Coding Question

Unable to understand the question.
Plz explain this question with the explanation part for sample test case

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. Recurrsion relation may give you time error

I got the question, but unable to get the approach you re suggesting for this problem. And, yes time error is occurring here. Please help me out for this

Imagine you have a floor of size n × m and you are given tiles of size 1× m.
Now you can either place the tiles vertically. Where a tile can be either place vertically,meaning it will only occupy a cell of width 1 and a complete height of M

there are 3 possibilities:

n>m - here you can place a tile vertically(left with n-m,m) as well as horizontally(left with n-1,m).
n==m then there are always 2 ways - horizontally or vertically.
n<m here you have only 1 choice,that is to place tile horizontally, so 1 way only.
Also mere recursion won’t help in passing all test cases, you have to use DP.

Another example: