# Break the number into three parts

Given a really large number, break it into 3 whole numbers such that they sum up to the original number and count number of ways to do so.

**Examples :**

Input : 3 Output : 10 The possible combinations where the sum of the numbers is equal to 3 are: 0+0+3 = 3 0+3+0 = 3 3+0+0 = 3 0+1+2 = 3 0+2+1 = 3 1+0+2 = 3 1+2+0 = 3 2+0+1 = 3 2+1+0 = 3 1+1+1 = 3 Input : 6 Output : 28

A total of 10 ways, so answer is 10.

**Naive Approach:** Try all combinations from 0 to the given number and check if they add upto the given number or not, if they do, increase the count by 1 and continue the process.

## C++

// C++ program to count number of ways to break // a number in three parts. #include <bits/stdc++.h> #define ll long long int using namespace std; // Function to count number of ways // to make the given number n ll count_of_ways(ll n) { ll count = 0; for (int i = 0; i <= n; i++) for (int j = 0; j <= n; j++) for (int k = 0; k <= n; k++) if (i + j + k == n) count++; return count; } // Driver Function int main() { ll n = 3; cout << count_of_ways(n) << endl; return 0; }

## Java

// Java program to count number of ways to break // a number in three parts import java.io.*; class GFG { // Function to count number of ways // to make the given number n static long count_of_ways(long n) { long count = 0; for (int i = 0; i <= n; i++) for (int j = 0; j <= n; j++) for (int k = 0; k <= n; k++) if (i + j + k == n) count++; return count; } // driver program public static void main(String[] args) { long n = 3; System.out.println(count_of_ways(n)); } } // Contributed by Pramod Kumar

## Python3

# Python3 program to count number of # ways to break # a number in three parts. # Function to count number of ways # to make the given number n def count_of_ways(n): count = 0 for i in range(0, n+1): for j in range(0, n+1): for k in range(0, n+1): if(i + j + k == n): count = count + 1 return count # Driver Function if __name__=='__main__': n = 3 print(count_of_ways(n)) # This code is contributed by # Sanjit_Prasad

## C#

// C# program to count number of ways // to break a number in three parts using System; class GFG { // Function to count number of ways // to make the given number n static long count_of_ways(long n) { long count = 0; for (int i = 0; i <= n; i++) for (int j = 0; j <= n; j++) for (int k = 0; k <= n; k++) if (i + j + k == n) count++; return count; } // driver program public static void Main() { long n = 3; Console.WriteLine(count_of_ways(n)); } } // This code is Contributed by vt_m.

## PHP

<?php // PHP program to count number // of ways to break a number // in three parts. // Function to count number of ways // to make the given number n function count_of_ways( $n) { $count = 0; for ($i = 0; $i <= $n; $i++) for ($j = 0; $j <= $n; $j++) for ($k = 0; $k <= $n; $k++) if ($i + $j + $k == $n) $count++; return $count; } // Driver Code $n = 3; echo count_of_ways($n); // This code is Contributed by vt_m. ?>

## Javascript

<script> // JavaScript program to count // number of ways to break // a number in three parts. // Function to count number of ways // to make the given number n function count_of_ways(n) { let count = 0; for(let i = 0; i <= n; i++) for(let j = 0; j <= n; j++) for(let k = 0; k <= n; k++) if (i + j + k == n) count++; return count; } // Driver code let n = 3; document.write(count_of_ways(n) + "<br>"); // This code is contributed by Surbhi Tyagi. </script>

**Output :**

10

**Time Complexity :** O(n^{3})

**Efficient Approach:** If we carefully observe the test cases then we realize that the number of ways to break a number n into 3 parts is equal to (n+1) * (n+2) / 2.

## C++

// C++ program to count number of ways to break // a number in three parts. #include <bits/stdc++.h> #define ll long long int using namespace std; // Function to count number of ways // to make the given number n ll count_of_ways(ll n) { ll count; count = (n + 1) * (n + 2) / 2; return count; } // Driver Function int main() { ll n = 3; cout << count_of_ways(n) << endl; return 0; }

## Java

// Java program to count number of ways to break // a number in three parts import java.io.*; class GFG { // Function to count number of ways // to make the given number n static long count_of_ways(long n) { long count = 0; count = (n + 1) * (n + 2) / 2; return count; } // driver program public static void main(String[] args) { long n = 3; System.out.println(count_of_ways(n)); } } // Contributed by Pramod Kumar

## Python3

# Python 3 program to count number of # ways to break a number in three parts. # Function to count number of ways # to make the given number n def count_of_ways(n): count = 0 count = (n + 1) * (n + 2) // 2 return count # Driver code n = 3 print(count_of_ways(n)) # This code is contributed by Shrikant13

## C#

// C# program to count number of ways to // break a number in three parts using System; class GFG { // Function to count number of ways // to make the given number n static long count_of_ways(long n) { long count = 0; count = (n + 1) * (n + 2) / 2; return count; } // driver program public static void Main() { long n = 3; Console.WriteLine(count_of_ways(n)); } } // This code is Contributed by vt_m.

## PHP

<?php // PHP program to count number // of ways to break a number // in three parts. // Function to count number of ways // to make the given number n function count_of_ways( $n) { $count; $count = ($n + 1) * ($n + 2) / 2; return $count; } // Driver Code $n = 3; echo count_of_ways($n); // This code is Contributed by vt_m. ?>

## Javascript

<script> // javascript program to count number of ways to // break a number in three parts // Function to count number of ways // to make the given number n function count_of_ways(n) { var count = 0; count = (n + 1) * (n + 2) / 2; return count; } // driver program var n = 3; document.write(count_of_ways(n)); // This code is contributed by bunnyram19. </script>

**Output :**

10

**Time Complexity:** O(1)

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