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

[Dave Britten]

Sharp PC-1403H version of Valentin's 71B program (I didn't really have to change much, aside from minor syntactic/keyword differences):

10 CLEAR:INPUT "ROWS?";M:INPUT "STEPS?";N:DIM A(M,M):DIM B(M,M)
15 A(1,1)=1:W=M-1:FOR I=1 TO N:GOSUB 100
20 P=A(1,1)/2:IF P LET B(2,1)=B(2,1)+P:B(2,2)=B(2,2)+P
25 P=A(M,1)/2:IF P LET B(W,1)=B(W,1)+P:B(M,2)=B(M,2)+P
30 P=A(M,M)/2:IF P LET B(W,W)=B(W,W)+P:B(M,W)=B(M,W)+P
35 FOR X=2 TO W:U=X-1:V=X+1:P=A(X,1)/4:Q=A(X,X)/4:R=A(M,X)/4
40 IF P LET B(U,1)=B(U,1)+P:B(V,1)=B(V,1)+P:B(X,2)=B(X,2)+P:B(V,2)=B(V,2)+P
45 IF Q LET B(U,U)=B(U,U)+Q:B(V,V)=B(V,V)+Q:B(X,U)=B(X,U)+Q:B(V,X)=B(V,X)+Q
50 IF R LET B(M,U)=B(M,U)+R:B(M,V)=B(M,V)+R:B(W,U)=B(W,U)+R:B(W,X)=B(W,X)+R
55 NEXT X:FOR X=3 TO W:U=X-1:V=X+1:FOR Y=2 TO U:R=Y-1:S=Y+1:P=A(X,Y)/6
60 IF P LET B(U,R)=B(U,R)+P:B(U,Y)=B(U,Y)+P:B(X,R)=B(X,R)+P
65 IF P LET B(X,S)=B(X,S)+P:B(V,Y)=B(V,Y)+P:B(V,S)=B(V,S)+P
70 NEXT Y:NEXT X:GOSUB 200:NEXT I:P=0:FOR Y=1 TO M:P=P+A(M,Y):NEXT Y:BEEP 3: PRINT P:END
100 FOR J=1 TO M:FOR K=1 TO J:B(J,K)=0:NEXT K:NEXT J:RETURN
200 FOR J=1 TO M:FOR K=1 TO J:A(J,K)=B(J,K):NEXT K:NEXT J:RETURN
300 "A"S=0:FOR I=1 TO M:FOR J=1 TO I:S=S+A(I,J):NEXT J:NEXT I:PRINT S:END

This model takes about 4 hours to run for the 30, 60 case, and uses about 15 KB RAM for the program + data. After the program finishes, you can press DEF A to calculate the total probability for the whole map (should be extremely close to 1). One could easily tack on some more lines with user-key labels for performing other calculations on the finished matrix (probability of ending in the starting position, on any edge, at specific coordinates, etc.).

I believe this model has some machine-code matrix routines that can be invoked from within BASIC. I'll have to see if those can be used to speed up any of the matrix copying.