# Program to implement Collatz Conjecture

Given a positive integer n, the task is to find whether this number reaches to 1 after performing following two operations:-

1. If n is even, then n = n/2.
2. If n is odd, then n = 3*n + 1.
3. Repeat above steps, until it becomes 1.

For example, for n = 12, we get the sequence 12, 6, 3, 10, 5, 16, 8, 4, 2, 1.

Examples:

```Input : n = 4
Output : Yes

Input : n = 5
Output : Yes
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

The idea is to simply follow given rules and recursively call function with reduced values until it reaches 1. If a value is seen again during recursion, then there is a cycle and we can’t reach 1. In this case, we return false.

## C++

 `// C++ program to implement Collatz Conjecture ` `#include ` `using` `namespace` `std; ` ` `  `// Function to find if n reaches to 1 or not. ` `bool` `isToOneRec(``int` `n, unordered_set<``int``> &s) ` `{ ` `    ``if` `(n == 1) ` `        ``return` `true``; ` ` `  `    ``// If there is a cycle formed, we can't r ` `    ``// reach 1. ` `    ``if` `(s.find(n) != s.end()) ` `        ``return` `false``; ` ` `  `    ``// If n is odd then pass n = 3n+1 else n = n/2 ` `    ``return` `(n % 2)? isToOneRec(3*n + 1, s) : ` `                    ``isToOneRec(n/2, s); ` `} ` ` `  `// Wrapper over isToOneRec() ` `bool` `isToOne(``int` `n) ` `{ ` `   ``// To store numbers visited using recursive calls. ` `   ``unordered_set<``int``> s; ` ` `  `   ``return` `isToOneRec(n, s); ` `} ` ` `  `// Drivers code ` `int` `main() ` `{ ` `    ``int` `n = 5; ` `    ``isToOne(n) ? cout << ``"Yes"` `: cout <<``"No"``; ` `    ``return` `0; ` `} `

## Java

 `// Jav program to implement Collatz Conjecture ` `import` `java.util.*; ` ` `  `class` `GFG  ` `{ ` ` `  `    ``// Function to find if n reaches to 1 or not. ` `    ``static` `boolean` `isToOneRec(``int` `n, HashSet s)  ` `    ``{ ` `        ``if` `(n == ``1``)  ` `        ``{ ` `            ``return` `true``; ` `        ``} ` ` `  `        ``// If there is a cycle formed, we can't r ` `        ``// reach 1. ` `        ``if` `(s.contains(n))  ` `        ``{ ` `            ``return` `false``; ` `        ``} ` ` `  `        ``// If n is odd then pass n = 3n+1 else n = n/2 ` `        ``return` `(n % ``2` `== ``1``) ? isToOneRec(``3` `* n + ``1``, s) ` `                ``: isToOneRec(n / ``2``, s); ` `    ``} ` ` `  `    ``// Wrapper over isToOneRec() ` `    ``static` `boolean` `isToOne(``int` `n)  ` `    ``{ ` `        ``// To store numbers visited using recursive calls. ` `        ``HashSet s = ``new` `HashSet(); ` ` `  `        ``return` `isToOneRec(n, s); ` `    ``} ` ` `  `    ``// Drivers code ` `    ``public` `static` `void` `main(String[] args)  ` `    ``{ ` `        ``int` `n = ``5``; ` `        ``if` `(isToOne(n))  ` `        ``{ ` `            ``System.out.print(``"Yes"``); ` `        ``}  ` `        ``else`  `        ``{ ` `            ``System.out.print(``"No"``); ` `        ``} ` `    ``} ` `} ` ` `  `/* This code contributed by PrinciRaj1992 */`

## Python3

 `# Python3 program to implement Collatz Conjecture ` ` `  `# Function to find if n reaches to 1 or not. ` `def` `isToOneRec(n: ``int``, s: ``set``) ``-``> ``bool``: ` `    ``if` `n ``=``=` `1``: ` `        ``return` `True` ` `  `    ``# If there is a cycle formed, ` `    ``# we can't reach 1. ` `    ``if` `n ``in` `s: ` `        ``return` `False` ` `  `    ``# If n is odd then pass n = 3n+1 else n = n/2 ` `    ``if` `n ``%` `2``: ` `        ``return` `isToOneRec(``3` `*` `n ``+` `1``, s) ` `    ``else``: ` `        ``return` `isToOneRec(n ``/``/` `2``, s) ` ` `  `# Wrapper over isToOneRec() ` `def` `isToOne(n: ``int``) ``-``> ``bool``: ` ` `  `    ``# To store numbers visited ` `    ``# using recursive calls. ` `    ``s ``=` `set``() ` ` `  `    ``return` `isToOneRec(n, s) ` ` `  `# Driver Code ` `if` `__name__ ``=``=` `"__main__"``: ` `    ``n ``=` `5` `    ``if` `isToOne(n): ` `        ``print``(``"Yes"``) ` `    ``else``: ` `        ``print``(``"No"``) ` ` `  `# This code is contributed by ` `# sanjeev2552 `

## C#

 `// C# program to implement  ` `// Collatz Conjecture ` `using` `System;  ` `using` `System.Collections.Generic;  ` `     `  `class` `GFG  ` `{ ` ` `  `    ``// Function to find if n reaches to 1 or not. ` `    ``static` `Boolean isToOneRec(``int` `n, HashSet<``int``> s)  ` `    ``{ ` `        ``if` `(n == 1)  ` `        ``{ ` `            ``return` `true``; ` `        ``} ` ` `  `        ``// If there is a cycle formed,  ` `        ``// we can't reach 1. ` `        ``if` `(s.Contains(n))  ` `        ``{ ` `            ``return` `false``; ` `        ``} ` ` `  `        ``// If n is odd then pass n = 3n+1 else n = n/2 ` `        ``return` `(n % 2 == 1) ? isToOneRec(3 * n + 1, s) ` `                            ``: isToOneRec(n / 2, s); ` `    ``} ` ` `  `    ``// Wrapper over isToOneRec() ` `    ``static` `Boolean isToOne(``int` `n)  ` `    ``{ ` `        ``// To store numbers visited using  ` `        ``// recursive calls. ` `        ``HashSet<``int``> s = ``new` `HashSet<``int``>(); ` ` `  `        ``return` `isToOneRec(n, s); ` `    ``} ` ` `  `    ``// Driver code ` `    ``public` `static` `void` `Main(String[] args)  ` `    ``{ ` `        ``int` `n = 5; ` `        ``if` `(isToOne(n))  ` `        ``{ ` `            ``Console.Write(``"Yes"``); ` `        ``}  ` `        ``else` `        ``{ ` `            ``Console.Write(``"No"``); ` `        ``} ` `    ``} ` `} ` ` `  `// This code contributed by Rajput-Ji `

Output:

