    ``HashMap mp = ``new` `HashMap(); ` ` `  `    ``// When no element is selected ` `    ``mp.put(``0``, ``1``); ` ` `  `    ``int` `answer = ``0``; ` `    ``int` `preXor = ``0``; ` `    ``for` `(``int` `i = ``0``; i < n; i++)  ` `    ``{ ` `        ``int` `value = ``1``; ` `        ``preXor ^= array[i]; ` ` `  `        ``// Check for all the powers of 2,  ` `        ``// till a MAX value ` `        ``for` `(``int` `j = ``1``; j <= MAX; j++)  ` `        ``{ ` `            ``int` `Y = value ^ preXor; ` `            ``if` `(mp.containsKey(Y))  ` `            ``{ ` `                ``answer += mp.get(Y); ` `            ``} ` `            ``value *= ``2``; ` `        ``} ` ` `  `        ``// Insert Current prefixxor in Hash Map ` `        ``if` `(mp.containsKey(preXor))  ` `        ``{ ` `            ``mp.put(preXor,mp.get(preXor) + ``1``); ` `        ``} ` `        ``else`  `        ``{ ` `            ``mp.put(preXor, ``1``); ` `        ``} ` `    ``} ` `    ``return` `answer; ` `} ` ` `  `// Driver Code ` `public` `static` `void` `main (String[] args) ` `{ ` `    ``int` `array[] = { ``2``, ``6``, ``7``, ``5``, ``8` `}; ` `     `  `    ``int` `n = array.length; ` `     `  `    ``System.out.println(findSubarray(array, n)); ` `} ` `} ` ` `  `// This code is contributed by PrinciRaj1992 `

## Python3

 `# Python3 Program to count number of subarrays ` `# with Bitwise-XOR as power of 2 ` `MAX` `=` `10` ` `  `# Function to find number of subarrays ` `def` `findSubarray(array, n): ` `     `  `    ``# Hash Map to store prefix XOR values ` `    ``mp ``=` `dict``() ` ` `  `    ``# When no element is selected ` `    ``mp[``0``] ``=` `1` ` `  `    ``answer ``=` `0` `    ``preXor ``=` `0` `    ``for` `i ``in` `range``(n): ` `        ``value ``=` `1` `        ``preXor ^``=` `array[i] ` ` `  `        ``# Check for all the powers of 2, ` `        ``# till a MAX value ` `        ``for` `j ``in` `range``(``1``, ``MAX` `+` `1``): ` `            ``Y ``=` `value ^ preXor ` `            ``if` `( Y ``in` `mp.keys()): ` `                ``answer ``+``=` `mp[Y] ` ` `  `            ``value ``*``=` `2` ` `  `        ``# Insert Current prefixxor in Hash Map ` `        ``if` `(preXor ``in` `mp.keys()): ` `            ``mp[preXor] ``+``=` `1` ` `  `        ``else``: ` `            ``mp[preXor] ``=` `1` ` `  `    ``return` `answer ` ` `  `# Driver Code ` `array ``=` `[``2``, ``6``, ``7``, ``5``, ``8``] ` ` `  `n ``=` `len``(array) ` ` `  `print``(findSubarray(array, n)) ` ` `  `# This code is contributed by Mohit Kumar `

## C#

 `// C# Program to count number of subarrays  ` `// with Bitwise-XOR as power of 2 ` `using` `System; ` `using` `System.Collections.Generic; ` ` `  `class` `GFG ` `{ ` `static` `int` `MAX = 10; ` ` `  `// Function to find number of subarrays ` `static` `int` `findSubarray(``int` `[]array, ``int` `n) ` `{ ` `    ``// Hash Map to store prefix XOR values ` `    ``Dictionary<``int``, ` `               ``int``> mp = ``new` `Dictionary<``int``, ` `                                        ``int``>(); ` ` `  `    ``// When no element is selected ` `    ``mp.Add(0, 1); ` ` `  `    ``int` `answer = 0; ` `    ``int` `preXor = 0; ` `    ``for` `(``int` `i = 0; i < n; i++)  ` `    ``{ ` `        ``int` `value = 1; ` `        ``preXor ^= array[i]; ` ` `  `        ``// Check for all the powers of 2,  ` `        ``// till a MAX value ` `        ``for` `(``int` `j = 1; j <= MAX; j++)  ` `        ``{ ` `            ``int` `Y = value ^ preXor; ` `            ``if` `(mp.ContainsKey(Y))  ` `            ``{ ` `                ``answer += mp[Y]; ` `            ``} ` `            ``value *= 2; ` `        ``} ` ` `  `        ``// Insert Current prefixxor in Hash Map ` `        ``if` `(mp.ContainsKey(preXor))  ` `        ``{ ` `            ``mp[preXor] = mp[preXor] + 1; ` `        ``} ` `        ``else` `        ``{ ` `            ``mp.Add(preXor, 1); ` `        ``} ` `    ``} ` `    ``return` `answer; ` `} ` ` `  `// Driver Code ` `public` `static` `void` `Main (String[] args) ` `{ ` `    ``int` `[]array = { 2, 6, 7, 5, 8 }; ` `     `  `    ``int` `n = array.Length; ` `     `  `    ``Console.WriteLine(findSubarray(array, n)); ` `} ` `} ` `     `  `// This code is contributed by 29AjayKumar `

Output:

```6
```

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