Regarding Tile Problem

#1

I have tried using top down as well as bottom up approach of DP to do this problem, still getting run time error.

#2

In this problem you have figured the base cases correct that if n<m then return 1 and if n==m return 2. The recurrsion relation will be that if n>m then add the two recursions . One with same function but n as n-1 and the other will be same function but with n= n-m . Now this will the two cases one in which tile are placed vertically will be where n=n-1 and the one where tiles are placed horizontally will be where n=n-m . And also i will recommend that rather than forming a recurrence relation try to take a array of size n+1 and fill it from index i= 1 where size of n =1 till index i= n and where each index has the total possible way of that case on that index i.