Q1. Iteration v.s. Recursion (50 Points) Implement the function for Binomial coe

Question

Q1. Iteration v.s. Recursion (50 Points) Implement the function for Binomial coefficient with 2 approaches, iteration and recursion respectively, followed the formulas below. C (n) F k! (n k)! Recursive formula One method uses the recursive, purely additive, formula for all integers n, k k Sn-1, with in values (a)- 1 for all integers n 20, Q1. Iteration vs. Recursion (Continued) In your implementation, use the interval timer on board to measure the elapsed time of executions for iterative approach and recursive approach respectively. Print out the elapsed time in the terminal window and compare the results. State the pros and cons of two methods from the views of time complexity, (memory) space complexity and the complexity in development developer's aspect).

Explanation / Answer

Compariosion of both technique respectively are as follows:

Pros and Cons for the above methods are the heavy push and pop of registers in each recursive call function thus leads to poor performance, we can clearly depict that recurssive is lot slower than iterative.

N Recursive Iterative 10 334 ticks 11 ticks 100 846 ticks 23 ticks 1000 3368 ticks 110 ticks 10000 9990 ticks 975 ticks 100000 stack overflow 9767 ticks

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