Review an answer - Decode Ways

Question

I\'m trying to solve a question and my question here is why doesn\'t my solution work?. Here\'s the question and below\'s the answer.

Question taken fr

Answer 1

My solution is based on the idea that the arrangement of items(char/digit) within a particular substring is completely independent of the same within a different substring. So we need to multiply each of those independent ways to get the total number of ways.

// nc is the number of consecutive 1's or 2's in a substring.
// Returns the number of ways these can be arranged  within 
// themselves to a valid expr.
int ways(int nc){
    int n = pow(2, (nc/2)); //this part can be memorized using map for optimization
    int m = n;
    if (nc%2) {
        m *= 2;
    }
    return n + m - 1;  
}
bool validTens(string A, int i){
    return (A[i] == '1' || (A[i] == '2' && A[i+1] <= '6'));
}
int numDecodings(string A) {
    int ans = 1;
    int nc;

    if ((A.length() == 0)||(A[0] == '0')) return 0;

    for(int i = 1; i < A.length();i++){
        if(A[i] == '0' && validTens(A, i-1) == false) return 0; //invalid string
        while(i < A.length() && validTens(A, i-1)) {
            if(A[i] == '0'){
                //think of '110' or '1210', the last two digits must be together
                if(nc > 0) nc--;  
            }
            else nc++;
            i++;
        }
        ans *= ways(nc);
        nc = 0;
    }
    return ans;
}