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***drdebcol*** · (This post was last modified: 12-21-2009 02:54 AM by drdebcol.)

Here is one mathematical problem ! It was on some competitions in programming !
You need to find path between dots in coordinate system !
If you have n dots and every dot has it's coordinates x and y !
First you need to have formula for finding length of path between two dots !
It is Euclid formula or Euclidean distance, look at the picture :
[Image: formula_coordinate.jpg]

And i wrote that in Pascal as function :

Code:

function length_between_two_dots(x1,y1,x2,y2:integer):real;

 begin

  length_between_two_dots:=sqrt(sqr(x2-x1)+sqr(y2-y1));

 end;

where sqrt represents sqare root and sqr represents square (for example sqr(5)=25 and sqrt(25)=5).
And you just need to find sum of those paths !
Number of paths is number_of_dots-1 ! or n-1 !
Because of that i made this loop :

Code:

for i:=1 to n-1 do

So here is the code in Turbo Pascal for Windows :

Code:

program length_in_system;

uses wincrt;

type

  tcoordinates=record

  x,y:integer;

  end;

var

  i,j,n:integer;

  total_length,k:real;

  a:array[1..100] of tcoordinates;

  s:string;

function length_between_two_dots(x1,y1,x2,y2:integer):real;

 begin

  length_between_two_dots:=sqrt(sqr(x2-x1)+sqr(y2-y1));

 end;

begin

writeln('************************************');

writeln('*Program for finding length of path*');

writeln('* on every segment and total path  *');

writeln('*           by Dr DEBCOL           *');

writeln('************************************');

writeln('Enter number of coordinates !');

readln(n);

writeln('Enter x and y coordinats in lines !');

for i:=1 to n do

readln(a[i].x,a[i].y);

    total_length:=0;

for i:=1 to n-1 do

  begin

    if i=n-1 then

      s:=''

    else

      s:='+';

    k:=length_between_two_dots(a[i].x,a[i].y,a[i+1].x,a[i+1].y);

    writeln(k:9:3,s);

    total_length:=total_length+k;

  end;

writeln(' = ',total_length:9:3);

end.