some time ago I started to learn Turbo Pascal.

Now I've got a complex question, for me that is.

I want to write a program that prints out Pascal's Triangle.

But I'm stuck since I started to figure out how to write this program.

The program has to ask the user how many rows it has to display, after that the program should give Pascal's Triangle up to the number of rows the user has determined.

I hope someone can help me with this problem.

I'm too stuck

Thanks for helping me!

Pepijn de Brouwer

It looks like you're new here. If you want to get involved, click one of these buttons!

- 140.8K All Categories
- 103.6K Programming Languages
- 6.4K Assembler Developer
- 401 Assembly Code Share
- 239 Getting started in assembly
- 4.6K x86 Assembly
- 1.9K Basic
- 97 Qbasic
- 39.9K C and C++
- 5.6K Beginner C/C++
- 330 C/C++ on Linux/Unix
- 450 C/C++ Windows API
- 522 C++ Builder
- 253 C++ Game Development
- 3.3K C++ MFC
- 103 C++.NET
- 404 Visual C++
- 2.9K C#
- 7.9K Delphi and Kylix
- 334 Advanced Delphi
- 360 Delphi beginners
- 4 Haskell
- 9.7K Java
- 56 Enterprise JavaBeans
- 1.3K Java Beginners
- 304 Java Server Pages
- 4.1K Pascal
- 1.3K Perl
- 11 Perl 6
- 2K PHP
- 546 Python
- 37 Ruby
- 4.4K VB.NET
- 258 Advanced VB.Net
- 1.6K VBA
- 20.8K Visual Basic
- 767 Access databases and VB
- 831 Advance Visual Basic
- 1.2K Beginner VB
- 2.6K Game programming
- 315 Console programming
- 90 DirectX Game dev
- 1 Minecraft
- 112 Newbie Game Programmers
- 2 Oculus Rift
- 9K Applications
- 1.8K Computer Graphics
- 279 3D Graphics
- 129 DirectX
- 125 OpenGL
- 740 Computer Hardware
- 9 Cooling & Overclocking
- 3.4K Database & SQL
- 1.1K Access
- 91 ADO Programming
- 288 MySQL
- 358 Oracle
- 440 SQL-Server
- 535 Electronics development
- 1.6K Matlab
- 628 Sound & Music
- 25 DirectSound
- 257 XML Development
- 3.3K Classifieds
- 199 Co-operative Projects
- 198 For sale
- 190 FreeLance Software City
- 1.9K Jobs Available
- 603 Jobs Wanted
- 209 Wanted
- 2.9K Microsoft .NET
- 1.8K ASP.NET
- 1.1K .NET General
- 22 .NET WEB-Services
- 129 .NET WinForms
- 14 .NET XML
- 50 ADO.NET
- 142 C# & VB.NET School Support
- 3.4K Miscellaneous
- 4 Join the Team
- 354 Comments on this site
- 69 Computer Emulators
- 2.1K General programming
- 187 New programming languages
- 621 Off topic board
- 200 Mobile & Wireless
- 72 Android
- 126 Palm Pilot
- 338 Multimedia
- 154 Demo programming
- 184 MP3 programming
- 0 Bash scripts
- 27 Cloud Computing
- 1 Witsbits Go Cloud
- 53 FreeBSD
- 1.7K LINUX programming
- 1 Awk scripting
- 332 Linux Support
- 0 Sed scripting
- 370 MS-DOS
- 0 Shell scripting
- 321 Windows CE & Pocket PC
- 4.1K Windows programming
- 177 COM/DCOM
- 61 Networking And Security
- 17 Windows 2003 Server
- 6 Windows Vista
- 176 Windows XP
- 939 Software Development
- 416 Algorithms
- 68 Object Orientation
- 24 RUP & UML
- 91 Project Management
- 95 Quality & Testing
- 268 Security
- 63 Evil Scripting
- 81 Hacking
- 7.7K WEB-Development
- 1.8K Active Server Pages
- 61 AJAX
- 4 Bootstrap Themes
- 55 CGI Development
- 28 ColdFusion
- 224 Flash development
- 1.4K HTML & WEB-Design
- 1.4K Internet Development
- 131 Mobile Internet & Messaging
- 211 Wireless development
- 2.2K JavaScript
- 37 JQuery
- 304 WEB Servers
- 153 Apache
- 79 IIS
- 150 WEB-Services / SOAP

## Comments

:

: some time ago I started to learn Turbo Pascal.

