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# Recaman’s sequence

Given an integer n. Print first n elements of Recaman’s sequence.
Examples:

```Input : n = 6
Output : 0, 1, 3, 6, 2, 7

Input  : n = 17
Output : 0, 1, 3, 6, 2, 7, 13, 20, 12, 21,
11, 22, 10, 23, 9, 24, 8```

It is basically a function with domain and co-domain as natural numbers and 0. It is recursively defined as below:
Specifically, let a(n) denote the (n+1)-th term. (0 is already there).
The rule says:

```a(0) = 0,
if n > 0 and the number is not
already included in the sequence,
a(n) = a(n - 1) - n
else
a(n) = a(n-1) + n. ```

Below is a simple implementation where we store all n Recaman Sequence numbers in an array. We compute the next number using the recursive formula mentioned above.

## C++

 `// C++ program to print n-th number in Recaman's``// sequence``#include ``using` `namespace` `std;` `// Prints first n terms of Recaman sequence``int` `recaman(``int` `n)``{``    ``// Create an array to store terms``    ``int` `arr[n];` `    ``// First term of the sequence is always 0``    ``arr[0] = 0;``    ``printf``(``"%d, "``, arr[0]);` `    ``// Fill remaining terms using recursive``    ``// formula.``    ``for` `(``int` `i=1; i< n; i++)``    ``{``        ``int` `curr = arr[i-1] - i;``        ``int` `j;``        ``for` `(j = 0; j < i; j++)``        ``{``            ``// If arr[i-1] - i is negative or``            ``// already exists.``            ``if` `((arr[j] == curr) || curr < 0)``            ``{``                ``curr = arr[i-1] + i;``                ``break``;``            ``}``        ``}` `        ``arr[i] = curr;``        ``printf``(``"%d, "``, arr[i]);``    ``}``}` `// Driver code``int` `main()``{``    ``int` `n = 17;``    ``recaman(n);``    ``return` `0;``}`

## Java

 `// Java program to print n-th number in Recaman's``// sequence``import` `java.io.*;` `class` `GFG {``    ` `    ``// Prints first n terms of Recaman sequence``    ``static` `void` `recaman(``int` `n)``    ``{``        ``// Create an array to store terms``        ``int` `arr[] = ``new` `int``[n];``    ` `        ``// First term of the sequence is always 0``        ``arr[``0``] = ``0``;``        ``System.out.print(arr[``0``]+``" ,"``);``    ` `        ``// Fill remaining terms using recursive``        ``// formula.``        ``for` `(``int` `i = ``1``; i < n; i++)``        ``{``            ``int` `curr = arr[i - ``1``] - i;``            ``int` `j;``            ``for` `(j = ``0``; j < i; j++)``            ``{``                ``// If arr[i-1] - i is negative or``                ``// already exists.``                ``if` `((arr[j] == curr) || curr < ``0``)``                ``{``                    ``curr = arr[i - ``1``] + i;``                    ``break``;``                ``}``            ``}``    ` `            ``arr[i] = curr;``            ``System.out.print(arr[i]+``", "``);``            ` `        ``}``    ``}``    ` `    ``// Driver code``    ``public` `static` `void` `main (String[] args)``    ``{``        ``int` `n = ``17``;``        ``recaman(n);` `    ``}``}` `// This code is contributed by vt_m`

## Python 3

 `# Python 3 program to print n-th``# number in Recaman's sequence` `# Prints first n terms of Recaman``# sequence``def` `recaman(n):` `    ``# Create an array to store terms``    ``arr ``=` `[``0``] ``*` `n` `    ``# First term of the sequence``    ``# is always 0``    ``arr[``0``] ``=` `0``    ``print``(arr[``0``], end``=``", "``)` `    ``# Fill remaining terms using``    ``# recursive formula.``    ``for` `i ``in` `range``(``1``, n):``    ` `        ``curr ``=` `arr[i``-``1``] ``-` `i``        ``for` `j ``in` `range``(``0``, i):``        ` `            ``# If arr[i-1] - i is``            ``# negative or already``            ``# exists.``            ``if` `((arr[j] ``=``=` `curr) ``or` `curr < ``0``):``                ``curr ``=` `arr[i``-``1``] ``+` `i``                ``break``            ` `        ``arr[i] ``=` `curr``        ``print``(arr[i], end``=``", "``)` `# Driver code``n ``=` `17` `recaman(n)` `# This code is contributed by Smitha.`

## C#

 `// C# program to print n-th number in Recaman's``// sequence``using` `System;` `class` `GFG {``    ` `    ``// Prints first n terms of Recaman sequence``    ``static` `void` `recaman(``int` `n)``    ``{``        ``// Create an array to store terms``        ``int` `[]arr = ``new` `int``[n];``    ` `        ``// First term of the sequence is always 0``        ``arr[0] = 0;``        ``Console.Write(arr[0]+``" ,"``);``    ` `        ``// Fill remaining terms using recursive``        ``// formula.``        ``for` `(``int` `i = 1; i < n; i++)``        ``{``            ``int` `curr = arr[i - 1] - i;``            ``int` `j;``            ``for` `(j = 0; j < i; j++)``            ``{``                ``// If arr[i-1] - i is negative or``                ``// already exists.``                ``if` `((arr[j] == curr) || curr < 0)``                ``{``                    ``curr = arr[i - 1] + i;``                    ``break``;``                ``}``            ``}``    ` `            ``arr[i] = curr;``        ``Console.Write(arr[i]+``", "``);``            ` `        ``}``    ``}``    ` `    ``// Driver code``    ``public` `static` `void` `Main ()``    ``{``        ``int` `n = 17;``        ``recaman(n);` `    ``}``}` `// This code is contributed by vt_m.`

## PHP

 ``

## Javascript

 ``

Output:

`0, 1, 3, 6, 2, 7, 13, 20, 12, 21, 11, 22, 10, 23, 9, 24, 8, `

Time Complexity : O(n2
Auxiliary Space : O(n), since n extra space has been added
Optimizations :
We can use hashing to store previously computed values and can make this program work in O(n) time.

