Computer Science: A Structured Programming Approach Using C, Third Edition
3rd Edition
ISBN: 9780534491321
Author: Behrouz A. Forouzan, Richard F. Gilberg
Publisher: Course Technology, Inc.
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Chapter 5, Problem 16PS
If
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Exercise III: Catalan numbers
For n e N, denote by c, to be the number of ways to form a "mountain range" with n
upstrokes (U) and n downstrokes (D) that all stay above a horizontal line. For instance:
for n = 1, only UD is allowed, so c = 1;
• for n = 2, only UUDD and UDUD are allowed, so c2 = 2.
1. Check that c3 = 5 by writing down or drawing all possible options.
2. Consider the power series
+00
g(x) = 2
n=0
(by definition co =
1) called the generating function of the sequence (en). Justify
that cn < 4" for each n, and deduce that the radius of convergence of g is at least
1/4.
3. It can be show that for r E (-1/4, 1/4),
g(x) = 1+ xg(r)?
and therefore
1- VI
4.x
g(x) =
2.x
Use this formula and the known power series of V1+ x to write the first terms of
the power series expansion of g, in the form
g(x) = co + c1x + c2x2 + C3x + c4x* + ·..
Show how you obtain a few terms, but you do not need to show all computations
and you can use a calculator for fractions. Check that you recover co,…
Consider the following code fragment:
if x > 10:if y < 5:print("A")else:print("B")else:print("B")
Which of the following code fragment is equivalent (that is, behaves exactly in the same way) as the fragment above?
Select one:
a.if x > 10 or y < 5:print("A")else:print("B")
b.if x > 10 and y < 5:print("A")else:print("B")
c.if x > 10 or y < 5:print("B")else:print("A")
d.if x > 10 and y < 5:print("B")else:print("A")
This Code print the first occurrences of x,
Please Modify the code to print the last occurrences of x and print how many times it exists? ( with explanation for each line if possible) many thanks.
Chapter 5 Solutions
Computer Science: A Structured Programming Approach Using C, Third Edition
Ch. 5 - Prob. 1PSCh. 5 - The expression in a selection statement can have...Ch. 5 - Each labeled statement may identify one or more...Ch. 5 - The character classification functions are found...Ch. 5 - Prob. 5PSCh. 5 - The logical operator is true only when both...Ch. 5 - Prob. 7PSCh. 5 - Two-way selection is implemented with the ...Ch. 5 - Prob. 9PSCh. 5 - Which of the following statements creates the...
Ch. 5 - There are two different ways to implement a...Ch. 5 - Which of the following statements about switch...Ch. 5 - Which of the following statements about the...Ch. 5 - Prob. 14PSCh. 5 - Prob. 15PSCh. 5 - If x=0,y=5,z=5, what is the value of x, y, and z...Ch. 5 - If x=3,y=0,andz=4, what is the value of the...Ch. 5 - Simplify the following expressions by removing the...Ch. 5 - Prob. 19PSCh. 5 - If originally x=4,y=0,andz=2, what is the value of...Ch. 5 - If originally x=4,y=0,andz=2, what is the value of...Ch. 5 - If originally x=4,y=0,andz=2, what is the value of...Ch. 5 - If originally x=4,y=0,andz=2, what is the value of...Ch. 5 - If originally x=0,y=0,andz=1, what is the value of...Ch. 5 - If originally x=4,y=0,andz=2, what is the value of...Ch. 5 - If originally x=0,y=0,andz=1, what is the value of...Ch. 5 - If originally x=0,y=0,andz=1, what is the value of...Ch. 5 - If originally x=0,y=0,andz=1, what is the value of...Ch. 5 - If originally x=0,y=0,andz=1, what is the value of...Ch. 5 - If originally x=0,y=0,andz=1, what is the value of...Ch. 5 - If originally x=2,y=1,andz=1, what is the value of...Ch. 5 - If originally x=1,y=3,andz=0, what is the value of...Ch. 5 - Evaluate the value of the following expressions:...Ch. 5 - Evaluate the value of the following expressions:...Ch. 5 - Write an if statement that will assign the value 1...Ch. 5 - Prob. 36PSCh. 5 - Write the code to add 4 to an integer variable,...Ch. 5 - Prob. 38PSCh. 5 - Write the code to print either zero or not zero...Ch. 5 - If the variable divisor is not zero, divide the...Ch. 5 - Prob. 41PSCh. 5 - Rewrite the following code using one if statement:...Ch. 5 - Rewrite the following code fragment using one...Ch. 5 - Write a code fragment that tests the value of an...Ch. 5 - Prob. 45PSCh. 5 - Prob. 46PSCh. 5 - Write a function called smallest that, given three...Ch. 5 - Prob. 48PSCh. 5 - Write a function called month_of_year that, given...Ch. 5 - Write a function called parkingcharge that, given...Ch. 5 - Prob. 51PSCh. 5 - Complete the incremental implementation of Program...Ch. 5 - Write a program that determines a student's grade....Ch. 5 - Prob. 54PSCh. 5 - Given a point, a line from the point forms an...Ch. 5 - Prob. 56PSCh. 5 - Write a program that asks the user to enter the...Ch. 5 - Prob. 58PSCh. 5 - This program is a simple guessing game. The...Ch. 5 - Write a program that, given a person's birth date...Ch. 5 - Write a program that calculates the change due a...Ch. 5 - Write a menu-driven program that allows a user to...Ch. 5 - Write a program that tests a user-entered...Ch. 5 - Write a program to compute the real roots of a...
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