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Maximize the bitwise OR of an array
• Difficulty Level : Medium
• Last Updated : 27 Aug, 2020

Given an array of N integers. The bitwise OR of all the elements of the array has to be maximized by performing one task. The task is to multiply any element of the array at-most k times with a given integer x.

Examples :

Input: a = {1, 1, 1}, k = 1, x = 2
Output: 3
Explanation: Any possible choice of doing one element
of the array will result the same three numbers 1, 1, 2.
So, the result is 1 | 1 | 2 = 3.

Input: a = {1, 2, 4, 8}, k = 2, x = 3
Output: 79

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

Approach: Precompute the prefix and suffix OR arrays.
In one iteration, multiply an element with x^k and do Bitwise OR it with prefix OR i.e. Bitwise OR of all previous elements and suffix OR i.e. Bitwise OR of all next elements and return the maximum value after all iterations.

## C++

 `// C++ program to maximize the Bitwise ` `// OR Sum in given array ` `#include ` `using` `namespace` `std; ` ` `  `// Function to maximize the bitwise ` `// OR sum ` `int` `maxOR(``long` `long` `arr[], ``int` `n, ``int` `k, ``int` `x) ` `{ ` `    ``long` `long` `preSum[n + 1], suffSum[n + 1]; ` `    ``long` `long` `res, ``pow` `= 1; ` ` `  `    ``// Compute x^k ` `    ``for` `(``int` `i = 0; i < k; i++) ` `        ``pow` `*= x; ` ` `  `    ``// Find prefix bitwise OR ` `    ``preSum[0] = 0; ` `    ``for` `(``int` `i = 0; i < n; i++) ` `        ``preSum[i + 1] = preSum[i] | arr[i]; ` ` `  `    ``// Find suffix bitwise OR ` `    ``suffSum[n] = 0; ` `    ``for` `(``int` `i = n - 1; i >= 0; i--) ` `        ``suffSum[i] = suffSum[i + 1] | arr[i]; ` ` `  `    ``// Find maximum OR  value ` `    ``res = 0; ` `    ``for` `(``int` `i = 0; i < n; i++) ` `        ``res = max(res, preSum[i] | (arr[i] * ``pow``) | suffSum[i + 1]); ` ` `  `    ``return` `res; ` `} ` ` `  `// Drivers code ` `int` `main() ` `{ ` `    ``long` `long` `arr[] = { 1, 2, 4, 8 }; ` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]); ` `    ``int` `k = 2, x = 3; ` ` `  `    ``cout << maxOR(arr, n, k, x) << ``"\n"``; ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java program to maximize the Bitwise ` `// OR Sum in given array ` `import` `java.io.*; ` ` `  `class` `GFG { ` `     `  `    ``// Function to maximize the bitwise OR sum ` `    ``public` `static` `long` `maxOR(``long` `arr[], ``int` `n, ` `                                  ``int` `k, ``int` `x) ` `    ``{ ` `        ``long` `preSum[] = ``new` `long``[n + ``1``]; ` `        ``long` `suffSum[] = ``new` `long``[n + ``1``]; ` `        ``long` `res = ``0``, pow = ``1``; ` ` `  `        ``// Compute x^k ` `        ``for` `(``int` `i = ``0``; i < k; i++) ` `            ``pow *= x; ` ` `  `        ``// Find prefix bitwise OR ` `        ``preSum[``0``] = ``0``; ` `        ``for` `(``int` `i = ``0``; i < n; i++) ` `            ``preSum[i + ``1``] = preSum[i] | arr[i]; ` ` `  `        ``// Find suffix bitwise OR ` `        ``suffSum[n] = ``0``; ` `        ``for` `(``int` `i = n - ``1``; i >= ``0``; i--) ` `            ``suffSum[i] = suffSum[i + ``1``] | arr[i]; ` ` `  `        ``// Find maximum OR value ` `        ``res = ``0``; ` `        ``for` `(``int` `i = ``0``; i < n; i++) ` `            ``res = Math.max(res, preSum[i] |  ` `                ``(arr[i] * pow) | suffSum[i + ``1``]); ` ` `  `        ``return` `res; ` `    ``} ` ` `  `    ``// Drivers code ` `    ``public` `static` `void` `main(String args[]) ` `    ``{ ` `        ``long` `arr[] = { ``1``, ``2``, ``4``, ``8` `}; ` `        ``int` `n = ``4``; ` `        ``int` `k = ``2``, x = ``3``; ` `         `  `        ``long` `ans = maxOR(arr, n, k, x); ` `        ``System.out.println(ans); ` `    ``} ` `} ` ` `  `// This code is contributed by Jaideep Pyne `

## Python 3

 `# Python3 program to maximize the Bitwise ` `# OR Sum in given array ` ` `  `# Function to maximize the bitwise ` `# OR sum ` `def` `maxOR(arr, n, k, x): ` ` `  `    ``preSum ``=` `[``0``] ``*` `(n ``+` `1``)  ` `    ``suffSum ``=` `[``0``] ``*` `(n ``+` `1``) ` `    ``pow` `=` `1` ` `  `    ``# Compute x^k ` `    ``for` `i ``in` `range``(``0` `,k): ` `        ``pow` `*``=` `x ` ` `  `    ``# Find prefix bitwise OR ` `    ``preSum[``0``] ``=` `0` `    ``for` `i ``in` `range``(``0``, n): ` `        ``preSum[i ``+` `1``] ``=` `preSum[i] | arr[i] ` ` `  `    ``# Find suffix bitwise OR ` `    ``suffSum[n] ``=` `0` `    ``for` `i ``in` `range``(n``-``1``, ``-``1``, ``-``1``): ` `        ``suffSum[i] ``=` `suffSum[i ``+` `1``] | arr[i] ` ` `  `    ``# Find maximum OR value ` `    ``res ``=` `0` `    ``for` `i ``in` `range``(``0` `,n): ` `        ``res ``=` `max``(res, preSum[i] |  ` `           ``(arr[i] ``*` `pow``) | suffSum[i ``+` `1``]) ` ` `  `    ``return` `res ` ` `  `# Drivers code ` `arr ``=` `[``1``, ``2``, ``4``, ``8` `] ` `n ``=` `len``(arr)  ` `k ``=` `2` `x ``=` `3` `print``(maxOR(arr, n, k, x)) ` ` `  `# This code is contributed by Smitha `

## C#

 `// C# program to maximize the Bitwise ` `// OR Sum in given array ` `using` `System; ` ` `  `class` `GFG { ` `     `  `    ``// Function to maximize the bitwise OR sum ` `    ``public` `static` `long` `maxOR(``long` `[]arr, ``int` `n, ` `                                  ``int` `k, ``int` `x) ` `    ``{ ` `        ``long` `[]preSum = ``new` `long``[n + 1]; ` `        ``long` `[]suffSum = ``new` `long``[n + 1]; ` `        ``long` `res = 0, pow = 1; ` ` `  `        ``// Compute x^k ` `        ``for` `(``int` `i = 0; i < k; i++) ` `            ``pow *= x; ` ` `  `        ``// Find prefix bitwise OR ` `        ``preSum[0] = 0; ` `        ``for` `(``int` `i = 0; i < n; i++) ` `            ``preSum[i + 1] = preSum[i] | arr[i]; ` ` `  `        ``// Find suffix bitwise OR ` `        ``suffSum[n] = 0; ` `        ``for` `(``int` `i = n - 1; i >= 0; i--) ` `            ``suffSum[i] = suffSum[i + 1] | arr[i]; ` ` `  `        ``// Find maximum OR value ` `        ``res = 0; ` `        ``for` `(``int` `i = 0; i < n; i++) ` `            ``res = Math.Max(res, preSum[i] |  ` `                ``(arr[i] * pow) | suffSum[i + 1]); ` ` `  `        ``return` `res; ` `    ``} ` ` `  `    ``// Drivers code ` `    ``public` `static` `void` `Main() ` `    ``{ ` `        ``long` `[]arr = { 1, 2, 4, 8 }; ` `        ``int` `n = 4; ` `        ``int` `k = 2, x = 3; ` `         `  `        ``long` `ans = maxOR(arr, n, k, x); ` `        ``Console.Write(ans); ` `    ``} ` `} ` ` `  `// This code is contributed by Smitha `

## PHP

 `= 0; ``\$i``--) ` `        ``\$suffSum``[``\$i``] = ``\$suffSum``[``\$i` `+ 1] |  ` `                                ``\$arr``[``\$i``]; ` ` `  `    ``// Find maximum OR value ` `    ``\$res` `= 0; ` `    ``for` `(``\$i` `= 0; ``\$i` `< ``\$n``; ``\$i``++) ` `        ``\$res` `= max(``\$res``, ``\$preSum``[``\$i``] |  ` `                   ``(``\$arr``[``\$i``] * ``\$pow``) |  ` `                    ``\$suffSum``[``\$i` `+ 1]); ` ` `  `    ``return` `\$res``; ` `} ` ` `  `// Driver Code ` `\$arr` `= ``array``(1, 2, 4, 8); ` `\$n` `= sizeof(``\$arr``); ` `\$k` `= 2; ``\$x` `= 3; ` ` `  `echo` `maxOR(``\$arr``, ``\$n``, ``\$k``, ``\$x``),``"\n"``; ` ` `  `// This code is contributed by jit_t ` `?> `

Output :

```79
```

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