StairCase

{There's a staircase with N steps, and you can climb 1 or 2 steps at a time. Given N, write a function that returns the number of unique ways you can climb the staircase.
 The order of the steps matters.

For example, if N is 4, then there are 5 unique ways:

1, 1, 1, 1
2, 1, 1
1, 2, 1
1, 1, 2
2, 2
What if, instead of being able to climb 1 or 2 steps at a time, you could climb any number from a set of positive integers X? For example,
if X = [1, 3, 5], you could climb 1, 3, or 5 steps at a time. Generalize your function to take in X.   }
program drouj;
uses WinCrt;
type
    tab = Array [1..100] of string;
var
    n : Byte;
    t : tab;
    Procedure saisie(var n : byte );
        begin
            repeat
                write('N= ');
                 read(n);
            until (n <=100)and (n>0);
        end;
        function verif(t: tab;k:byte;ch: string): Boolean;
            Var
                a: byte;
            Begin
                a:=1;
                while (t[a]<> ch ) and (a<=k) do
                    a:=a+1;
                verif := a >k;
            end;
                Function calcul(n: Byte):integer;
                    Var
                        s,x:integer;
                        ls:longint;
                        a,k:byte;
                        t: tab;
                        tt: toch;
                        ch: string;
                    Begin
                        k:=1;
                        for a:=1 to n*n do
                            begin
                                s:=0;
                                ls:=0;
                                repeat
                                    repeat
                                        x:=random(2)+1;
                                    until x+s <= n ;
                                    s:=s+x;
                                    ls:=ls*10+x;
                                until s = n ;

                                str(ls,ch);
                                if a=1 then
                                    t[1] := ch
                                Else
                                    if verif(t,k,ch) then
                                        begin
                                            k:=k+1;
                                            t[k]:=ch;
                                        end;
                            end;
                            calcul:=k;
                    end;
Begin
    saisie(n);
    write('There are ',calcul(n),' unique ways to climb the stairs');
End.