[VA] SRC #012a - Then and Now: Probability

[J-F Garnier]

I just finished to debug my code.
Valentin's hint to check that the sum of the probability of all cells should be 1 was very helpful to discover several coding errors :-)

The principle of my code is, I believe, similar to Fernando's solution, but the triangle cells are computed in a different order, row by row.
Also I took advantage of the symmetry of the starting condition.
Note that I used the fact that the HP BASIC doesn't enter a FOR loop if the final index is smaller than the starting index. This is not true in all BASIC, if needed enable back lines 160 and 220.
Note also that I used some HP-71 Math ROM matrix statements (and for the fun, one statement of the Math 2B version :-)

My code is longer, partially because I avoided multi-statement lines for clarity.
The result is very slightly different: 9.51234350205E-6 [updated, was 9.51234350213E-6 in the previous version]

Here is my code [updated: lines 90, 140 and 240 replaced by lines 91, 141 and 241]:

 10 OPTION BASE 1
 20 N=30 ! rows
 30 S=60 ! steps
 40 DIM A(N,N),B(N,N)
 50 ! set up A
 60 MAT A=ZER @ MAT B=ZER
 70 A(1,1)=1
 80 FOR X=1 TO S
 90 ! B(1,1)=(A(2,1)+A(2,2))/4 ! row 1
 91   B(1,1)=A(2,1)/4+A(2,2)/4 ! row 1
100   B(2,1)=A(1,1)/2+A(2,2)/4+A(3,1)/4+A(3,2)/6
120   B(2,2)=B(2,1) ! row 2
130   B(3,1)=A(2,1)/4+A(3,2)/6+A(4,1)/4+A(4,2)/6
140 ! B(3,2)=(A(2,1)+A(2,2)+A(3,1)+A(3,3))/4+(A(4,2)+A(4,3))/6
141   B(3,2)=A(2,1)/4+A(2,2)/4+A(3,1)/4+A(3,3)/4+A(4,2)/6+A(4,3)/6
150   B(3,3)=B(3,1) ! row 3
160   ! IF N<6 THEN 310
170   ! rows 4..N-2
180   FOR I=4 TO N-2
190     B(I,1)=A(I-1,1)/4+A(I,2)/6+A(I+1,1)/4+A(I+1,2)/6
210     B(I,2)=A(I-1,1)/4+A(I-1,2)/6+A(I,1)/4+A(I,3)/6+A(I+1,2)/6+A(I+1,3)/6
220     ! IF I<5 THEN 270
230     FOR J=3 TO INT((I+1)/2)
240 !     B(I,J)=(A(I-1,J-1)+A(I-1,J)+A(I,J-1)+A(I,J+1)+A(I+1,J)+A(I+1,J+1))/6
241       B(I,J)=A(I-1,J-1)/6+A(I-1,J)/6+A(I,J-1)/6+A(I,J+1)/6+A(I+1,J)/6+A(I+1,J+1)/6
250       B(I,I+1-J)=B(I,J)
260     NEXT J
270     B(I,I-1)=B(I,2)
280     B(I,I)=B(I,1)
290   NEXT I
310   ! row N-1
320   B(N-1,1)=A(N-2,1)/4+A(N-1,2)/6+A(N,1)/2+A(N,2)/4
330   B(N-1,2)=A(N-2,1)/4+A(N-2,2)/6+A(N-1,1)/4+A(N-1,3)/6+A(N,2)/4+A(N,3)/4
340   FOR J=3 TO INT(N/2)
350     B(N-1,J)=A(N-2,J-1)/6+A(N-2,J)/6+A(N-1,J-1)/6+A(N-1,J+1)/6+A(N,J)/4+A(N,J+1)/4
360     B(N-1,N-J)=B(N-1,J)
370   NEXT J
380   B(N-1,N-1)=B(N-1,1)
390   B(N-1,N-2)=B(N-1,2)
400   ! row N
410   B(N,1)=A(N-1,1)/4+A(N,2)/4
420   B(N,2)=A(N,1)/2+A(N,3)/4+A(N-1,1)/4+A(N-1,2)/6
430   FOR J=3 TO INT((N+1)/2)
440     B(N,J)=A(N,J-1)/4+A(N,J+1)/4+A(N-1,J-1)/6+A(N-1,J)/6
450     B(N,N+1-J)=B(N,J)
460   NEXT J
470   B(N,N-1)=B(N,2)
480   B(N,N)=B(N,1)
490   !
500   MAT A=B
550 NEXT X
555 ! output result
560 DIM C(N)
570 MAT C=RSUM(A)
580 DISP "PROB.=";C(N)

>RUN
PROB.= 9.512343502105-6


Now, I would be curious to see RPN/RPL solutions :-)

J-F