Long stairs

From Rosetta Code
Revision as of 20:42, 27 August 2022 by Thundergnat (talk | contribs) (syntax highlighting fixup automation)
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.

11l

Translation of: C
V secs_tot = 0
V steps_tot = 0
print(‘Seconds    steps behind    steps ahead’)

L(trial) 1..10000
   V sbeh = 0
   V slen = 100
   V secs = 0
   L sbeh < slen
      sbeh++
      L 5
         I random:(slen) < sbeh
            sbeh++
         slen++

      secs++
      I trial == 1 & secs C 600..609
         print(‘#.        #.            #.’.format(secs, sbeh, slen - sbeh))

   secs_tot += secs
   steps_tot += slen

print(‘Average secs taken: #.6’.format(secs_tot / 10000.0))
print(‘Average final length of staircase: #.6’.format(steps_tot / 10000.0))
Output:
Seconds    steps behind    steps ahead
600        1906            1194
601        1910            1195
602        1913            1197
603        1918            1197
604        1923            1197
605        1929            1196
606        1934            1196
607        1936            1199
608        1940            1200
609        1943            1202
Average secs taken: 2920.077500
Average final length of staircase: 14700.387500

AutoHotkey

result := "Sec    steps behind    steps ahead"
x := longStairs(609)
for i, s in x.4
    result .= "`n" i+599 "`t" s "`t`t" x.2 - s
tests := 10000
loop % tests
{
    x := longStairs()
    totSteps += x.1
    totSec += x.3
}
MsgBox, 262144, , % result .= "`n`nAfter " tests " tests:`nAverage time taken = " totSec/tests " Sec"
        .    "`nAverage Stair length = " totSteps/tests " steps"
return

longStairs(t:=0){
    Stairs := [], last10Steps := [], s := 0
    loop 100
        Stairs[A_Index] := 0
    loop 
    {
        Stairs[++s] := "S"                        ; take a step forward
        if (last10Steps.count()>=10)
            last10Steps.RemoveAt(1)
        last10Steps.push(s)
        loop 5                                    ; add 5 steps to stairs
        {
            Random, stp, 1, % Stairs.Count()
            Stairs.InsertAt(stp, "x")
            s += s > stp ? 1 : 0
        }
        escT := s = Stairs.Count() ? A_Index : 0
        if (A_Index = t || escT)                  ; reached time limit or Escaped
            break
    }
    return [s, Stairs.Count(), escT, last10Steps]
}
Output:
Sec	steps behind	steps ahead
600	1991		1154
601	1993		1152
602	1997		1148
603	2001		1144
604	2004		1141
605	2008		1137
606	2010		1135
607	2013		1132
608	2016		1129
609	2018		1127

After 10000 tests:
Average time taken = 3063.260000 Sec
Average Stair length = 15416.300000 steps

C

#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

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

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

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

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

Go

Translation of: Wren
package main

import (
    "fmt"
    "math/rand"
    "time"
)

func main() {
    rand.Seed(time.Now().UnixNano())
    totalSecs := 0
    totalSteps := 0
    fmt.Println("Seconds    steps behind    steps ahead")
    fmt.Println("-------    ------------    -----------")
    for trial := 1; trial < 10000; trial++ {
        sbeh := 0
        slen := 100
        secs := 0
        for sbeh < slen {
            sbeh++
            for wiz := 1; wiz < 6; wiz++ {
                if rand.Intn(slen) < sbeh {
                    sbeh++
                }
                slen++
            }
            secs++
            if trial == 1 && secs > 599 && secs < 610 {
                fmt.Printf("%d        %d            %d\n", secs, sbeh, slen-sbeh)
            }
        }
        totalSecs += secs
        totalSteps += slen
    }
    fmt.Println("\nAverage secs taken:", float64(totalSecs)/10000)
    fmt.Println("Average final length of staircase:", float64(totalSteps)/10000)
}
Output:

Sample run:

Seconds    steps behind    steps ahead
-------    ------------    -----------
600        2138            962
601        2143            962
602        2148            962
603        2153            962
604        2159            961
605        2163            962
606        2167            963
607        2172            963
608        2177            963
609        2183            962