: Now I've got a complex question, for me that is.

:

: I want to write a program that prints out Pascal's Triangle.

: But I'm stuck since I started to figure out how to write this program.

:

: The program has to ask the user how many rows it has to display, after that the program should give Pascal's Triangle up to the number of rows the user has determined.

:

: I hope someone can help me with this problem.

: I'm too stuck

:

: Thanks for helping me!

:

:

: Pepijn de Brouwer

:

Hi Pepijn!

In the first line will 1, in the second will 1 and 1. In all lines the first and last element will be 1.

In pursuance (in counting ...) there are 3 versions for getting non-winger elements:

a) count them as sum of two elements "above" them:

1

1 1

1 2 1

1 3 3 1

...

But for this You need store at one time at least half of elements of the last line. For this You need static or dinamic array, and for large line numbers large memory.

b) for these elements one-by-one use the binomial coefficients' formula by expression "k under n", that is (you have see two-lines-height parentheses ...),

/n

k/

where "k under n" = n!/(k!*(n-k)!); here x! (i.e. factorial of x) = 1*2*3*4*...*(x-1)*x, while 0!=1.

In our case k = 0...n is the index of elements in one (in the nth) line.

This method isn't require many memory, but counting of factorials on the one hand is time-waster, on the second it results very large numbers while the elements still aren't large.

c) the simplest way is based on equality

(k under n) = (k-1 under n) * (n - (k-1)) / k.

This formula follows from previous formula in section b.

The program, using this method:

[code]

Program Pascal_Triangle;

var

NMax,

N,

K,

E : longint;

begin

Write ('How many lines: ');

ReadLn (NMax);

for N := 0 to NMax-1 do begin

E := 1; (* for K=0; this is "0 under N" *)

Write (E);

for K := 1 to N do begin

(* (K u N) = (K-1 u N) * (N - (K-1)) / K : *)

E := E * (N - K + 1) div K;

Write (' ', E);

end;

WriteLn;

end;

end.

[/code]

Best regards:

gyapesz

But this brings me to another question.

Can someone help me figure out what the variables stand for?

What do Nmax, N, K and E mean?

I guess 'Nmax' gives the number of rows, but I'm not sure.

Thanks for helping me out in advance!

Pepijn de Brouwer

:

: But this brings me to another question.

: Can someone help me figure out what the variables stand for?

: What do Nmax, N, K and E mean?

: I guess 'Nmax' gives the number of rows, but I'm not sure.

:

: Thanks for helping me out in advance!

:

:

: Pepijn de Brouwer

:

Hi Pepijn!

NMax

is the requested number of rows.

N = 0..NMax-1

is the index (running counter) for the rows.

K = 0..N (N is other for each row)

is the index (running counter) for elements in the Nth row; but because of algorithm's method, for K=0 we calculate the element separately and the rows' _cycles_ will run for K=1..N only.

E

is the running element; it's value is recalculated (and printed) for each element of each row, one by one.

in example below NMax = 5:

[code]

1 N=0 K=0 (=N) E= 1

1 1 N=1 K=0..1 (=N) E= 1, then 1

1 2 1 N=2 K=0..2 (=N) E= 1, then 2, then 1

1 3 3 1 N=3 K=0..3 (=N) E= 1, 3, 3, 1

1 4 6 4 1 N=4 (=NMax-1) K=0..4 (=N) E= 1, 4, 6, 4, 1

[/code]

Best regards

gyapesz