Answered: In lisp programming Consider the two…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

See similar textbooks

Related questions

Question

In lisp programming

Consider the two versions of the function computing the combinations. Add a global variable counter and increment it by one at the top of both functions. This will count the number of function calls required to complete the calculations in each case. Try the two versions of the function for a few pairs of numbers n and m and print out the value of the counter after each of them. Don't forget to reset the counter to 0 before each call. Comment on the observed difference between the numbers of function calls.

Combinations
C(n, m) = n!/(m! (n-m)!)
C(n, m) = C(n-1, m) + C(n-1, m-1)
(defun comb (nm)
(cond
((= nm) 1)
((= m 0) 1)
((= m 1) n)
(t (+ (comb (- n 1) m)
(comb (- n 1) (- m 1))))))
(comb 3 2); 3
(comb 5 2); 10
Improved version with DP:
(defun el10 (nm)
(+ (* n 10) m)) ; 10*n+m
(setq C (make-vector 100 mil))
(defun comb1 (nm)
(let ((res 0))
(if (setq res (elt C (el10 n m))) res
(setq res
(cond
((= nm) 1)
((= m 0) 0)
((= m 1) n)
(t (+ (comb1 (- n 1) m)
(- n 1)
(comb1
(- m 1))))))
(aset C (el10 nm) res))))
(comb1 7 3) ; 35
(comb1 10 5); 252

Expert Solution

Step by step

Solved in 3 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.

Similar questions