|CS19002 Programming and Data Structures Laboratory||Spring 2009, Section 2|
In this assignment, your task is to compute the number of ways in which you can eat m Idlis in n days.
Suppose that you have to eat at least one Idli per day, and you eat a whole number of Idlis on each day. Consider the function E(m,i,n) which stands for the number of ways you eat m Idlis from Day i to Day n. Suppose that you eat k Idlis on Day i. Then, the number of remaining possibilities is E(m-k,i+1,n). Now vary k. Also supply suitable boundary conditions.
Write a recursive function to implement E(m,i,n).
Report the output of your program for the following two inputs.m = 13, n = 10 m = 32, n = 16
Remark: The answer is actually a simple closed-form expression given by the binomial coefficient C(m-1,n-1). Your algorithm must not make use of this formula. You need to employ the recursive approach as mentioned above.
Repeat Part 1 with the added constraint that you are allowed to eat at most B Idlis per Day, where B is a positive integer to be supplied by the user.
You may write a new function for E(m,i,n) in this case. Alternatively, you may rewrite the function of Part 1 and pass B always to it. The value B = 0 implies that there is no limit on the number of Idlis that can be consumed per day (Part 1). For B >= 1, you consider the bound (Part 2).
Report the output of your program for the following two inputs.m = 13, n = 10, B = 2 m = 32, n = 16, B = 8