n steps with 1, 2 or 3 steps taken. How many ways to get to the top?

Question

If we have n steps and we can go up 1 or 2 steps at a time, there is a Fibonacci relation between the number of steps and the ways to climb them. IF and ONLY if we do not co

Answer 1

Recursive memoization based C++ solution: You ask a stair how many ways we can go to top? If its not the topmost stair, its going to ask all its neighbors and sum it up and return you the result. If its the topmost stair its going to say 1.

vector getAllStairsFromHere(vector& numSteps,  int& numStairs, int currentStair)
{
    vector res;

    for(auto it : numSteps)
        if(it + currentStair <= numStairs)
            res.push_back(it + currentStair);

    return res;
}


int numWaysToClimbUtil(vector& numSteps, int& numStairs, int currentStair, map& memT)
{
    auto it = memT.find(currentStair);
    if(it != memT.end())
        return it->second;

    if(currentStair >= numStairs)
        return 1;

    int numWaysToClimb = 0;
    auto choices = getAllStairsFromHere(numSteps,  numStairs, currentStair);
    for(auto it : choices)
        numWaysToClimb += numWaysToClimbUtil(numSteps, numStairs, it, memT);


    memT.insert(make_pair(currentStair, numWaysToClimb));
    return memT[currentStair];
}


int numWaysToClimb(vectornumSteps, int numStairs)
{
    map memT;
    int currentStair = 0;
    return numWaysToClimbUtil(numSteps, numStairs, currentStair, memT);
}