Find the number of ways to divide number into four parts such that a = c and b = d

Given a number N. Find the number of ways to divide a number into four parts(a, b, c, d) such that a = c and b = d and a not equal to b.

Examples:

Input : N = 6
Output : 1
Expalantion : four parts are {1, 2, 1, 2}

Input : N = 20
Output : 4
Expalantion : possible ways are {1, 1, 9, 9}, {2, 2, 8, 8}, {3, 3, 7, 7} and {4, 4, 6, 6}.

Approach :
If the given N is odd the answer is 0, because the sum of four parts will not be even number.

If n is divisible by 4 then answer will be n/4 -1(here a equals to b can be possible so subtract that possibility) otherwise n/4.

Below is the implementation of the above approach :

C++

// C++ implementation for above approach 
#include <bits/stdc++.h> 
using namespace std; 
  
// Function to find the number of ways to divide 
// N into four parts such that a = c and b = d 
int possibleways(int n) 
{ 
    if (n % 2 == 1) 
        return 0; 
    else if (n % 4 == 0) 
        return n / 4 - 1; 
    else
        return n / 4; 
} 
  
// Driver code 
int main() 
{ 
    int n = 20; 
    cout << possibleways(n); 
    return 0; 
} 

Java

// Java implementation for above approach 
class GFG 
{ 
      
// Function to find the number of ways to divide 
// N into four parts such that a = c and b = d 
static int possibleways(int n) 
{ 
    if (n % 2 == 1) 
        return 0; 
    else if (n % 4 == 0) 
        return n / 4 - 1; 
    else
        return n / 4; 
} 
  
// Driver code 
public static void main(String[] args) 
{ 
    int n = 20; 
    System.out.println(possibleways(n)); 
} 
} 
  
// This code contributed by Rajput-Ji 

Python3

# Python3 implementation for above approach 
  
# Function to find the number of ways  
# to divide N into four parts  
# such that a = c and b = d 
def possibleways(n): 
  
    if (n % 2 == 1): 
        return 0; 
    elif (n % 4 == 0): 
        return n // 4 - 1; 
    else: 
        return n // 4; 
  
# Driver code 
n = 20; 
print(possibleways(n)); 
  
# This code is contributed by mits 

C#

// C# implementation for above approach 
class GFG 
{ 
      
// Function to find the number of ways to divide 
// N into four parts such that a = c and b = d 
static int possibleways(int n) 
{ 
    if (n % 2 == 1) 
        return 0; 
    else if (n % 4 == 0) 
        return n / 4 - 1; 
    else
        return n / 4; 
} 
  
// Driver code 
static void Main() 
{ 
    int n = 20; 
    System.Console.WriteLine(possibleways(n)); 
} 
} 
  
// This code is contributed by mits 

PHP

<?php 
// PHP implementation for above approach 
  
// Function to find the number of ways to divide 
// N into four parts such that a = c and b = d 
function possibleways($n) 
{ 
    if ($n % 2 == 1) 
        return 0; 
    else if ($n % 4 == 0) 
        return $n / 4 - 1; 
    else
        return $n / 4; 
} 
  
// Driver code 
$n = 20; 
echo possibleways($n); 
  
// This code is contributed by ajit 
?> 

Output:

My Personal Notes

C++

Java

Python3

C#

PHP

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