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

- 141.1K All Categories
- 104.5K Programming Languages
- 6.4K Assembler Developer
- 1.8K Basic
- 39.8K C and C++
- 4.3K C#
- 7.9K Delphi and Kylix
- 4 Haskell
- 9.6K Java
- 4.1K Pascal
- 1.3K Perl
- 2K PHP
- 508 Python
- 48 Ruby
- 4.3K VB.NET
- 1.6K VBA
- 20.8K Visual Basic
- 2.6K Game programming
- 310 Console programming
- 88 DirectX Game dev
- 1 Minecraft
- 110 Newbie Game Programmers
- 2 Oculus Rift
- 8.9K Applications
- 1.8K Computer Graphics
- 726 Computer Hardware
- 3.4K Database & SQL
- 522 Electronics development
- 1.6K Matlab
- 628 Sound & Music
- 256 XML Development
- 3.3K Classifieds
- 194 Co-operative Projects
- 182 For sale
- 189 FreeLance Software City
- 1.9K Jobs Available
- 600 Jobs Wanted
- 201 Wanted
- 2.9K Microsoft .NET
- 1.7K ASP.NET
- 1.1K .NET General
- 3.2K Miscellaneous
- 3 Join the Team
- 0 User Profiles
- 349 Comments on this site
- 59 Computer Emulators
- 2K General programming
- 178 New programming languages
- 608 Off topic board
- 163 Mobile & Wireless
- 37 Android
- 124 Palm Pilot
- 335 Multimedia
- 151 Demo programming
- 184 MP3 programming
- 0 Bash scripts
- 19 Cloud Computing
- 53 FreeBSD
- 1.7K LINUX programming
- 367 MS-DOS
- 0 Shell scripting
- 320 Windows CE & Pocket PC
- 4.1K Windows programming
- 885 Software Development
- 405 Algorithms
- 68 Object Orientation
- 87 Project Management
- 90 Quality & Testing
- 234 Security
- 7.5K WEB-Development
- 1.8K Active Server Pages
- 61 AJAX
- 2 Bootstrap Themes
- 55 CGI Development
- 19 ColdFusion
- 222 Flash development
- 1.4K HTML & WEB-Design
- 1.4K Internet Development
- 2.2K JavaScript
- 33 JQuery
- 286 WEB Servers
- 142 WEB-Services / SOAP

hetbrouwertje
Posts: **2**Member

in Pascal

Hello,

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

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

Terms of use / Privacy statement / Publisher: Lars Hagelin

Programmers Heaven articles / Programmers Heaven files / Programmers Heaven uploaded content / Programmers Heaven C Sharp ebook / Operated by CommunityHeaven LLC

© 1997-2015 Programmersheaven.com - All rights reserved.

## Comments

19Member:

: 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

2MemberBut 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

19Member:

: 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