hats

hats.js

//http://repl.it/IOn

function problem(colors, prisoners) {
  function randomHat() {
    return Math.floor(Math.random() * colors);
  }

  function randomHats() {
    var hats = [];
    for (var i = 0; i<prisoners; i++) {
      hats.push(randomHat());
    }
    return hats;
  }

  function zip() {
    var arrays = [].slice.call(arguments);
    return arrays[0].map(function(_,i){
      return arrays.map(function(array){return array[i]});
    });
  }

  function play(strategy, hats, log) {
    hats = hats || randomHats();
    log = log || console.log;
    var guesses = [];
    var hatsRemaining = hats.slice(0);

    log && log('----- problem -----');
    log && log('colors =', colors);
    log && log('strategy =', strategy.name);
    log && log('hats =', hats.join('|'));

    while (hatsRemaining.length > 0) {
      var hat = hatsRemaining.shift();
      //log && log('----- round #' + guesses.length + ' -----');
      //log && log('behind =', guesses, 'hat =', hat, 'ahead =', hatsRemaining);

      guesses.push(strategy(guesses, hatsRemaining, colors));

      //log && log('guess =', guesses.slice(-1)[0]);
    }

    var deaths = zip(hats, guesses).map(function (pair) {
      return pair[0] === pair[1] ? '.' : 'X';
    });
    var survivors = deaths.reduce(function(total, death) {
      return death === '.' ? total + 1 : total;
    }, 0);

    log && log('----- result -----');
    log && log('guesses =', guesses.join('|'));
    log && log('deaths =', deaths.join(''));
    log && log('survivors =', survivors);
    log && log('----- end -----');
    return survivors;
  }

  return {
    randomHat: randomHat,
    randomHats: randomHats,
    play: play
  };
}

function random(guesses, ahead, colors) {
  return problem(colors).randomHat();
}

function smart(guesses, ahead, colors) {
  function sum(hats) {
    return hats.reduce(function (sum, hat) {
      return sum + hat;
    }, 0);
  }

  if (guesses.length === 0) {
    return sum(guesses.concat(ahead)) % colors;
  }

  var first = guesses[0];
  var everyoneElse = guesses.slice(1).concat(ahead);
  var everyoneElseSum = sum(everyoneElse) % colors;
  var guess = (first - everyoneElseSum + colors) % colors;

  return guess;
}

problem(3, 10).play(smart);

//other examples:
//problem(3, 20).play(random);
//problem(6, 100).play(smart);