I'm working on modernizing Rosetta Code's infrastructure. Starting with communications. Please accept this time-limited open invite to RC's Slack.. --Michael Mol (talk) 20:59, 30 May 2020 (UTC)

Long stairs

From Rosetta Code
Long stairs is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

An evil wizard has trapped you in the stairwell of his castle. Your only hope of escape is to run up all 100 steps to reach the top, and you can run one step per second. Unfortunately the wizard uses magic to lengthen the staircase by five steps per second. The new steps are inserted randomly between existing steps, so if you're lucky some of them might be beneath you and not ahead of you.

Can you escape, or are you doomed to run up an ever-lengthening staircase forever?

Write a program to simulate your escape attempt. How are you doing after ten minutes? For every second between 600 and 609 seconds inclusive print the number of steps behind you and the number still ahead of you.

If you escaped, run 10,000 tests and print the average time taken and the average final length of the staircase.

C[edit]

 
#include <stdio.h>
#include <stdlib.h>
#include <time.h>
 
int main(void) {
int trial, secs_tot=0, steps_tot=0; //keep track of time and steps over all the trials
int sbeh, slen, wiz, secs; //all the variables related to an individual trial
time_t t;
srand((unsigned) time(&t)); //random number seed
printf( "Seconds steps behind steps ahead\n" );
for( trial=1;trial<=10000;trial++ ) { //10000 attempts for the runner
sbeh = 0; slen = 100; secs = 0; // initialise this trial
while(sbeh<slen) { //as long as the runner is still on the stairs
sbeh+=1; //runner climbs a step
for(wiz=1;wiz<=5;wiz++) { //evil wizard conjures five new steps
if(rand()%slen < sbeh)
sbeh+=1; //maybe a new step is behind us
slen+=1; //either way, the staircase is longer
}
secs+=1; //one second has passed
if(trial==1&&599<secs&&secs<610)
printf("%d  %d  %d\n", secs, sbeh, slen-sbeh );
 
}
secs_tot+=secs;
steps_tot+=slen;
}
printf( "Average secs taken: %f\n", secs_tot/10000.0 );
printf( "Average final length of staircase: %f\n", steps_tot/10000.0 );
return 0;
}
Output:

Seconds steps behind steps ahead 600 2147 953 601 2151 954 602 2156 954 603 2160 955 604 2166 954 605 2169 956 606 2174 956 607 2180 955 608 2184 956 609 2188 957 Average secs taken: 2921.493200 Average final length of staircase: 14707.466000

Factor[edit]

USING: combinators.random io kernel math math.order prettyprint ;
 
: position ( -- n ) 0 ;
: stairs ( -- n ) 100 ;
: new ( -- m n ) position stairs ;
: incd ( m n -- o p ) swap 1 + swap ;
: seconds ( m -- n ) 100 - 5 / ;
: window? ( n -- ? ) seconds 600 609 between? ;
: zap ( m n -- o p ) 2dup / [ incd ] whenp 1 + ;
: barrage ( m n -- o p ) 5 [ zap ] times ;
: .n ( n -- ) pprint 7 [ bl ] times ;
: .stats ( m n -- ) dup seconds .n over .n swap - .n nl ;
: .header ( -- ) "Seconds behind ahead" print ;
: ?.status ( m n -- o p ) dup window? [ 2dup .stats ] when ;
: tick ( m n -- o p ) incd barrage ;
: demo ( m n -- o p ) tick ?.status ;
: sim-with ( q -- n ) new rot [ 2dup < ] swap while drop ; inline
: first ( -- n ) [ demo ] sim-with ;
: sim ( -- n ) [ tick ] sim-with ;
: sims ( -- n ) 0 first + 9999 [ sim + ] times ;
: steps ( m -- n ) "Avg. steps: " write 10000 / dup . ;
: time ( n -- ) "Avg. seconds: " write seconds . ;
: main ( -- ) .header sims nl steps time ;
 
main
Output:
Seconds  behind     ahead
600       2067       1033       
601       2073       1032       
602       2078       1032       
603       2082       1033       
604       2087       1033       
605       2091       1034       
606       2096       1034       
607       2099       1036       
608       2103       1037       
609       2108       1037       

Avg. steps: 14731+23/200
Avg. seconds: 2926+223/1000

And for fun, a version without stack effects.

