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

[Albert Chan]

(10-16-2022 05:52 PM)Valentin Albillo Wrote:  Another pretty obvious optimization would be to take advantage of the symmetry, as the man's starting location is at the top corner; this would cut running time and required RAM roughly in half but it loses generality, i.e.: arbitrary non-symmetrically placed starting positions (one or more) would not run at all, and it would complicate the coding somewhat; also, for a one-time program which already runs suitably fast it's really a moot point.

Here is my code, removed symmetry for generality.

For other starting positions, edit LINE 30, with M = first empty row.
Tips: we can *still* use symmetry, by rotation for the smallest starting M

10 DESTROY ALL @ INPUT "[VA]SRC012A R,S= ";R,S @ SETTIME 0
20 OPTION BASE 0 @ T=R+1 @ REAL P(T,T),Q(T,T)
30 P(1,1)=1 @ M=2
40 FOR K=1 TO S
50 MAT Q=P @ Q(1,1)=Q(1,1)*3 ! BUILD Q
60 FOR I=2 TO M-(M=R) @ Q(I,1)=Q(I,1)*1.5 @ Q(I,I)=Q(I,I)*1.5 @ NEXT I
70 IF M<>R THEN 100
80 FOR J=2 TO R-1 @ Q(R,J)=Q(R,J)*1.5 @ NEXT J
90 Q(R,1)=Q(R,1)*3 @ Q(R,R)=Q(R,R)*3
100 FOR I=1 TO M @ FOR J=1 TO I ! BUILD P
110 P(I,J)=Q(I+1,J)+Q(I+1,J+1)+Q(I,J-1)+Q(I,J+1)+Q(I-1,J-1)+Q(I-1,J)
120 NEXT J @ NEXT I
130 M=M+(M<R)
140 DISP K;TIME
150 NEXT K
160 T=0 @ FOR J=1 TO R @ T=T+P(R,J) @ NEXT J
170 DISP TIME;R;S;T/6^S


>RUN
[VA]SRC012A R,S= 30,60
...
87.6      30 60      9.51234350205E-6

As expected, without symmetry, speed almost cut in half.