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Construct the Array using given bitwise AND, OR and XOR
• Difficulty Level : Expert
• Last Updated : 26 Sep, 2020

Given Bitwise AND, OR, and XOR of N elements of an array denoted by a, b, c. The task is to find the elements of the array. If there exists no such array then print “-1”.
Examples:

Input: N = 3, a = 4, b = 6, c = 6.
Output: {4, 4, 6}
Explanation:
Bitwise AND of array = 4 & 4 & 6 = 4
Bitwise OR of array = 4 | 4 | 6 = 6
Bitwise XOR of array = 4 ^ 4 ^ 6 = 6
Input: N = 2, a = 4, b = 6, c = 6.
Output: -1

Approach:

1. For Bitwise AND, if ith bit is set in a, then in the array every element must have ith bit set because if even one element’s ith bit is 0 then bitwise AND of the array will result in ith bit to be 0.
2. Secondly, if ith bit is not set in a, then OR and XOR values need to be handled simultaneously. If ith bit is set in b, then at least one element must have ith bit set. So, set ith bit in the only first element of the array.
3. Now, if ith bit was set in b then ith bit must be checked in c. If that bit is set in c then there’s no problem as the first element’s ith bit is already set so 1 ^ 0 = 1. If that bit is not set in c then set the ith bit of the second element. Now, there will not be any effect in b and for c, 1 ^ 1 will be 0.
4. Then, just calculate Bitwise AND, OR, and XOR of the array to check if it’s equal or not. If results are not equal then the array is not possible else given array is the answer.

Below is the implementation of the approach:

## C++

 `// C++ program for the above approach``#include ``using` `namespace` `std;` `// Function to find the array``void` `findArray(``int` `n, ``int` `a,``               ``int` `b, ``int` `c)``{``    ``int` `arr[n + 1] = {};` `    ``// Loop through all bits in number``    ``for` `(``int` `bit = 30; bit >= 0; bit--) {` `        ``// If bit is set in AND``        ``// then set it in every element``        ``// of the array``        ``int` `set = a & (1 << bit);``        ``if` `(set) {``            ``for` `(``int` `i = 0; i < n; i++)``                ``arr[i] |= set;``        ``}` `        ``// If bit is not set in AND``        ``else` `{` `            ``// But set in b(OR)``            ``if` `(b & (1 << bit)) {` `                ``// Set bit position``                ``// in first element``                ``arr |= (1 << bit);` `                ``// If bit is not set in c``                ``// then set it in second``                ``// element to keep xor as``                ``// zero for bit position``                ``if` `(!(c & (1 << bit))) {``                    ``arr |= (1 << bit);``                ``}``            ``}``        ``}``    ``}` `    ``int` `aa = INT_MAX, bb = 0, cc = 0;` `    ``// Calculate AND, OR``    ``// and XOR of array``    ``for` `(``int` `i = 0; i < n; i++) {``        ``aa &= arr[i];``        ``bb |= arr[i];``        ``cc ^= arr[i];``    ``}` `    ``// Check if values are equal or not``    ``if` `(a == aa && b == bb && c == cc) {``        ``for` `(``int` `i = 0; i < n; i++)``            ``cout << arr[i] << ``" "``;``    ``}` `    ``// If not, then array``    ``// is not possible``    ``else``        ``cout << ``"-1"``;``}` `// Driver Code``int` `main()``{``    ``// Given Bitwise AND, OR, and XOR``    ``int` `n = 3, a = 4, b = 6, c = 6;` `    ``// Function Call``    ``findArray(n, a, b, c);` `    ``return` `0;``}`

## Java

 `// Java program for the above approach``import` `java.io.*;` `class` `GFG{` `// Function to find the array``static` `void` `findArray(``int` `n, ``int` `a,``                      ``int` `b, ``int` `c)``{``    ``int` `arr[] = ``new` `int``[n + ``1``];` `    ``// Loop through all bits in number``    ``for``(``int` `bit = ``30``; bit >= ``0``; bit--)``    ``{``        ` `       ``// If bit is set in AND``       ``// then set it in every element``       ``// of the array``       ``int` `set = a & (``1` `<< bit);``       ``if` `(set != ``0``)``       ``{``           ``for``(``int` `i = ``0``; i < n; i++)``              ``arr[i] |= set;``       ``}``       ` `       ``// If bit is not set in AND``       ``else``       ``{``           ` `           ``// But set in b(OR)``           ``if` `((b & (``1` `<< bit)) != ``0``)``           ``{``               ` `               ``// Set bit position``               ``// in first element``               ``arr[``0``] |= (``1` `<< bit);``               ` `               ``// If bit is not set in c``               ``// then set it in second``               ``// element to keep xor as``               ``// zero for bit position``               ``if` `((c & (``1` `<< bit)) == ``0``)``               ``{``                   ``arr[``1``] |= (``1` `<< bit);``               ``}``           ``}``       ``}``    ``}``    ``int` `aa = Integer.MAX_VALUE, bb = ``0``, cc = ``0``;``    ` `    ``// Calculate AND, OR``    ``// and XOR of array``    ``for``(``int` `i = ``0``; i < n; i++)``    ``{``       ``aa &= arr[i];``       ``bb |= arr[i];``       ``cc ^= arr[i];``    ``}` `    ``// Check if values are equal or not``    ``if` `(a == aa && b == bb && c == cc)``    ``{``        ``for``(``int` `i = ``0``; i < n; i++)``           ``System.out.print(arr[i] + ``" "``);``    ``}` `    ``// If not, then array``    ``// is not possible``    ``else``        ``System.out.println(``"-1"``);``}` `// Driver code``public` `static` `void` `main(String[] args)``{``    ` `    ``// Given Bitwise AND, OR, and XOR``    ``int` `n = ``3``, a = ``4``, b = ``6``, c = ``6``;` `    ``// Function Call``    ``findArray(n, a, b, c);``}``}` `// This code is contributed by Pratima Pandey`

