vb.net print barcode zebra RECURSION in Java

Generator Data Matrix in Java RECURSION

RECURSION
Decoding ECC200 In Java
Using Barcode Control SDK for Java Control to generate, create, read, scan barcode image in Java applications.
Generating ECC200 In Java
Using Barcode generation for Java Control to generate, create ECC200 image in Java applications.
The output is:
Data Matrix 2d Barcode Reader In Java
Using Barcode recognizer for Java Control to read, scan read, scan image in Java applications.
Make Barcode In Java
Using Barcode generator for Java Control to generate, create barcode image in Java applications.
Move Move Move Move Move Move Move top top top top top top top disk disk disk disk disk disk disk from from from from from from from peg peg peg peg peg peg peg A A C A B B A to to to to to to to peg peg peg peg peg peg peg C. B. B. C. A. C. C.
Barcode Reader In Java
Using Barcode reader for Java Control to read, scan read, scan image in Java applications.
Painting Data Matrix 2d Barcode In Visual C#.NET
Using Barcode generator for VS .NET Control to generate, create ECC200 image in VS .NET applications.
To solve the problem for three disks, the call at line 3 passes 3 to n, 'A' to x, 'B' to y, and 'C' to z. Since n > 1, line 10 executes next, passing 2 to n, 'A' to x, 'B' to z, and 'C' to y. Again, since n > 1, line 10 executes next, passing 1 to n, 'A' to x, 'B' to y, and 'C' to z. In that call, n = 1, so line 8 executes, printing the first line of output:
Data Matrix Drawer In .NET
Using Barcode creator for ASP.NET Control to generate, create Data Matrix ECC200 image in ASP.NET applications.
Data Matrix 2d Barcode Maker In .NET
Using Barcode maker for VS .NET Control to generate, create Data Matrix 2d barcode image in .NET framework applications.
Move top disk from peg A to peg C.
Painting Data Matrix 2d Barcode In VB.NET
Using Barcode maker for VS .NET Control to generate, create DataMatrix image in .NET framework applications.
Painting Data Matrix 2d Barcode In Java
Using Barcode maker for Java Control to generate, create Data Matrix ECC200 image in Java applications.
That call returns to where the previous call left off at line 10, proceeding to line 11, where n = 2, x = 'A', y = 'C', and z = 'B'. That prints the second line of output:
EAN / UCC - 13 Generator In Java
Using Barcode generator for Java Control to generate, create GTIN - 13 image in Java applications.
Code 39 Extended Generation In Java
Using Barcode encoder for Java Control to generate, create Code 3/9 image in Java applications.
Move top disk from peg A to peg B.
Generating Code11 In Java
Using Barcode encoder for Java Control to generate, create Code11 image in Java applications.
Read ECC200 In None
Using Barcode decoder for Software Control to read, scan read, scan image in Software applications.
Then line 12 executes, this time passing 1 to n, 'C' to x, 'A' to y, and 'B' to z. In that call, n = 1 again, so line 8 executes, printing the third line of output:
Bar Code Encoder In Java
Using Barcode creation for Eclipse BIRT Control to generate, create bar code image in BIRT applications.
Barcode Generator In None
Using Barcode drawer for Software Control to generate, create barcode image in Software applications.
Move top disk from peg C to peg B.
Printing EAN128 In None
Using Barcode creator for Font Control to generate, create EAN 128 image in Font applications.
UCC - 12 Maker In Java
Using Barcode encoder for Eclipse BIRT Control to generate, create GS1 - 12 image in BIRT applications.
That call returns to where the second recursive call had left off at line 12. Since that is the last executable statement in the method, it also returns, back to where the first recursive call had left off at line 10. So it proceeds to line 11 with n = 3, x = 'A', y = 'B', and z = 'C'. That prints the fourth line of output:
Create UPC-A Supplement 2 In None
Using Barcode drawer for Office Word Control to generate, create UCC - 12 image in Microsoft Word applications.