## C++

 `// C++ program to print n-th number in Recaman's``// sequence``#include ``using` `namespace` `std;` `// Prints first n terms of Recaman sequence``void` `recaman(``int` `n)``{``    ``if` `(n <= 0)``      ``return``;` `    ``// Print first term and store it in a hash``    ``printf``(``"%d, "``, 0);``    ``unordered_set<``int``> s;``    ``s.insert(0);` `    ``// Print remaining terms using recursive``    ``// formula.``    ``int` `prev = 0;``    ``for` `(``int` `i=1; i< n; i++)``    ``{``        ``int` `curr = prev - i;` `        ``// If arr[i-1] - i is negative or``        ``// already exists.``        ``if` `(curr < 0 || s.find(curr) != s.end())``           ``curr = prev + i;` `        ``s.insert(curr);` `        ``printf``(``"%d, "``, curr);``        ``prev = curr;``    ``}``}` `// Driver code``int` `main()``{``    ``int` `n = 17;``    ``recaman(n);``    ``return` `0;``}`

## Java

 `// Java program to print n-th number``// in Recaman's sequence``import` `java.util.*;` `class` `GFG``{` `// Prints first n terms of Recaman sequence``static` `void` `recaman(``int` `n)``{``    ``if` `(n <= ``0``)``    ``return``;` `    ``// Print first term and store it in a hash``    ``System.out.printf(``"%d, "``, ``0``);``    ``HashSet s = ``new` `HashSet();``    ``s.add(``0``);` `    ``// Print remaining terms using``    ``// recursive formula.``    ``int` `prev = ``0``;``    ``for` `(``int` `i = ``1``; i< n; i++)``    ``{``        ``int` `curr = prev - i;` `        ``// If arr[i-1] - i is negative or``        ``// already exists.``        ``if` `(curr < ``0` `|| s.contains(curr))``            ``curr = prev + i;` `        ``s.add(curr);` `        ``System.out.printf(``"%d, "``, curr);``        ``prev = curr;``    ``}``}` `// Driver code``public` `static` `void` `main(String[] args)``{``    ``int` `n = ``17``;``    ``recaman(n);``}``}` `// This code is contributed by Rajput-Ji`

## Python3

 `# Python3 program to print n-th number in``# Recaman's sequence` `# Prints first n terms of Recaman sequence``def` `recaman(n):` `    ``if``(n <``=` `0``):``        ``return` `    ``# Print first term and store it in a hash``    ``print``(``0``, ``","``, end``=``'')``    ``s ``=` `set``([])``    ``s.add(``0``)` `    ``# Print remaining terms using recursive``    ``# formula.``    ``prev ``=` `0``    ``for` `i ``in` `range``(``1``, n):` `        ``curr ``=` `prev ``-` `i` `        ``# If arr[i-1] - i is negative or``        ``# already exists.``        ``if``(curr < ``0` `or` `curr ``in` `s):``            ``curr ``=` `prev ``+` `i` `        ``s.add(curr)` `        ``print``(curr, ``","``, end``=``'')``        ``prev ``=` `curr` `# Driver code``if` `__name__``=``=``'__main__'``:``    ``n ``=` `17``    ``recaman(n)` `# This code is contributed by``# Sanjit_Prasad`

## C#

 `// C# program to print n-th number``// in Recaman's sequence``using` `System;``using` `System.Collections.Generic;` `class` `GFG``{` `// Prints first n terms of Recaman sequence``static` `void` `recaman(``int` `n)``{``    ``if` `(n <= 0)``    ``return``;` `    ``// Print first term and store it in a hash``    ``Console.Write(``"{0}, "``, 0);``    ``HashSet<``int``> s = ``new` `HashSet<``int``>();``    ``s.Add(0);` `    ``// Print remaining terms using``    ``// recursive formula.``    ``int` `prev = 0;``    ``for` `(``int` `i = 1; i < n; i++)``    ``{``        ``int` `curr = prev - i;` `        ``// If arr[i-1] - i is negative or``        ``// already exists.``        ``if` `(curr < 0 || s.Contains(curr))``            ``curr = prev + i;` `        ``s.Add(curr);` `        ``Console.Write(``"{0}, "``, curr);``        ``prev = curr;``    ``}``}` `// Driver code``public` `static` `void` `Main(String[] args)``{``    ``int` `n = 17;``    ``recaman(n);``}``}` `// This code is contributed by Princi Singh`

## PHP

 ``

## Javascript

 ``

Output:

`0, 1, 3, 6, 2, 7, 13, 20, 12, 21, 11, 22, 10, 23, 9, 24, 8, `

Time Complexity : O(n)
Auxiliary Space : O(n), since n extra space has been taken.
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