USING: combinators.random effects.parser io kernel math
math.order parser prettyprint stack-checker words ;
 
<< SYNTAX: .: [ scan-new-word parse-definition dup infer ]
with-definition define-declared ; >>
 
.: position 0 ;
.: stairs 100 ;
.: new position stairs ;
.: incd swap 1 + swap ;
.: seconds 100 - 5 / ;
.: window? seconds 600 609 between? ;
.: zap 2dup / [ incd ] whenp 1 + ;
.: barrage 5 [ zap ] times ;
.: .n pprint 7 [ bl ] times ;
.: .stats dup seconds .n over .n swap - .n nl ;
.: .header "Seconds behind ahead" print ;
.: ?.status dup window? [ 2dup .stats ] when ;
.: tick incd barrage ;
.: demo tick ?.status ;
.: first new [ 2dup < ] [ demo ] while drop ;
.: sim new [ 2dup < ] [ tick ] while drop ;
.: sims 0 first + 9999 [ sim + ] times ;
.: steps "Avg. steps: " write 10000 / dup . ;
.: time "Avg. seconds: " write seconds . ;
.: main .header sims nl steps time ;
 
main

Fermat[edit]

 
time_tot:=0; {we'll keep track of the total time and steps across all the trials}
steps_tot:=0;
!!('Seconds ','Steps behind ','Steps ahead');
for trial = 1 to 10 do
s_behind:=0; {initialise staircase and runner for this trial}
stair_len:=100;
time:=0;
while s_behind < stair_len do
s_behind:=s_behind + 1;
for wiz = 1 to 5 do
stair_len:=stair_len + 1; {evil wizard creates a step} {(mwaahahaha)}
if (Rand|stair_len) < s_behind then
s_behind:=s_behind + 1;
fi
od;
time:=time+1; {another second has passed}
if trial = 1 and 599<time and time<610 then
 !!(time, ' ', s_behind, ' ',stair_len-s_behind)
fi;
od;
time_tot:=time_tot+time;
steps_tot:=steps_tot+stair_len;
od;
 
!!(time_tot/10000);
!!(steps_tot/10000);
Output:

Seconds Steps behind Steps ahead

600        2125            975
601        2129            976
602        2132            978
603        2136            979
604        2142            978
605        2146            979
606        2151            979
607        2156            979
608        2162            978
609        2166            979
 3697083 / 1250
 3722083 / 250

FreeBASIC[edit]

 
randomize timer
dim as uinteger steps_behind = 0, stairs_length = 100, seconds, j
dim as uinteger seconds_tot, steps_tot
print "Seconds", "steps behind", "steps ahead"
for trial as uinteger = 1 to 10000 'We'll have the runner try this 10000 times
steps_behind = 0 'runner starts at the bottom
seconds = 0 'reset time taken
stairs_length = 100 'Staircase has 100 steps
while steps_behind < stairs_length 'if the runner hasn't reached the top
steps_behind += 1 'go up one step
for j = 1 to 5 'The evil wizard conjures another five steps
if int(rnd*stairs_length) < steps_behind then steps_behind += 1
'there's a chance that a new step will be behind you
stairs_length += 1 'but either way the staircase is one step longer
next j
seconds += 1 'that all took one second
if trial = 1 and seconds >599 and seconds < 610 then print seconds, steps_behind, stairs_length - steps_behind
'for the first attempt, see how the runner is doing after ten minutes
wend
seconds_tot += seconds 'if the runner escaped, track the time taken and the length of the stairs
steps_tot += stairs_length
next trial
 
print "Average time taken: ";seconds_tot/10000; " seconds."
print "Average final staircase length: ";steps_tot/10000; " steps."
'if you noticed that last number is about 100*exp(5), that's no coincidence
Output:

Seconds steps behind steps ahead 600 2032 1068 601 2038 1067 602 2042 1068 603 2045 1070 604 2048 1072 605 2053 1072 606 2055 1075 607 2060 1075 608 2064 1076 609 2068 1077 Average time taken: 2921.9457 seconds. Average final staircase length: 14709.7285 steps.

GW-BASIC[edit]

 
10 RANDOMIZE TIMER
20 TIMET = 0 : STEPST = 0
30 FOR TRIAL = 1 TO 10000
40 TIME = 0
50 SBEH = 0
60 SLEN = 100
70 SBEH = SBEH + 1
80 IF SBEH >= SLEN THEN GOTO 160
90 FOR WIZ = 1 TO 5
100 IF INT(RND*SLEN)<SBEH THEN SBEH = SBEH + 1
110 SLEN = SLEN + 1
120 NEXT WIZ
130 TIME = TIME + 1
140 IF TRIAL = 1 AND 599<TIME AND TIME <610 THEN PRINT TIME, SBEH, SLEN-SBEH
150 GOTO 70
160 TIMET = TIMET+TIME+1
170 STEPST = STEPST + SLEN
180 NEXT TRIAL
190 PRINT TIMET/10000
200 PRINT STEPST/10000

Julia[edit]

""" https://rosettacode.org/wiki/Long_stairs """
 
using Statistics
 
struct LongStairs
startstep::Int
startlength::Int
climbersteps::Int
addsteps::Int
end
 
Base.length(LongStairs) = typemax(Int)
Base.eltype(ls::LongStairs) = Vector{Int}
 
function Base.iterate(s::LongStairs, param = (s.startstep, s.startlength))
pos, len = param
pos += s.climbersteps
pos += sum(pos .> rand(1:len, s.addsteps))
len += s.addsteps
return [pos, len], (pos, len)
end
 
ls = LongStairs(1, 100, 1, 5)
 
println("Seconds Behind Ahead\n----------------------")
for (secs, (pos, len)) in enumerate(collect(Iterators.take(ls, 609))[600:609])
println(secs + 599, " ", pos, " ", len - pos)
end
 
println("Ten thousand trials to top:")
times, heights = Int[], Int[]
for trial in 1:10_000
trialstairs = LongStairs(1, 100, 1, 5)
for (sec, (step, height)) in Iterators.enumerate(trialstairs)
if step >= height
push!(times, sec)
push!(heights, height)
break
end
end
end
@show mean(times), mean(heights)
 
Output:
Seconds  Behind  Ahead
----------------------
601      1938    1167
602      1944    1166
603      1948    1167
604      1952    1168
605      1956    1169
606      1959    1171
607      1963    1172
608      1967    1173
609      1971    1174
Ten thousand trials to top:
(mean(times), mean(heights)) = (2927.0853, 14735.4265)

Pascal[edit]

Free Pascal[edit]

Trying to calculate results of multiple random rounds.Now a partial step forward 1/CntOfSpellStairs for every spell stair.
Now results are much closer.

program WizardStaircase;
const
StartStairLength = 100;
StairsPerSpell = 5;
rounds = 10000;
 
procedure OutActual(trials,behind,infront:longword);
begin
writeln(trials:5,infront+behind:12,behind:10,inFront:9);
end;
 
function OneRun(StairsPerSpell:Cardinal;WithOutput:boolean):longword;
var
inFront,behind,total,i,trials: Cardinal;
begin
trials := 0;
total := StartStairLength;
inFront := total;
behind := 0;
repeat
inc(trials);
inc(behind);
dec(infront);
//spell
i := StairsPerSpell;
repeat
if random(total) < behind then
inc(behind)
else
inc(infront);
inc(total);
dec(i);
until i=0;
if WithOutput then
begin
if (trials <= 609)AND(trials>=600) then
OutActual(trials,behind,infront);
end;
until infront = 0;
OneRun := total;
end;
 
procedure CheckDouble(StairsPerSpell:Cardinal);
var
behind,infront,relpos,total,One,relSpell : double;
i : LongInt;
begin
write(StairsPerSpell:3);
One := 1.0;
behind := 0.0;
inFront := StartStairLength;
total := StartStairLength;
relSpell := One/StairsPerSpell;
repeat
i := StairsPerSpell;
//doing a partial move per one stair per spell
repeat
relpos := (behind+relSpell)/total;
behind := behind + relpos +relSpell;
inFront := inFront+(One-relpos)-relSpell;
total := total+One;
dec(i);
until i= 0;
until infront < One;
writeln((total-StartStairLength)/StairsPerSpell:10:0,total:14:0);
end;
 
