Question

Please solve the following question using C++, without any library except for <iostream> and <string>.

3.5 Palindromi c numbers in other bases Write a function multibase which returns all the bases in which an integer is a palindrome Consider the number 21, which in base 10 is not a palindrome. However, if we write 21 in base 2, the result is 10101, which is a palindrome. In base 4, 21 is written as 111 In base 6, 21 is written as 33 In base 20, 21 is written as 11 Hence, the function multibase (21) returns the string "2 4 6 20" since these are the bases in which the number 21 is a palindrome. Here is the function signature string multibase(int x) The function multibase returns all the bases in which x is palindromic, from 2 to x-1 inclusive. Each palindromic base should be separated from the previous one by a space

Answer 1

C++ Code:

#include<iostream>

#include<string>

using namespace std;

string multibase(int x)

{

              string bases = ""; //to store all bases

             

              int i, n, j; //variables

              int result[x/2]; //array to store values in each base

              //loop 2 to x-1

              for(int i=2; i<x; i++)

              {

                             n = x; //set n to x

                             j = 0; //index of result

                             //convert to each base

                             while(n>0)

                            {

                                           result[j] = (n%i);

                                           n = n/i;

                                           j++; //increment j

                             }

                             int flag = 1; //assume value is palindrome

                             int l = 0, r = j - 1; //left and right indices of array result

                             //check palindrome or not

                             while(r>l)

                             {

                                           //if any corresponding values are not same break

                                           if(result[l++] != result[r--])

                                           {

                                                          flag = 0;

                                                          break;

                                           }

                             }

                             //if palindrome

                             if(flag == 1)

                             {

                                           string s = ""; //to convert int to string

                                           n = i; //base value

                                           while(n>0)

                                           {

                                                          int k = n%10;

                                                          n = n/10;

                                                          s.push_back((char)(k + '0')); //push each reminder

                                           }

                                           //add s in reverse to bases

                                           for(j=s.length()-1; j>=0;j--)

                                                          bases = bases + s[j];

                                           bases = bases + " "; //add space

                             }

              }

             

              return bases; //return bases

}

int main()

{

              cout<<"multibase(21) : "<<multibase(21)<<endl;

              return 0;

}

OUTPUT: