Strobogrammatic number

For the given length n, find all n-length Strobogrammatic numbers.

Strobogrammatic Number is a number whose numeral is rotationally symmetric so that it appears the same when rotated 180 degrees. In other words, Strobogrammatic Number appears the same right-side up and upside down.

0 after 180° rotation : (0 → 0)
1 after 180° rotation : (1 → 1)
8 after 180° rotation : (8 → 8)
6 after 180° rotation : (6 → 9)
9 after 180° rotation : (9 → 6)

Examples :

Input : n = 2
Output : 88  11  96  69

Input : n = 4
Output : 8008 1001 9006 6009 8888 1881 9886 6889 8118 1111
        9116 6119 8968 1961 9966 6969 8698 1691 9696 6699

Code:

Below is the Python3 implementation :

C++

#include <bits/stdc++.h>
using namespace std;

vector<string> numdef(int n, int length)
{
    vector<string> result;
    if (n == 0){
        result.push_back("");
        return result;
    }
    if (n == 1) {
        result.push_back("1");
        result.push_back("0");
        result.push_back("8");
        return result;
    }
    vector<string> middles = numdef(n - 2, length);

    for (string middle : middles) {
        if (n != length)
            result.push_back("0" + middle + "0");

        result.push_back("8" + middle + "8");
        result.push_back("1" + middle + "1");
        result.push_back("9" + middle + "6");
        result.push_back("6" + middle + "9");
    }

    if (n == 2) {
        result.push_back("11");
        result.push_back("88");
        result.push_back("69");
        result.push_back("96");
        if (n != length) {
            result.push_back("00");
        }
    }
    return result;
}

vector<string> strobogrammatic_num(int n)
{
    vector<string> result = numdef(n, n);
    return result;
}

int main()
{
    // Print all Strobogrammatic number for n = 2
    for (string num : strobogrammatic_num(2))
        cout << num << " ";
    return 0;
}

// code contributed by Oprix

Java

import java.util.*;

class GFG {

  // definition function
  static ArrayList<String> numdef(int n, int length) {
    ArrayList<String> result = new ArrayList<String>();
    if (n == 0){
      result.add("");
      return result;
    }
    if (n == 1) {
      result.add("1");
      result.add("0");
      result.add("8");
      return result;
    }

    ArrayList<String> middles = numdef(n - 2, length);

    for (String middle : middles) {
      if (n != length)
        result.add("0" + middle + "0");

      result.add("8" + middle + "8");
      result.add("1" + middle + "1");
      result.add("9" + middle + "6");
      result.add("6" + middle + "9");
    }

    // For even n, add these additional cases
    if (n % 2 == 0) {
        result.add("11");
        result.add("88");
        result.add("69");
        result.add("96");
        if (n != length) {
            result.add("00");
        }
    }
    
    return result;
  }

  // strobogrammatic function
  static ArrayList<String> strobogrammatic_num(int n) {
    ArrayList<String> result = numdef(n, n);
    return result;
  }

  // Driver Code
  public static void main(String[] args) {
    // Print all Strobogrammatic
    // number for n = 3
    for (String num : strobogrammatic_num(3))
      System.out.print(num + " ");
  }
}

// This code is contributed by Oprix

Python3

# Python program to print all
# Strobogrammatic numbers of length n

# Strobogrammatic function
def strobogrammatic_num(n):
    result = numdef(n, n)
    return result

# Definition function
def numdef(n, length):
    if n == 0: return [""]
    if n == 1: return ["1", "0", "8"]

    middles = numdef(n - 2, length)
    result = []

    for middle in middles:
        if n != length:
            result.append("0" + middle + "0")

        result.append("8" + middle + "8")
        result.append("1" + middle + "1")
        result.append("9" + middle + "6")
        result.append("6" + middle + "9")

    # For even n, add these additional cases
    if n % 2 == 0:
        result.append("11")
        result.append("88")
        result.append("69")
        result.append("96")
        if n != length:
            result.append("00")

    return result

# Driver Code
if __name__ == '__main__':
    # Print all Strobogrammatic
    # numbers for n = 2
    print(strobogrammatic_num(2))

C#

using System;
using System.Collections.Generic;

class GFG 
{

  // definition function
  static List<string> numdef(int n, int length)
  {
    List<string> result = new List<string>();
    if (n == 0)
      return result;
    if (n == 1) {
      result.Add("1");
      result.Add("0");
      result.Add("8");
      return result;
    }

    List<string> middles = numdef(n - 2, length);

    foreach(string middle in middles)
    {
      if (n != length)
        result.Add("0" + middle + "0");

      result.Add("8" + middle + "8");
      result.Add("1" + middle + "1");
      result.Add("9" + middle + "6");
      result.Add("6" + middle + "9");
    }

    // For even n, add these additional cases
    if (n % 2 == 0) {
        result.Add("11");
        result.Add("88");
        result.Add("69");
        result.Add("96");
        if (n != length) {
            result.Add("00");
        }
    }
    return result;
  }

  // strobogrammatic function
  static List<string> strobogrammatic_num(int n)
  {
    List<string> result = numdef(n, n);
    return result;
  }

  // Driver Code
  public static void Main(string[] args)
  {
    // Print all Strobogrammatic
    // number for n = 3
    foreach(string num in(strobogrammatic_num(3)))
      Console.Write(num + " ");
  }
}

// This code is contributed by Oprix

Javascript

// JavaScript program to print all
// Strobogrammatic number of length n
  
// strobogrammatic function 
function strobogrammatic_num(n) {
    let result = numdef(n, n);
    return result;
}

// definition function
function numdef(n, length) {      
    if (n == 0) return [""];
    if (n == 1) return ["1", "0", "8"];
      
    let middles = numdef(n - 2, length);
    let result = [];
      
    for (var middle of middles) {
        if (n != length)           
            result.push("0" + middle + "0");

        result.push("8" + middle + "8");
        result.push("1" + middle + "1");
        result.push("9" + middle + "6");
        result.push("6" + middle + "9");
    }

    // For even n, add these additional cases
    if (n % 2 === 0) {
        result.push("11");
        result.push("88");
        result.push("69");
        result.push("96");
        if (n != length) {
            result.push("00");
        }
    }
    
    return result;
}

// Driver Code
// Print all Strobogrammatic 
// number for n = 3
console.log(strobogrammatic_num(3));

Output

88 11 96 69 11 88 69 96 

Time Complexity: O(5^n)
Auxiliary Space: O(5^n)
Reference : https://en.wikipedia.org/wiki/Strobogrammatic_number