788. Rotated Digits

Q:

X is a good number if after rotating each digit individually by 180 degrees, we get a valid number that is different from X.  Each digit must be rotated - we cannot choose to leave it alone.

A number is valid if each digit remains a digit after rotation. 0, 1, and 8 rotate to themselves; 2 and 5 rotate to each other (on this case they are rotated in a different direction, in other words 2 or 5 gets mirrored); 6 and 9 rotate to each other, and the rest of the numbers do not rotate to any other number and become invalid.

Now given a positive number N, how many numbers X from 1 to N are good?

Example:
Input: 10
Output: 4
Explanation: 
There are four good numbers in the range [1, 10] : 2, 5, 6, 9.
Note that 1 and 10 are not good numbers, since they remain unchanged after rotating.

Note:

• N  will be in range [1, 10000].

A:

class Solution {
public:
    int rotatedDigits(int N) {
        unordered_map<int,int> M;
        M['0']='0';
        M['1']='1';
        M['8']='8';
        M['2']='5';
        M['5']='2';
        M['6']='9';
        M['9']='6';
        int res = 0;
        for(int v=1; v<=N; ++v){
            if(isValid(M, v)){
                res++;
            }
        }
        return res;
    }
private:
    bool isValid(unordered_map<int,int> &M , int v){
        string strV = to_string(v);
        string strV2 = "";
        for(char ch : strV){
            if(M.find(ch) == M.end()){
                return false;
            }
            strV2 += M[ch];
        }
        return strV != strV2;
    }
};