100 prisoners: Difference between revisions
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<lang EasyLang>for i range 100 |
<lang EasyLang>for i range 100 |
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drawer[] &= i |
drawer[] &= i |
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for i range 100 |
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sampler[] &= i |
sampler[] &= i |
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Revision as of 09:00, 5 November 2019
| This page uses content from Wikipedia. The original article was at 100 prisoners problem. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance) |
- The Problem
- 100 prisoners are individually numbered 1 to 100
- A room having a cupboard of 100 opaque drawers numbered 1 to 100, that cannot be seen from outside.
- Cards numbered 1 to 100 are placed randomly, one to a drawer, and the drawers all closed; at the start.
- Prisoners start outside the room
- They can decide some strategy before any enter the room.
- Prisoners enter the room one by one, can open a drawer, inspect the card number in the drawer, then close the drawer.
- A prisoner can open no more than 50 drawers.
- A prisoner tries to find his own number.
- A prisoner finding his own number is then held apart from the others.
- If all 100 prisoners find their own numbers then they will all be pardoned.
- The task
- Simulate several thousand instances of the game where the prisoners randomly open draws
- Simulate several thousand instances of the game where the prisoners use the optimal strategy mentioned in the wikipedia article, of:
- First opening the drawer whose outside number is his prisoner number.
- If the card within has his number then he succeeds otherwise he opens the drawer with the same number as that of the revealed card. (until he opens his maximum).
Show and compare the computed probabilities of success for the two strategies, here, on this page.
- References
- The unbelievable solution to the 100 prisoner puzzle standupmaths (Video).
- 100 Prisoners Escape Puzzle DataGenetics.
EasyLang
<lang EasyLang>for i range 100
drawer[] &= i sampler[] &= i
. subr shuffle_drawer
for i = 99 downto 1 r = random (i + 1) swap drawer[r] drawer[i] .
. subr play_random
call shuffle_drawer
found = 1
prisoner = 0
while prisoner < 100 and found = 1
found = 0
i = 0
while i < 50 and found = 0
r = random (100 - i)
card = drawer[sampler[r]]
swap sampler[r] sampler[100 - i - 1]
if card = prisoner
found = 1
.
i += 1
.
prisoner += 1
.
. subr play_optimal
call shuffle_drawer
prisoner = 0
found = 1
while prisoner < 100 and found = 1
reveal = prisoner
found = 0
i = 0
while i < 50 and found = 0
card = drawer[reveal]
if card = prisoner
found = 1
.
reveal = card
i += 1
.
prisoner += 1
.
. n = 10000 pardoned = 0 for round range n
call play_random pardoned += found
. print "random: " & 100.0 * pardoned / n & "%"
pardoned = 0 for round range n
call play_optimal pardoned += found
. print "optimal: " & 100.0 * pardoned / n & "%"</lang>
- Output:
random: 0.000% optimal: 30.800%
Factor
<lang factor>USING: arrays formatting fry io kernel math random sequences ;
- setup ( -- seq seq ) 100 <iota> dup >array randomize ;
- rand ( -- ? )
setup [ 50 sample member? not ] curry find nip >boolean not ;
- trail ( m seq -- n )
50 pick '[ [ nth ] keep over _ = ] replicate [ t = ] any? 2nip ;
- optimal ( -- ? ) setup [ trail ] curry [ and ] map-reduce ;
- simulate ( m quot -- x )
dupd replicate [ t = ] count swap /f 100 * ; inline
"Simulation count: 10,000" print 10,000 [ rand ] simulate "Random play success: " 10,000 [ optimal ] simulate "Optimal play success: " [ write "%.2f%%\n" printf ] 2bi@</lang>
- Output:
Simulation count: 10,000 Random play success: 0.00% Optimal play success: 31.11%
Perl 6
<lang perl6>my @prisoners = ^100; my $half = floor +@prisoners / 2;
sub random ($n) {
^$n .race.map( {
my @drawers = @prisoners.pick: *;
@prisoners.map( -> $prisoner {
my $found = 0;
for @drawers.pick($half) -> $card {
$found = 1 and last if $card == $prisoner
}
last unless $found;
$found
}
).sum == @prisoners
}
).grep( *.so ).elems / $n * 100
}
sub optimal ($n) {
^$n .race.map( {
my @drawers = @prisoners.pick: *;
@prisoners.map( -> $prisoner {
my $found = 0;
my $card = @drawers[$prisoner];
if $card == $prisoner {
$found = 1
} else {
for ^($half - 1) {
$card = @drawers[$card];
$found = 1 and last if $card == $prisoner
}
}
last unless $found;
$found
}
).sum == @prisoners
}
).grep( *.so ).elems / $n * 100
}
my $n = 10_000; say " Simulation count: $n\n" ~ sprintf(" Random play wins: %4.1f%% of simulations\n", random $n) ~ sprintf("Optimal play wins: %4.1f%% of simulations\n", optimal $n);</lang>
- Output:
Simulation count: 10000 Random play wins: 0.0% of simulations Optimal play wins: 31.9% of simulations
Python
<lang python>import random
def play_random(n):
# using 0-99 instead of ranges 1-100
pardoned = 0