Average secs taken: 2917.9058
Average final length of staircase: 14689.519

J

stairsim=:{{
  t=. 0 NB. fifths of a second
  echo ;_8 _16 _20{.each 'seconds';'steps to top';'steps from bottom'
  for_trial. i.1e4 do.
    loc=. {.'min max'=. 0 100
    while. loc < max do.
      if. 0=5|t=.t+1 do.
        loc=. loc+1 
        if. 0=trial do.
          if. 1=2999 3046 I.t do.
            echo 8 16 20":(t%5),(max-loc),(loc-min)
          end.
        end.
      end.
      ins=. min+?max-min
      if. ins < loc do. min=. min-1 else. max=. max+1 end.
    end.
  end.
  echo 'Average steps taken: ',":t%5e4
  echo 'Average length of staircase: ',":100+t%1e4
}}
Example run:
   stairsim''
 seconds    steps to top   steps from bottom
     600            1142                1957
     601            1142                1962
     602            1141                1968
     603            1141                1973
     604            1142                1977
     605            1143                1981
     606            1143                1986
     607            1143                1991
     608            1144                1995
     609            1144                2000
Average steps taken: 3026.43
Average length of staircase: 15232.2

jq

Works with: jq

Works with gojq, the Go implementation of jq

Neither the C nor the Go-based implmentations of jq currently have a built-in PRNG, so for the present task /dev/urandom is used as a source of entropy by invoking jq as follows:

cat /dev/urandom | tr -cd '0-9' | fold -w 1 | jq -nrf long-stairs.jq

where long-stairs.jq contains the jq program shown below. For simplicity and since the intermediate output has the character of a probe, the program uses `debug` statements to show the intermediate results.

# 0 <= output < $n
def rand($n):

  def ntimes(f): range(0; .) | f;
  
  # input: an array of length ($n|tostring|length)
  def r:
    . as $in
    | (join("") | tonumber) as $m
    | if $m < $n then $m
      else $in[1:] + [input] | r
      end;
  [$n | tostring | length | ntimes(input)] | r;

# $n specifies the number of iterations
def task($n):
  (reduce range(1; $n + 1) as $trial (null;
    .sbeh = 0
    | .slen = 100
    | .secs = 0
    | until (.sbeh >= .slen;
        .sbeh += 1
        | reduce range(1;6) as $wiz (.;
            if (rand( .slen) < .sbeh) then .sbeh += 1 else . end
            | .slen += 1 )
        | .secs += 1
        | if ($trial == 1 and .secs > 599 and .secs < 610)
          then  ([.secs, .sbeh, .slen - .sbeh] | debug) as $debug | .
          else .
          end )
    | .totalSecs  += .secs
    | .totalSteps += .slen ) ) ;

"Seconds    steps behind    steps ahead",
"-------    ------------    -----------",
(1E4 as $n
| task($n)
| "\nAverage secs taken over \($n) trials: \(.totalSecs/$n)",
  "Average final length of staircase: \(.totalSteps/$n)"
)
Output:
Seconds    steps behind    steps ahead
-------    ------------    -----------
["DEBUG:",[600,1916,1184]]
["DEBUG:",[601,1919,1186]]
["DEBUG:",[602,1920,1190]]
["DEBUG:",[603,1924,1191]]
["DEBUG:",[604,1926,1194]]
["DEBUG:",[605,1931,1194]]
["DEBUG:",[606,1934,1196]]
["DEBUG:",[607,1938,1197]]
["DEBUG:",[608,1942,1198]]
["DEBUG:",[609,1945,1200]]

Average secs taken over 10000 trials: 3211.962
Average final length of staircase: 16159.81

Julia

""" 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

Free Pascal

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

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

#!/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

""" 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

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

Vlang

Translation of: Wren
Library: Vlang-rand
import rand
 
fn main() {
    mut total_secs := 0
    mut total_steps := 0
    println("Seconds    steps behind    steps ahead")
    println("-------    ------------    -----------")
    for trial in 1..10000 {
        mut sbeh := 0
        mut slen := 100
        mut secs := 0
        for sbeh < slen {
            sbeh++
            for _ in 1..5 {
                if rand.intn(slen) or {0} < sbeh {
                    sbeh++
                }
                slen++
            }
            secs++
            if trial == 1 && secs > 599 && secs < 610 {
                println("$secs        $sbeh            ${slen-sbeh}")
            }
        }
        total_secs += secs
        total_steps += slen
    }
    println("\nAverage secs taken: ${total_secs/10000}")
    println("Average final length of staircase: ${total_steps/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   

Wren

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