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EBK BUILDING JAVA PROGRAMS
4th Edition
ISBN: 9780134323718
Author: Stepp
Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)
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Chapter 12, Problem 16E
Program Plan Intro
Sierpinski carpet program
Program plan:
- Import the required packages.
- Create the class “SierpinskiCarpet”.
- Define the “size” to “243”
- Define the “main()” method.
- Create an object for scanner class.
- Get the value from the user.
- Initialize drawing panel.
- Create an object for graphics.
- Call the method “drawBox()”.
- Define the method “drawBox()”.
- Check whether the “stage” is greater than “0”.
- Get the size.
- Call the method “fillRect” to fill the size.
- Traverse the “for” loop to refer the row.
- Traverse the “for” loop to refer the column.
-
- Call the method “drawBox()” recursively.
- Check whether the “stage” is greater than “0”.
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Recursion can be direct or indirect. It is direct when a function calls itself and it is indirect recursion when a function calls another function that then calls the first function. To illustrate solving a problem using recursion, consider the Fibonacci series: - 1,1,2,3,5,8,13,21,34...The way to solve this problem is to examine the series carefully. The first two numbers are 1. Each subsequent number is the sum of the previous two numbers. Thus, the seventh number is the sum of the sixth and fifth numbers. More generally, the nth number is the sum of n - 2 and n - 1, as long as n > 2.Recursive functions need a stop condition. Something must happen to cause the program to stop recursing, or it will never end. In the Fibonacci series, n < 3 is a stop condition. The algorithm to use is this:
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The Polish mathematician Wacław Sierpiński described the pattern in 1915, but it has appeared in Italian art since the 13th century. Though the Sierpinski triangle looks complex, it can be generated with a short recursive function. Your main task is to write a recursive function sierpinski() that plots a Sierpinski triangle of order n to standard drawing. Think recursively: sierpinski() should draw one filled equilateral triangle (pointed downwards) and then call itself recursively three times (with an appropriate stopping condition). It should draw 1 filled triangle for n = 1; 4 filled triangles for n = 2; and 13 filled triangles for n = 3; and so forth.
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public class Sierpinski {
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Chapter 12 Solutions
EBK BUILDING JAVA PROGRAMS
Ch. 12.1 -
What is recursion? How does a recursive method...Ch. 12.1 - Prob. 2SCPCh. 12.1 - Prob. 3SCPCh. 12.1 - Prob. 4SCPCh. 12.1 - Prob. 5SCPCh. 12.1 - Prob. 6SCPCh. 12.1 - Prob. 7SCPCh. 12.2 - Prob. 8SCPCh. 12.2 -
What would be the effect if the code for the...Ch. 12.2 -
What would be the effect if the code for the...
Ch. 12.3 - Prob. 11SCPCh. 12.3 - Prob. 12SCPCh. 12.3 - Prob. 13SCPCh. 12.3 - Prob. 14SCPCh. 12.3 - Prob. 15SCPCh. 12.3 - Prob. 16SCPCh. 12.3 - Prob. 17SCPCh. 12.3 - Prob. 18SCPCh. 12.3 - Prob. 19SCPCh. 12.4 - Prob. 20SCPCh. 12.4 - Prob. 21SCPCh. 12.5 - Why is recursion an effective way to implement a...Ch. 12.5 - Prob. 23SCPCh. 12.5 - Prob. 24SCPCh. 12.5 - Prob. 25SCPCh. 12.5 - Prob. 26SCPCh. 12.5 - Prob. 27SCPCh. 12.5 - Prob. 28SCPCh. 12 - Prob. 1ECh. 12 - Write a method called writeNums that takes an...Ch. 12 - Write a method called writeSequence that accepts...Ch. 12 - Write a recursive method called doubleDigits that...Ch. 12 - Prob. 5ECh. 12 - Prob. 6ECh. 12 - Prob. 7ECh. 12 - Write a recursive method called multiplyEvens that...Ch. 12 - Prob. 9ECh. 12 - Prob. 10ECh. 12 - Prob. 11ECh. 12 - Write a recursive method called isReverse that...Ch. 12 - Prob. 13ECh. 12 - Prob. 14ECh. 12 - Prob. 15ECh. 12 - Prob. 16ECh. 12 - Prob. 17ECh. 12 - Prob. 18ECh. 12 - Prob. 19ECh. 12 - Prob. 20ECh. 12 - Prob. 21ECh. 12 - Prob. 22E
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