A simulation of 2 solutions to the prisoners with the light switch problem

prisoners.js

function solve(prisoner_count, hard_limit) {
	var prisoners = [];
	var startTime = ((new Date()).getTime());
	for(var x = 0 ; x < prisoner_count ; x++) {
		prisoners[x] = false;
	}

	// Pick a random prisoner
	function pickPrisoner() {
		return Math.floor(Math.random() * prisoner_count);
	}

	var leader = pickPrisoner();
	var leaderSwitchCount = 0;
	var prisonerHasSwitchedOnLight = {};

	var switchOnSlowApproach = false;
	var switchOnFastApproach = false;
	var day = 0;
	var dayAllWereLoaded = null;
	var fastSolved = false;
	var slowSolved = false;
	var window = {};
	var quiet = true;
	while(!fastSolved || !slowSolved) {
		day++;
		var p = pickPrisoner();
		if(!quiet) {
			console.log("Day " + day + 
				": Prisoner #" + p + 
				", light is " + (switchOnSlowApproach ? "ON" : "OFF") + 
				(dayAllWereLoaded ? " " + (day - dayAllWereLoaded) + " days late (all loaded on day "+dayAllWereLoaded+")" : "")
			);
		}
		prisoners[p] = true;

		if(!fastSolved) {
			if(p === leader) {
				if(switchOnFastApproach) {
					leaderSwitchCount++;
					if(leaderSwitchCount === prisoner_count - 1) {
						fastSolved = day;
					}
					switchOnFastApproach = false;
				}
				switchOnFastApproach = false;
			} else if(!prisonerHasSwitchedOnLight[p]  && !switchOnFastApproach) {
				switchOnFastApproach = true;
				prisonerHasSwitchedOnLight[p] = true;
			}
		}

		if(!slowSolved) {
			if(window[p]) {
				switchOnSlowApproach = true;
			}
			window[p] = true;

			if(day !== 0 && day % prisoner_count === 0) {
				if(switchOnSlowApproach === false) {
					slowSolved = day;
				}
				switchOnSlowApproach = false;
				window = {};
			}

			// check if all were loaded.
			if(dayAllWereLoaded === null) {
				var allLoaded = true;
				for(var p in prisoners) {
					if(!prisoners[p]) {
						allLoaded = false;
					}
				}

				if(allLoaded) {
					dayAllWereLoaded = day;
				}
			}
		}

		if(day > hard_limit) {
			break ;
		}
	}

	return {
		"slow":slowSolved,
		"fast":fastSolved,
		"actual": dayAllWereLoaded,
		"count":prisoner_count,
		"time": ((new Date()).getTime() - startTime)
	}
}

var counts = [
	5,
	10,
	25,
	50,
	100,
	200,
	400
];
var hard_limit = 365000000; // if they dont get out in a million years, give up?
var iterations_per_count = 20;
console.log("prisoners,actual,slow,fast,sim_time_seconds");
for(var x = 0 ; x < counts.length ; x++) {
	for(var y = 0 ; y < iterations_per_count ; y++) {
		var res = solve(counts[x], hard_limit);	
		console.log(res.count +","+res.actual+","+res.slow+","+ res.fast+","+(res.time / 1000.0));
	}
}
// console.log(prisoner_count + ", " + slowSolved + " total days for certainty in slow algorithm, " + fastSolved + ", for fast algorithm " + dayAllWereLoaded + " days in reality.");