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Count ways to construct array with even product from given array such that absolute difference of same indexed elements is at most 1
  • Last Updated : 11 Jan, 2021

Given an array A[] of size N, the task is to count the numbers of ways to construct an array B[] of size N, such that the absolute difference at the same indexed elements must be less than or equal to 1, i.e. abs(A[i] – B[i]) ≤ 1, and the product of elements of the array B[] must be an even number.

Examples:

Input: A[] = { 2, 3 } 
Output:
Explanation: 
Possible values of the array B[] are { { 1, 2 }, { 1, 4 }, { 2, 2 }, { 2, 4 }, { 3, 2 }, { 3, 4 } } 
Therefore, the required output is 7.

Input: A[] = { 90, 52, 56, 71, 44, 8, 13, 30, 57, 84 } 
Output: 58921 
 

Approach: The idea is to first count the number of ways to construct an array, B[] such that abs(A[i] – B[i]) <= 1 and then remove those arrays whose product of elements is not an even number. Follow the below steps to solve the problem:



  • Possible values of B[i] such that abs(A[i] – B[i]) <= 1 are { A[i], A[i] + 1, A[i] – 1 }. Therefore, the total count of ways to construct an array, B[] such that abs(A[i] – B[i]) less than or equal to 1 is 3N.
  • Traverse the array and store the count of even numbers in the array A[] say, X.
  • If A[i] is an even number then (A[i] – 1) and (A[i] + 1) must be an odd number. Therefore, the total count of ways to the construct array, B[] whose product is not an even number is 2X.
  • Finally, print the value of (3N – 2X).

Below is the implementation of the above approach:

C++

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// C++ program to implement
// the above approach
 
#include <bits/stdc++.h>
using namespace std;
 
// Function to find count the ways to construct
// an array, B[] such that abs(A[i] - B[i]) <=1
// and product of elements of B[] is even
void cntWaysConsArray(int A[], int N)
{
 
    // Stores count of arrays B[] such
    // that abs(A[i] - B[i]) <=1
    int total = 1;
 
    // Stores count of arrays B[] whose
    // product of elements is not even
    int oddArray = 1;
 
    // Traverse the array
    for (int i = 0; i < N; i++) {
 
        // Update total
        total = total * 3;
 
        // If A[i] is an even number
        if (A[i] % 2 == 0) {
 
            // Update oddArray
            oddArray *= 2;
        }
    }
 
    // Print 3^N - 2^X
    cout << total - oddArray << "\n";
}
 
// Driver Code
int main()
{
    int A[] = { 2, 4 };
    int N = sizeof(A) / sizeof(A[0]);
 
    cntWaysConsArray(A, N);
 
    return 0;
}

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Java

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// Java Program to implement the
// above approach
import java.util.*;
class GFG
{
  
// Function to find count the ways to construct
// an array, B[] such that abs(A[i] - B[i]) <=1
// and product of elements of B[] is even
static void cntWaysConsArray(int A[], int N)
{
 
    // Stores count of arrays B[] such
    // that abs(A[i] - B[i]) <=1
    int total = 1;
 
    // Stores count of arrays B[] whose
    // product of elements is not even
    int oddArray = 1;
 
    // Traverse the array
    for (int i = 0; i < N; i++)
    {
 
        // Update total
        total = total * 3;
 
        // If A[i] is an even number
        if (A[i] % 2 == 0)
        {
 
            // Update oddArray
            oddArray *= 2;
        }
    }
 
    // Print 3^N - 2^X
    System.out.println( total - oddArray);
}
  
// Driver Code
public static void main(String[] args)
{
    int A[] = { 2, 4 };
    int N = A.length;
    cntWaysConsArray(A, N);
}
}
 
// This code is contributed by code_hunt.

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Python3

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# Python3 program to implement
# the above approach
 
# Function to find count the ways to construct
# an array, B[] such that abs(A[i] - B[i]) <=1
# and product of elements of B[] is even
def cntWaysConsArray(A, N) :
 
    # Stores count of arrays B[] such
    # that abs(A[i] - B[i]) <=1
    total = 1;
 
    # Stores count of arrays B[] whose
    # product of elements is not even
    oddArray = 1;
 
    # Traverse the array
    for i in range(N) :
 
        # Update total
        total = total * 3;
 
        # If A[i] is an even number
        if (A[i] % 2 == 0) :
 
            # Update oddArray
            oddArray *= 2;
   
    # Print 3^N - 2^X
    print(total - oddArray);
 
# Driver Code
if __name__ == "__main__" :
    A = [ 2, 4 ];
    N = len(A);
    cntWaysConsArray(A, N);
     
    # This code is contributed by AnkThon

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C#

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// C# program to implement the
// above approach
using System;
 
class GFG{
  
// Function to find count the ways to construct
// an array, []B such that abs(A[i] - B[i]) <=1
// and product of elements of []B is even
static void cntWaysConsArray(int []A, int N)
{
     
    // Stores count of arrays []B such
    // that abs(A[i] - B[i]) <=1
    int total = 1;
 
    // Stores count of arrays []B whose
    // product of elements is not even
    int oddArray = 1;
 
    // Traverse the array
    for(int i = 0; i < N; i++)
    {
         
        // Update total
        total = total * 3;
 
        // If A[i] is an even number
        if (A[i] % 2 == 0)
        {
             
            // Update oddArray
            oddArray *= 2;
        }
    }
 
    // Print 3^N - 2^X
    Console.WriteLine(total - oddArray);
}
  
// Driver Code
public static void Main(String[] args)
{
    int []A = { 2, 4 };
    int N = A.Length;
     
    cntWaysConsArray(A, N);
}
}
 
// This code is contributed by shikhasingrajput

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Output: 

5

 

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

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