var
i,
mySpell,
attempt,
minStairs,
maxStairs,
total : longword;
begin
randomize;
writeln('Seconds steps total behind ahead');
total := OneRun(StairsPerSpell,true);
 
writeln(' average stairs needed steps minimum maximum');
for mySpell := 1 to 7 do
begin
write(mySpell:3,' ');
total := 0;
minStairs := High(minStairs);
maxStairs := low(maxStairs);
For i := rounds-1 downto 0 do
begin
attempt:= OneRun(mySpell,false);
if minStairs>attempt then
minstairs := attempt;
if maxStairs<attempt then
maxstairs := attempt;
inc(total,attempt);
end;
writeln((total-StartStairLength)/rounds/mySpell:12:3,total/rounds:14:3,minStairs:9,maxStairs:10);
end;
writeln;
 
writeln(' calculated ');
For i := 1 to 10 do
CheckDouble(i);
end.
@ TIO.RUN:
Seconds  steps total  behind    ahead
  600        3100      2260      840
  601        3105      2264      841
  602        3110      2269      841
  603        3115      2275      840
  604        3120      2281      839
  605        3125      2285      840
  606        3130      2291      839
  607        3135      2295      840
  608        3140      2300      840
  609        3145      2302      843
      average stairs needed steps minimum   maximum
  1       271.090       271.100      239       313
  2       367.570       735.150      540       954
  3       663.998      1992.003     1234      2911
  4      1353.416      5413.674     2748      8980
  5      2933.418     14667.099     6715     27210
  6      6648.557     39891.354    18394     80050
  7     15550.874    108856.130    42380    218892

 calculated 
  1       170           270
  2       317           734
  3       633          1999
  4      1333          5432
  5      2933         14765
  6      6673         40138
  7     15573        109111
  8     37063        296604
  9     89573        806257
 10    219154       2191640

Real time: 55.269 s

Phix[edit]

with javascript_semantics -- (nb expect blank screen for ~30s)

integer total_seconds = 0,
        total_steps = 0
printf(1,"time  behind  ahead\n")
printf(1,"----  ------  -----\n")
for trial=1 to 10_000 do
    integer stairs_length = 100,
            steps_behind = 0,
            seconds = 0
    while steps_behind < stairs_length do
        steps_behind += 1
        for wizard=1 to 5 do
            steps_behind += (rnd()*stairs_length < steps_behind)
            stairs_length += 1
        end for
        seconds += 1
        if trial=1 and seconds>=600 and seconds<=609 then
            printf(1,"%4d %7d %6d\n", {seconds, steps_behind, stairs_length-steps_behind})
        end if
    end while
    total_seconds += seconds
    total_steps += stairs_length
    if trial=1 then printf(1,"\n") end if
end for
printf(1,"Average seconds: %f, average steps: %f\n",
         {total_seconds/10000,total_steps/10000})
Output:
time  behind  ahead
----  ------  -----
 600    1978   1122
 601    1980   1125
 602    1986   1124
 603    1990   1125
 604    1995   1125
 605    1999   1126
 606    2002   1128
 607    2004   1131
 608    2008   1132
 609    2012   1133

Average seconds: 2913.609300, average steps: 14668.046500

Perl[edit]

#!/usr/bin/perl
 
use strict; # https://rosettacode.org/wiki/Long_stairs
use warnings;
 
my $sumseconds = my $sumsizes = my $runs = 0;
for ( 1 .. 1e4 )
{
$runs++;
my $behind = 0;
my $ahead = 100;
my $seconds = 0;
while( $ahead > 0 )
{
rand() <= ($ahead / ($behind + $ahead)) ? $ahead++ : $behind++ for 1 .. 5;
$behind++; # one step up
$ahead--;
$seconds++;
$_ == 1 and 600 <= $seconds <= 609 and
print "step $seconds: $behind behind, $ahead ahead\n";
}
$sumsizes += $behind;
$sumseconds += $seconds;
}
printf "\naverage stair length %d average seconds %d\n",
$sumsizes / $runs, $sumseconds / $runs;
Output:
step 600: 2233 behind, 867 ahead
step 601: 2237 behind, 868 ahead
step 602: 2241 behind, 869 ahead
step 603: 2247 behind, 868 ahead
step 604: 2249 behind, 871 ahead
step 605: 2254 behind, 871 ahead
step 606: 2258 behind, 872 ahead
step 607: 2262 behind, 873 ahead
step 608: 2268 behind, 872 ahead
step 609: 2273 behind, 872 ahead

average stair length 15438 average seconds 3067

Python[edit]

