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# Program to implement Collatz Conjecture

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

1. If n is even, then n = n/2.
2. If n is odd, then n = 3*n + 1.
3. Repeat the 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```

The idea is to simply follow given rules and recursively call the 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``;``     ``s.insert(n);``//inserting elements to the s` `    ``// 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

 `// Java 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`

## Javascript

 ``

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 reach 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.`

## Javascript

 ``

## PHP

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

Output

`Yes`

Time complexity: O(1)
Auxiliary space: O(1)

We strongly recommend to refer below problem as an exercise:
Maximum Collatz sequence length
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