Given a positive integer n, the task is to find whether this number reaches 1 after performing the following two operations:-
- If n is even, then n = n/2.
- If n is odd, then n = 3*n + 1.
- 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++ program to implement Collatz Conjecture #include<bits/stdc++.h> 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 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<Integer> 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<Integer> s = new HashSet<Integer>();
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 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# 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 |
<script> // Javascript program to implement Collatz Conjecture
// Function to find if n reaches to 1 or not.
function isToOneRec(n, s)
{
if (n == 1)
{
return true ;
}
// If there is a cycle formed,
// we can't reach 1.
if (s.has(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()
function isToOne(n)
{
// To store numbers visited using
// recursive calls.
let s = new Set();
return isToOneRec(n, s);
}
let n = 5;
if (isToOne(n))
{
document.write( "Yes" );
}
else
{
document.write( "No" );
}
// This code is contributed by divyeshrabadiya07.
</script> |
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++ program to implement Collatz Conjecture #include<bits/stdc++.h> 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 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 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# 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. |
<script> // Javascript program to implement Collatz Conjecture
// Function to find if n
// reaches to 1 or not.
function isToOne(n)
{
// Return true if n
// is positive
return (n > 0);
}
let n = 5;
if (isToOne(n) == true )
document.write( "Yes" ) ;
else
document.write( "No" );
// This code is contributed by mukesh07.
</script> |
<?php // PHP program to implement Collatz Conjecture // Function to find if n reaches // to 1 or not. function isToOne( $n )
{ // Return true if n is positive
if ( $n > 0)
return true;
return false;
} // Driver code $n = 5;
isToOne( $n )? print ( "Yes" ) : print ( "No" );
// This code is contributed by princiraj1992 ?> |
Yes
Time complexity: O(1)
Auxiliary space: O(1)
We strongly recommend to refer below problem as an exercise:
Maximum Collatz sequence length