Creating UPC A In C#
Using Barcode maker for .NET Control to generate, create GTIN - 12 image in Visual Studio .NET applications.
Move top disk from peg A to peg C.
Then line 12 executes, passing 2 to n, 'B' to x, 'A' to y, and 'C' to z. That call, HanoiTowers(2, 'B', 'A', 'C'), recursively moves the stack of two disks from peg B to to peg C via peg A and generates the last three lines of output:
Move top disk from peg B to peg A. Move top disk from peg B to peg C. Move top disk from peg A to peg C.
Since the previous four moves had already transferred the largest disk from peg A to peg C, this completes the task.
MUTUAL RECURSION When a function calls itself, it is called direct recursion. Another form of recursion is when a function calls other functions that call other functions that eventually call the original function. This is called indirect recursion. Its most common form is when two functions call each other. This is called mutual recursion. (See Figure 9.6.)
Figure 9.6 Types of recursion
EXAMPLE 9.16 The Sine and Cosine Functions Computed by Mutual Recursion
The sine and cosine functions from trigonometry can be defined in several different ways, and there are several different algorithms for computing their values. The simplest (although not the most efficient) is via mutual recursion. It is based upon the identities: sin2 = 2sin cos cos2 = 1 2(sin )2 and the two Taylor polynomials: sin x x x 3/6
RECURSION
[CHAP. 9
cos x 1 x 2/2 which are close approximations for small values of x.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
public class TestMutualRecursion { public static void main(String[] args) { String fmt1 = "%18s%18s%18s%n"; String fmt2 = "%18.13f%18.13f%18.13f%n"; System.out.printf(fmt1, "s(x) ", "Math.sin(x) ", "error "); for (double x = 0.0; x < 1.0; x += 0.1) { System.out.printf(fmt2, s(x), Math.sin(x), Math.sin(x) - s(x)); } System.out.printf(fmt1, "c(x) ", "Math.cos(x) ", "error "); for (double x = 0.0; x < 1.0; x += 0.1) { System.out.printf(fmt2, c(x), Math.cos(x), c(x) - Math.cos(x)); } } public static double s(double x) { if (-0.005 < x && x < 0.005) { return x - x*x*x/6; // basis } return 2*s(x/2)*c(x/2); // recursion } public static double c(double x) { if (-0.005 < x && x < 0.005) { return 1.0 - x*x/2; // basis } return 1 - 2*s(x/2)*s(x/2); // recursion } }
The output is:
Math.sin(x) error 0.0000000000000 0.0000000000000 0.0998334166468 0.0000000000005 0.1986693307951 0.0000000000009 0.2955202066613 0.0000000000069 0.3894183423087 0.0000000000018 0.4794255386042 0.0000000000051 0.5646424733950 0.0000000000120 0.6442176872377 0.0000000000015 0.7173560908995 0.0000000000027 0.7833269096275 0.0000000000043 0.8414709848079 0.0000000000063 Math.cos(x) error 1.0000000000000 0.0000000000000 0.9950041652780 0.0000000000000 0.9800665778412 0.0000000000002 0.9553364891256 0.0000000000021 0.9210609940029 0.0000000000007 0.8775825618904 0.0000000000028 0.8253356149097 0.0000000000082 0.7648421872845 0.0000000000013 0.6967067093472 0.0000000000027 0.6216099682707 0.0000000000054 0.5403023058681 0.0000000000098 This works because on each recursive call x is divided by 2, and eventually it reaches the basis criterion (-0.005 < x && x < 0.005), which stops the recursion. s(x) 0.0000000000000 0.0998334166464 0.1986693307941 0.2955202066544 0.3894183423069 0.4794255385991 0.5646424733831 0.6442176872362 0.7173560908969 0.7833269096232 0.8414709848016 c(x) 1.0000000000000 0.9950041652781 0.9800665778414 0.9553364891277 0.9210609940036 0.8775825618932 0.8253356149179 0.7648421872857 0.6967067093499 0.6216099682760 0.5403023058779
CHAP. 9]
Copyright © OnBarcode.com . All rights reserved.