[PeterP] Solving Project Euler #18 and #67 with the HP-71B

[PeterP]

(10-28-2022 11:42 PM)Valentin Albillo Wrote:    
Hi, PeterP,

PeterP Wrote:Just stumbled upon this Project Euler 18 and this Project Euler 67.

I guess you haven't read my article on solving PE's problems (heartily recommended !)

HP Article VA051 - Boldly Going - Climbing Project Euler

12-page article, featuring Project Euler, a fantastic project which attempts (and succeeds, in spades !) at providing a huge supply of challenging math+programming problems which are immensely fun to try and solve, learning loads of new concepts while sharpening your skills in the process.

In this article I tell my story with Project Euler and how I dealt with it back in 2011 using the vintage 1984 HP-71B (emulated & physical), which is orders of magnitude slower and less capable than the hardware/software combinations Project Euler's problems are intended for (i.e.: fast modern CPUs + high-level compiled languages), thus enormously upping the ante when tackling them with ancient hardware and interpreted BASIC. See for yourself how I did ! Seven carefully-selected sample PE problems discussed and solved, namely:


Project Euler problem #015 ─ Lattice paths
Project Euler problem #017 ─ Number letter counts
Project Euler problem #040 ─ Champernowne's constant
Project Euler problem #077 ─ Prime summations
Project Euler problem #093 ─ Arithmetic expressions
Project Euler problem #094 ─ Almost equilateral triangles
Project Euler problem #104 ─ Pandigital Fibonacci ends

PeterP Wrote:I wonder if 67 could be solved by the 71b...

But of course the HP-71B can solve those nearly-trivial problems with ease !

This is the original program I wrote 11 years ago to find and submit both answers to PE:

For PE18:

100  DESTROY ALL @ OPTION BASE 1 @ K=15 @ INTEGER A(K,K)
110  DATA 75,95,64,17,47,82,18,35,87,10,20,04,82,47,65,19,01,23,75,03
120  DATA 34,88,02,77,73,07,63,67,99,65,04,28,06,16,70,92,41,41,26,56
130  DATA 83,40,80,70,33,41,48,72,33,47,32,37,16,94,29,53,71,44,65,25
140  DATA 43,91,52,97,51,14,70,11,33,28,77,73,17,78,39,68,17,57,91,71
150  DATA 52,38,17,14,91,43,58,50,27,29,48,63,66,04,68,89,53,67,30,73
160  DATA 16,69,87,40,31,04,62,98,27,23,09,70,98,73,93,38,53,60,04,23
500  FOR I=1 TO K @ FOR J=1 TO I @ READ A(I,J) @ NEXT J @ NEXT I
510  FOR I=K TO 1 STEP -1 @ FOR J=1 TO I-1 @ A(I-1,J)=A(I-1,J)+MAX(A(I,J),A(I,J+1))
520  NEXT J @ NEXT I @ DISP "Max. sum:";A(1,1)

>RUN
       Max. sum: 1074

For PE67:

Same program, just change K=15 at line 100 to K=100 and the DATA statements, of course !

By the way, you'll need a large amount of RAM, just the A matrix needs 100x100x3 ~ 30 Kb, and the DATA statements (or much better, a previously created HP-71B file) containing the 2-digit numbers will require another 15 Kb or so to define the 5,050 values which will be read into matrix A at the beginning.

And come to that, you'd better find a way to automatically read them from the PE-supplied text file and make them available to the HP-71B. That is, if you don't cherish the idea of manually keying them in yourself.

Upon running the program, you'll get:

>RUN
       Max. sum: 7273

Best of luck with the remaining PE problems and, if you need help with solving some of them using the HP-71B, just ask and I'll see if I already created a solution in the distant past.

Best regards.
V.

Wonderful! Thank you so much for the article which I will enjoy reading and learning from on this intercontinental flight. I made it through the first few PEs with the hp41 (and almost through 808, one of the more recent ones). I admit to having switched recently for them to quasi the 71b, using a similar basic emulation on my iOS, as alas, sadly, there is none for the 71b (which would make many things easier by using Math, Math2, and JPC. Who knows, maybe someone gets inspired and builds a port, I for one would buy one immediately).

We are stuck on the gate / runway for another 30’ at least it seems, so I get some extra time.