## Python3

 `# Python3 program for``# the above approach``import` `sys` `# Function to find the array``def` `findArray(n, a, b, c):` `    ``arr ``=` `[``0``] ``*` `(n ``+` `1``)` `    ``# Loop through all bits in number``    ``for` `bit ``in` `range` `(``30``, ``-``1``, ``-``1``):` `        ``# If bit is set in AND``        ``# then set it in every element``        ``# of the array``        ``set` `=` `a & (``1` `<< bit)``        ``if` `(``set``):``            ``for` `i ``in` `range` `(n):``                ``arr[i] |``=` `set` `        ``# If bit is not set in AND``        ``else` `:` `            ``# But set in b(OR)``            ``if` `(b & (``1` `<< bit)):` `                ``# Set bit position``                ``# in first element``                ``arr[``0``] |``=` `(``1` `<< bit)` `                ``# If bit is not set in c``                ``# then set it in second``                ``# element to keep xor as``                ``# zero for bit position``                ``if` `(``not` `(c & (``1` `<< bit))):``                    ``arr[``1``] |``=` `(``1` `<< bit)` `    ``aa ``=` `sys.maxsize``    ``bb ``=` `0``    ``cc ``=` `0` `    ``# Calculate AND, OR``    ``# and XOR of array``    ``for` `i ``in` `range` `(n):``        ``aa &``=` `arr[i]``        ``bb |``=` `arr[i]``        ``cc ^``=` `arr[i]` `    ``# Check if values are equal or not``    ``if` `(a ``=``=` `aa ``and` `b ``=``=` `bb ``and` `c ``=``=` `cc):``        ``for` `i ``in` `range` `(n):``            ``print` `(arr[i], end ``=` `" "``)``   ` `    ``# If not, then array``    ``# is not possible``    ``else``:``        ``print` `(``"-1"``)` `# Driver Code``if` `__name__ ``=``=``"__main__"``:``  ` `    ``# Given Bitwise AND, OR, and XOR``    ``n ``=` `3``    ``a ``=` `4``    ``b ``=` `6``    ``c ``=` `6` `    ``# Function Call``    ``findArray(n, a, b, c)``    ` `# This code is contributed by Chitranayal`

## C#

 `// C# program for the above approach``using` `System;` `class` `GFG{` `// Function to find the array``static` `void` `findArray(``int` `n, ``int` `a,``                      ``int` `b, ``int` `c)``{``    ``int` `[]arr = ``new` `int``[n + 1];` `    ``// Loop through all bits in number``    ``for``(``int` `bit = 30; bit >= 0; bit--)``    ``{``       ` `       ``// If bit is set in AND``       ``// then set it in every element``       ``// of the array``       ``int` `set` `= a & (1 << bit);``       ``if` `(``set` `!= 0)``       ``{``           ``for``(``int` `i = 0; i < n; i++)``              ``arr[i] |= ``set``;``       ``}``       ` `       ``// If bit is not set in AND``       ``else``       ``{``           ` `           ``// But set in b(OR)``           ``if` `((b & (1 << bit)) != 0)``           ``{``               ` `               ``// Set bit position``               ``// in first element``               ``arr |= (1 << bit);``               ` `               ``// If bit is not set in c``               ``// then set it in second``               ``// element to keep xor as``               ``// zero for bit position``               ``if` `((c & (1 << bit)) == 0)``               ``{``                   ``arr |= (1 << bit);``               ``}``           ``}``       ``}``    ``}``    ``int` `aa = ``int``.MaxValue, bb = 0, cc = 0;``    ` `    ``// Calculate AND, OR``    ``// and XOR of array``    ``for``(``int` `i = 0; i < n; i++)``    ``{``       ``aa &= arr[i];``       ``bb |= arr[i];``       ``cc ^= arr[i];``    ``}` `    ``// Check if values are equal or not``    ``if` `(a == aa && b == bb && c == cc)``    ``{``        ``for``(``int` `i = 0; i < n; i++)``           ``Console.Write(arr[i] + ``" "``);``    ``}` `    ``// If not, then array``    ``// is not possible``    ``else``        ``Console.WriteLine(``"-1"``);``}` `// Driver code``public` `static` `void` `Main(String[] args)``{``    ` `    ``// Given Bitwise AND, OR, and XOR``    ``int` `n = 3, a = 4, b = 6, c = 6;` `    ``// Function Call``    ``findArray(n, a, b, c);``}``}` `// This code is contributed by gauravrajput1`
Output:
```6 4 4

```

Time Complexity: O(31*N)

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