# Confusing Number II in C++

C++Server Side ProgrammingProgramming

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

• mapping := 1

• mapping := 9

• mapping := 6

• mapping := 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;
mapping = 1;
mapping = 9;
mapping = 6;
mapping = 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