```Yes
```

The above program is inefficient. The idea is to use Collatz Conjecture. It states that if n is a positive then somehow it will reaches to 1 after a certain amount of time. So, by using this fact it can be done in O(1) i.e. just check if n is a positive integer or not.
Note that the answer would be false for negative numbers. For negative numbers, the above operations would keep number negative and it would never reach 1.

## C++

 `// C++ program to implement Collatz Conjecture ` `#include ` `using` `namespace` `std; ` ` `  `// Function to find if n reaches to 1 or not. ` `bool` `isToOne(``int` `n) ` `{ ` `    ``// Return true if n is positive ` `    ``return` `(n > 0); ` `} ` ` `  `// Drivers code ` `int` `main() ` `{ ` `    ``int` `n = 5; ` `    ``isToOne(n) ? cout << ``"Yes"` `: cout <<``"No"``; ` `    ``return` `0; ` `} `

## Java

 `// Java program to implement Collatz ` `// Conjecture ` `class` `GFG { ` `     `  `    ``// Function to find if n reaches ` `    ``// to 1 or not. ` `    ``static` `boolean` `isToOne(``int` `n) ` `    ``{ ` `         `  `        ``// Return true if n is positive ` `        ``return` `(n > ``0``); ` `    ``} ` `     `  `    ``// Drivers code ` `    ``public` `static` `void` `main(String[] args) ` `    ``{ ` `        ``int` `n = ``5``; ` `         `  `        ``if``(isToOne(n) == ``true``) ` `            ``System.out.println(``"Yes"``); ` `        ``else` `            ``System.out.println(``"No"``); ` `    ``} ` `} ` ` `  `// This code is contributed by Smitha. `

## Python 3

 `# Python 3 program to implement ` `# Collatz Conjecture ` ` `  `# Function to find if n  ` `# reaches to 1 or not. ` `def` `isToOne(n): ` ` `  `    ``# Return true if n ` `    ``# is positive ` `    ``return` `(n > ``0``) ` ` `  `# Drivers code ` `n ``=` `5` ` `  `if` `isToOne(n) ``=``=` `True``: ` `    ``print``(``"Yes"``) ` `else``: ` `    ``print``(``"No"``) ` `     `  `# This code is contributed ` `# by Smitha. `

## C#

 `// C# program to implement ` `// Collatz Conjecture ` `using` `System; ` ` `  `class` `GFG { ` `     `  `    ``// Function to find if n ` `    ``// reaches to 1 or not. ` `    ``static` `bool` `isToOne(``int` `n) ` `    ``{ ` `         `  `        ``// Return true if n  ` `        ``// is positive ` `        ``return` `(n > 0); ` `    ``} ` `     `  `    ``// Drivers code ` `    ``public` `static` `void` `Main() ` `    ``{ ` `        ``int` `n = 5; ` `         `  `        ``if``(isToOne(n) == ``true``) ` `            ``Console.Write(``"Yes"``) ; ` `        ``else` `            ``Console.Write(``"No"``); ` `    ``} ` `} ` ` `  `// This code is contributed ` `// by Smitha. `

## PHP

 ` 0) ` `        ``return` `true; ` `    ``return` `false; ` `} ` ` `  `// Driver code ` `\$n` `= 5; ` `isToOne(``\$n``)? ``print``(``"Yes"``) : ``print``(``"No"``); ` ` `  `// This code is contributed by princiraj1992 ` `?> `

Output:

```Yes
```

We strongly recommend to refer below problem as an exercise:

Maximum Collatz sequence length

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