Confusing Number II in C++

Suppose we have a digit, now if we rotate that digit by 180 degrees to form new digits. When 0, 1, 6, 8, 9 are rotated 180 degrees, they become 0, 1, 9, 8, 6 respectively. But when 2, 3, 4, 5 and 7 are rotated 180 degrees, they become invalid.

A confusing number is a number that when rotated 180 degrees becomes a new number. So, if we have a positive integer N, we have to find the number of confusing numbers between 1 and N inclusive.

So, if the input is like 20, then the output will be 6

To solve this, we will follow these steps −

• Define one map mapping

• Define an array valid

• Define a function solve(), this will take num, rotate, digit, N,

• if rotate is not equal to num, then −

  • (increase ret by 1)

• for initialize i := 0, when i < size of valid, update (increase i by 1), do −

  • dig := valid[i]

  • if num * 10 + dig > N, then

    • Come out from the loop

  • solve(num * 10 + dig, Define one map, digit * 10, N)

• From the main method do the following −

• ret := 0

• valid := { 0, 1, 6, 8, 9 }

• mapping[0] := 0

• mapping[1] := 1

• mapping[6] := 9

• mapping[9] := 6

• mapping[8] := 8

• solve(1, 1, 10, N)

• solve(6, 9, 10, N)

• solve(9, 6, 10, N)

• solve(8, 8, 10, N)

• return ret

Let us see the following implementation to get better understanding −

Example

 Live Demo

#include <bits/stdc++.h>
using namespace std;
typedef long long int lli;
class Solution {
   public:
   int ret;
   map <int, int> mapping;
   vector <int> valid;
   void solve(lli num, lli rotate, lli digit, lli N){
      if (rotate != num) {
         ret++;
      }
      for (int i = 0; i < valid.size(); i++) {
         int dig = valid[i];
         if (num * 10 + dig > N) {
            break;
         }
         solve(num * 10 + dig, mapping[dig] * digit + rotate, digit * 10, N);
      }
   }
   int confusingNumberII(int N) {
      ret = 0;
      valid = { 0, 1, 6, 8, 9 };
      mapping[0] = 0;
      mapping[1] = 1;
      mapping[6] = 9;
      mapping[9] = 6;
      mapping[8] = 8;
      solve(1, 1, 10, N);
      solve(6, 9, 10, N);
      solve(9, 6, 10, N);
      solve(8, 8, 10, N);
      return ret;
   }
};
main(){
   Solution ob;
   cout << (ob.confusingNumberII(20));
}

Input

20

Output

6