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Count distinct ways to replace array elements such that product of the array becomes even
• Last Updated : 26 Mar, 2021

Given an array arr[] consisting of N odd integers, the task is to count the different number of ways to make the product of all array elements even, by repeatedly changing any set of elements to any values. Since the count can be very large, print it to modulo 109 + 7.

Examples:

Input: arr[] = {1, 3}
Output: 3
Explanation: All possible ways to make the product of array elements odd are as follows:
Replace arr by any even integer. The array arr[] modifies to {even, 3}. Therefore, the product of the array = even * 3 = even.
Replace arr by any even integer. The array arr[] modifies to {1, even}. Therefore, the product of the array = 1 * even = even.
Replace arr and arr by even integers. Since both array elements become even, the product of the array becomes even. Therefore, the total number of distinct ways to make the array even is 3.

Input: arr[] = {1, 2, 3, 4, 5}
Output: 31

Approach: The idea to solve the given problem is based on the observation that the product of an array is even only when at least one even element is present in the array. Therefore, the total number of distinct ways can be calculated by the number of distinct subsets of the given array.

Below is the implementation of the above approach:

## C++

 `// C++ program for the above approach``#include ``#define M 1000000007``using` `namespace` `std;` `// Function to find the value of (x^y)``long` `long` `power(``long` `long` `x, ``long` `long` `y,``                ``long` `long` `p)``{``    ``// Stores the result``    ``long` `long` `res = 1;` `    ``while` `(y > 0) {` `        ``// If y is odd, then``        ``// multiply x with res``        ``if` `(y & 1)``            ``res = (res * x) % p;` `        ``// y must be even now``        ``y = y >> 1;` `        ``// Update x``        ``x = (x * x) % p;``    ``}``    ``return` `res;``}` `// Function to count the number of ways``// to make the product of an array even``// by replacing array elements``int` `totalOperations(``int` `arr[], ``int` `N)``{``    ``// Find the value ( 2 ^ N ) % M``    ``long` `long` `res = power(2, N, M);` `    ``// Exclude empty subset``    ``res--;` `    ``// Print the answer``    ``cout << res;``}` `// Driver Code``int` `main()``{``    ``int` `arr[] = { 1, 2, 3, 4, 5 };``    ``int` `N = ``sizeof``(arr) / ``sizeof``(arr);` `    ``totalOperations(arr, N);` `    ``return` `0;``}`

## Java

 `// Java program for the above approach``import` `java.io.*;` `class` `GFG{``    ` `static` `long` `M = ``1000000007``;` `// Function to find the value of (x^y)``static` `long` `power(``long` `x, ``long` `y, ``long` `p)``{``    ` `    ``// Stores the result``    ``long` `res = ``1``;`` ` `    ``while` `(y > ``0``)``    ``{``        ` `        ``// If y is odd, then``        ``// multiply x with res``        ``if` `((y & ``1``) > ``0``)``            ``res = (res * x) % p;`` ` `        ``// y must be even now``        ``y = y >> ``1``;`` ` `        ``// Update x``        ``x = (x * x) % p;``    ``}``    ``return` `res;``}`` ` `// Function to count the number of ways``// to make the product of an array even``// by replacing array elements``static` `int` `totalOperations(``int` `arr[], ``int` `N)``{``    ` `    ``// Find the value ( 2 ^ N ) % M``    ``long` `res = power(``2``, N, M);`` ` `    ``// Exclude empty subset``    ``res--;`` ` `    ``// Print the answer``    ``System.out.print(res);``    ``return` `0``;``}`` ` `// Driver Code``public` `static` `void` `main(String[] args)``{``    ``int` `arr[] = { ``1``, ``2``, ``3``, ``4``, ``5` `};``    ``int` `N = arr.length;``    ` `    ``totalOperations(arr, N);``}``}` `// This code is contributed by rag2127`

## Python3

 `# Python3 program for the above approach``M ``=` `1000000007` `# Function to find the value of (x^y)``def` `power(x, y, p):``    ` `    ``global` `M``    ` `    ``# Stores the result``    ``res ``=` `1` `    ``while` `(y > ``0``):` `        ``# If y is odd, then``        ``# multiply x with res``        ``if` `(y & ``1``):``            ``res ``=` `(res ``*` `x) ``%` `p;` `        ``# y must be even now``        ``y ``=` `y >> ``1` `        ``# Update x``        ``x ``=` `(x ``*` `x) ``%` `p` `    ``return` `res` `# Function to count the number of ways``# to make the product of an array even``# by replacing array elements``def` `totalOperations(arr, N):``    ` `    ``# Find the value ( 2 ^ N ) % M``    ``res ``=` `power(``2``, N, M)` `    ``# Exclude empty subset``    ``res``-``=``1` `    ``# Print the answer``    ``print` `(res)` `# Driver Code``if` `__name__ ``=``=` `'__main__'``:``    ` `    ``arr ``=` `[``1``, ``2``, ``3``, ``4``, ``5``]``    ``N ``=` `len``(arr)` `    ``totalOperations(arr, N)` `# This code is contributed by mohit kumar 29`

## C#

 `// C# program for the above approach``using` `System;``class` `GFG {``    ` `static` `long` `M = 1000000007;` `// Function to find the value of (x^y)``static` `long` `power(``long` `x, ``long` `y, ``long` `p)``{``    ` `    ``// Stores the result``    ``long` `res = 1;`` ` `    ``while` `(y > 0)``    ``{``        ` `        ``// If y is odd, then``        ``// multiply x with res``        ``if` `((y & 1) > 0)``            ``res = (res * x) % p;`` ` `        ``// y must be even now``        ``y = y >> 1;`` ` `        ``// Update x``        ``x = (x * x) % p;``    ``}``    ``return` `res;``}`` ` `// Function to count the number of ways``// to make the product of an array even``// by replacing array elements``static` `int` `totalOperations(``int``[] arr, ``int` `N)``{``    ` `    ``// Find the value ( 2 ^ N ) % M``    ``long` `res = power(2, N, M);`` ` `    ``// Exclude empty subset``    ``res--;`` ` `    ``// Print the answer``    ``Console.Write(res);``    ``return` `0;``}` `// Calculating gcd``static` `int` `gcd(``int` `a, ``int` `b)``{``    ``if` `(b == 0)``        ``return` `a;``        ` `    ``return` `gcd(b, a % b);``}` `// Driver code``static` `void` `Main()``{``    ``int``[] arr = { 1, 2, 3, 4, 5 };``    ``int` `N = arr.Length;``    ` `    ``totalOperations(arr, N);``}``}` `// This code is contributed by sanjoy_62.`

## Javascript

 ``
Output:
`31`

Time Complexity: O(log N)
Auxiliary Space: O(1)

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