Generate 10-digit number using a phone keypad

Question

Given a phone keypad as shown below:

1 2 3
4 5 6
7 8 9
  0

How many different 10-digit numbers can be formed starting from 1? The constrain

Answer 1

Recursive memoization approach:

vector> lupt = { {4, 6}, {6, 8}, {9, 7}, {4, 8}, {3, 9, 0},
                             {},     {1,7,0}, {6, 2}, {1, 3}, {2, 4} };

int numPhoneNumbersUtil(int startdigit, int& phonenumberlength, int currCount, map< pair,int>& memT)
{
    int noOfCombs = 0;
    vector enddigits;

    auto it = memT.find(make_pair(startdigit,currCount));
    if(it != memT.end())
    {
        noOfCombs = it->second;
        return noOfCombs;
    }

    if(currCount == phonenumberlength)
    {
        return 1;
    }

    enddigits = lupt[startdigit];
    for(auto it : enddigits)
    {
        noOfCombs += numPhoneNumbersUtil(it, phonenumberlength, currCount + 1, memT);
    }

    memT.insert(make_pair(make_pair(startdigit,currCount), noOfCombs));
    return memT[make_pair(startdigit,currCount)];

}

int numPhoneNumbers(int startdigit, int phonenumberlength)
{
    map,int> memT;
    int currentCount = 1; //the first digit has already been added
    return  numPhoneNumbersUtil(startdigit, phonenumberlength, currentCount, memT);
}