""" https://rosettacode.org/wiki/Long_stairs """
 
from numpy import mean
from random import sample
 
def gen_long_stairs(start_step, start_length, climber_steps, add_steps):
secs, behind, total = 0, start_step, start_length
while True:
behind += climber_steps
behind += sum([behind > n for n in sample(range(total), add_steps)])
total += add_steps
secs += 1
yield (secs, behind, total)
 
 
ls = gen_long_stairs(1, 100, 1, 5)
 
print("Seconds Behind Ahead\n----------------------")
while True:
secs, pos, len = next(ls)
if 600 <= secs < 610:
print(secs, " ", pos, " ", len - pos)
elif secs == 610:
break
 
print("\nTen thousand trials to top:")
times, heights = [], []
for trial in range(10_000):
trialstairs = gen_long_stairs(1, 100, 1, 5)
while True:
sec, step, height = next(trialstairs)
if step >= height:
times.append(sec)
heights.append(height)
break
 
print("Mean time:", mean(times), "secs. Mean height:", mean(heights))
 
Output:
Seconds  Behind  Ahead
----------------------
600       2122     978
601       2127     978
602       2130     980
603       2135     980
604       2139     981
605       2144     981
606       2149     981
607       2153     982
608       2157     983
609       2162     983

Ten thousand trials to top:
Mean time: 2780.502 secs. Mean height: 14002.51

Raku[edit]

my ($trials, $t-total, $s-total) = 10000;
 
say 'Seconds steps behind steps ahead';
 
race for ^$trials {
my $stairs = 100;
my $location = 0;
my $seconds = 0;
 
loop {
++$seconds;
++$location;
last if $location > $stairs;
for (1..$stairs).roll(5) {
++$location if $_ <= $location;
++$stairs;
}
say " $seconds $location {$stairs-$location}" if !$_ && (599 < $seconds < 610);
}
 
$t-total += $seconds;
$s-total += $stairs;
}
 
say "Average seconds: {$t-total/$trials}, Average steps: {$s-total/$trials}";
Sample output:
Seconds  steps behind  steps ahead
  600        2143         957
  601        2149         956
  602        2153         957
  603        2158         957
  604        2164         956
  605        2170         955
  606        2175         955
  607        2178         957
  608        2183         957
  609        2187         958
Average seconds: 2716.0197,  Average steps: 13677.143

Wren[edit]

Translation of: C
Library: Wren-fmt
import "random" for Random
import "./fmt" for Fmt
 
var totalSecs = 0
var totalSteps = 0
var rand = Random.new()
System.print("Seconds steps behind steps ahead")
System.print("------- ------------ -----------")
for (trial in 1..10000) {
var sbeh = 0
var slen = 100
var secs = 0
while (sbeh < slen) {
sbeh = sbeh + 1
for (wiz in 1..5) {
if (rand.int(slen) < sbeh) sbeh = sbeh + 1
slen = slen + 1
}
secs = secs + 1
if (trial == 1 && secs > 599 && secs < 610) {
Fmt.print("$d $d $d", secs, sbeh, slen - sbeh)
}
}
totalSecs = totalSecs + secs
totalSteps = totalSteps + slen
}
Fmt.print("\nAverage secs taken: $h", totalSecs/10000)
Fmt.print("Average final length of staircase: $h", totalSteps/10000)
Output:

Sample run:

Seconds    steps behind    steps ahead
-------    ------------    -----------
600        2112            988
601        2115            990
602        2121            989
603        2126            989
604        2130            990
605        2135            990
606        2141            989
607        2146            989
608        2150            990
609        2155            990

Average secs taken: 2914.465   
Average final length of staircase: 14672.325