04 Examples

What would be a programming language without examples? … just …

  • Hello World
  • Christmas tree – ASCII-Art
  • Geo-Art
  • Search for four digits
  • Distance
  • Divide
  • Complex numbers
  • Almost perfect numbers
  • Sum of divisors

Hello World

PRINT "HELLO WORLD"

Prints “Hello World” in the output.

Christmas tree – ASCII art

Z = 1
WHILE Z != 0
  INPUT "ZEILEN:", Z
  IF Z = 0 THEN 
    BREAK
  ENDIF
  PRINT ""
  FOR J = Z TO 1 STEP - 1
    ZEILE = " "
      FOR I = 1 TO J
    ZEILE = ZEILE + " "
    NEXT
    FOR K = 1 TO (Z+1-J)*2-1 
      ZEILE = ZEILE + "#"
    NEXT
    PRINT ZEILE
  NEXT  
    ZEILE = ""
    FOR L = 1 TO Z+1
      ZEILE = ZEILE + " "
    NEXT
    ZEILE = ZEILE + "#"
    PRINT ZEILE   
  PRINT ""
WEND  

Asks for the number of lines and prints a fir tree in the output.
0 terminates the program.

Geo-Art

REM mit Button lat/lon Koordinaten holen
a = GETLAT()
b = GETLON()
c = 0.0
FOR i = 1 TO 10
  PROJECTION(a, b, 100.0, c)
  c = c + 36.0
  x = GETLAT()
  y = GETLON()
  WPTSADD(x, y)
NEXT

Reads in a coordinate and saves a circle with radius 100m and 10 points at a distance of 36 degrees in the waypoint list.

Search for four digits

FOR Z = 1 TO 9
FOR A = 1 TO 9
FOR H = 1 TO 9
FOR L = 0 TO 9
C = 0
U = Z * 1000 + A * 100 + H * 10 + L
V = A * 1000 + H * 100 + Z * 10 + L
W = H * 1000 + A * 100 + Z * 10 + L
IF ISSQR(U) = 1 THEN
C = C + 1
ENDIF
IF ISSQR(V) = 1 THEN
C = C + 1
ENDIF
IF ISSQR(W) = 1 THEN
C = C + 1
ENDIF
IF C = 3 THEN
PRINT "ZAHL: "; Z, A, H, L
ENDIF
NEXT
NEXT
NEXT
NEXT

Four digits are searched for which, when combined accordingly, form three four-digit square numbers.

Distance

R = 197
LAT = 50.9621667
LON = 11.03585
C = 0
FOR M = 0 TO 999
FOR S = 1 TO 2
FOR N = 0 TO 999
X = 50 + (57 + M / 1000) / 60
Y = 11 + (S + N / 1000) / 60
D = DISTANCE(LAT, LON, X, Y)
IF D <= R THEN
C = C + 1
ENDIF
NEXT
NEXT
NEXT
PRINT "Points within radius ", R, " are ", C

Searches the number of possible coordinates that lie within a radius R around the coordinate (LAT|LON).

Divide

FOR A = 1 TO 9
FOR B = 0 TO 9
Z = A * 10000 + 6790 + B
C = Z / 72
R = MOD(Z, 72)
IF R = 0 THEN
PRINT Z, A,B,C
ENDIF
NEXT
NEXT

Someone buys 72 identical products.
These products all cost the same price C and this price is an integer euro amount. (so 1 euro or 2 euros or 3 euros and so on).

The total amount of the purchase price is A679B euros.

Where B is a number from the set of integers from 0 to 9
and A is a number from the set of integers from 1 to 9.
So the total purchase price is five digits.

What are A and B?
And how much does a single product cost now?

Complex numbers

DATA 1.91372648, 2.4914364, 3.05909465, 0.71522325
DIM L
FOR I = 1 TO 2
LISTCLEAR(L)
READ X
READ Y
POLAR(L, X, Y)
PRINT L
NEXT

Reads one complex number at a time from a block of data in the form of Cartesian coordinates and converts them to their polar form.

Almost perfect numbers

DIM T
FOR I = 15 TO 99
LISTCLEAR(T)
DIVISORS(T, I)
S = SUM(T) - I
D = I - 4
IF S = D THEN
PRINT I, D, T
ENDIF
NEXT

What we are looking for are not perfect numbers, but – let us say – “almost perfect numbers”.

They are defined like this:
A natural number n is said to be an “almost perfect number”, if the sum of all its (positive) divisors except itself is smaller than the number n by a certain difference.

Question: what is the next larger almost perfect number A with respect to the difference 4 after 14?

Sum of divisors

DIM T
FOR I = 1 TO 999
LISTCLEAR(T)
DIVISORS(T, I)
S = SUM(T) - I
IF S > I THEN
PRINT I, S, T
END
ENDIF
NEXT

There are indeed also natural numbers for which the sum of all their (positive) divisors except themselves is greater than the number itself. What is the smallest natural number B for which this is the case?