# 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 :**

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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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