in_drawer = list(range(100))
sampler = list(range(100))
for _round in range(n):
random.shuffle(in_drawer)
found = False
for prisoner in range(100):
found = False
for reveal in random.sample(sampler, 50):
card = in_drawer[reveal]
if card == prisoner:
found = True
break
if not found:
break
if found:
pardoned += 1
return pardoned / n * 100 # %
def play_optimal(n):
# using 0-99 instead of ranges 1-100
pardoned = 0
in_drawer = list(range(100))
for _round in range(n):
random.shuffle(in_drawer)
for prisoner in range(100):
reveal = prisoner
found = False
for go in range(50):
card = in_drawer[reveal]
if card == prisoner:
found = True
break
reveal = card
if not found:
break
if found:
pardoned += 1
return pardoned / n * 100 # %
if __name__ == '__main__':
n = 100_000
print(" Simulation count:", n)
print(f" Random play wins: {play_random(n):4.1f}% of simulations")
print(f"Optimal play wins: {play_optimal(n):4.1f}% of simulations")</lang>
- Output:
Simulation count: 100000 Random play wins: 0.0% of simulations Optimal play wins: 31.1% of simulations
REXX
<lang rexx>/*REXX program to simulate the problem of 100 prisoners: random, and optimal strategy.*/ parse arg men trials seed . /*obtain optional arguments from the CL*/ if men== | men=="," then men= 100 /*the number of prisoners for this run.*/ if trials== | trials=="," then trials= 100000 /*the number of simulations for methods*/ if datatype(seed, 'W') then call random ,,seed /*seed for the random number generator.*/ $.1= ' a simple '; $.2= "an optimal" /*literals used for the SAY instruction*/ try= men % 2 /*number tries for searching for a card*/
do method=1 for 2; pards= 0 /*perform two types of methods. */
do trials; call genCards /*perform number of trials for methods.*/
do p=1 for men /*have each prisoner go through trial. */
if method==1 then call simple /*perform the simple method. */
else call pick /* " " optimal " */
end /*p*/
pards= pards + (#==men) /*calculate how many prisoners pardoned*/
end /*trials*/
say men ' prisoners in ' commas(trials) " trials, percentage wins with" $.method,
"strategy: " left(, pards==0)format(pards / trials * 100, , 1)"%"
end /*method*/
exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ commas: parse arg _; do c=length(_)-3 to 1 by -3; _= insert(',', _, c); end; return _ /*──────────────────────────────────────────────────────────────────────────────────────*/ genCards: #= 0; do k=1 for men; @.k= k; end /*put a card in a drawer*/
do men*2; a= random(1,men); b= random(1,men) /*randomize the drawers.*/
parse value @.a @.b with @.b @.a /*switch two drawers. */
end /*men*2*/; return
/*──────────────────────────────────────────────────────────────────────────────────────*/ simple: do try; ?= random(1, men); if @.?==p then do; #= #+1; return; end
end /*try*/; return /* [↑] has a prisoner found his own card?*/
/*──────────────────────────────────────────────────────────────────────────────────────*/ pick: ?=p; do try; if @.?==p then do; #=#+1; return; end /*Found his own card?*/
?= @.? /*choose next drawer from previous card*/
end /*try*/
return /*only choose 1/2 of the num of drawers*/</lang>
- output when using the default inputs:
100 prisoners in 100,000 trials, percentage wins with a simple strategy: 0.0% 100 prisoners in 100,000 trials, percentage wins with an optimal strategy: 31.2%
Rust
Fairly naive implementation. Could probably be made more idiomatic. Depends on extern rand crate.
Cargo.toml <lang toml>[dependencies] rand = '0.7.2'</lang>
src/main.rs <lang rust>extern crate rand;
use rand::prelude::*;
// Do a full run of checking boxes in a random order for a single prisoner fn check_random_boxes(prisoner: u8, boxes: &[u8]) -> bool {
let checks = {
let mut b: Vec<u8> = (1u8..=100u8).collect();
b.shuffle(&mut rand::thread_rng());
b
};
checks.into_iter().take(50).any(|check| boxes[check as usize - 1] == prisoner)
}
// Do a full run of checking boxes in the optimized order for a single prisoner fn check_ordered_boxes(prisoner: u8, boxes: &[u8]) -> bool {
let mut next_check = prisoner;
(0..50).any(|_| {
next_check = boxes[next_check as usize - 1];
next_check == prisoner
})
}
fn main() {
let mut boxes: Vec<u8> = (1u8..=100u8).collect();
let trials = 100000;
let ordered_successes = (0..trials).filter(|_| {
boxes.shuffle(&mut rand::thread_rng());
(1u8..=100u8).all(|prisoner| check_ordered_boxes(prisoner, &boxes))
}).count();
let random_successes = (0..trials).filter(|_| {
boxes.shuffle(&mut rand::thread_rng());
(1u8..=100u8).all(|prisoner| check_random_boxes(prisoner, &boxes))
}).count();
println!("{} / {} ({:.02}%) successes in ordered", ordered_successes, trials, ordered_successes as f64 * 100.0 / trials as f64);
println!("{} / {} ({:.02}%) successes in random", random_successes, trials, random_successes as f64 * 100.0 / trials as f64);
}</lang>
- Output:
31106 / 100000 (31.11%) successes in ordered 0 / 100000 (0.00%) successes in random