allFilledProbability.js

(function($) {
  $(function() {
    $("#calculate").on("click", execute);

    function execute() {
      if (typeof($(this).val() * 1) != "number") {
        alert("Please input a number.");
      } else if ($("#friends").val() * 1 < $("#days").val() * 1) {
        $("#answer").empty().append((0).toFixed(20) + " %");
      } else {
        calculate();
      }
    }

    function calculate() {
      var friends = $("#friends").val();
      friends = parseInt(friends);
      var days = $("#days").val();
      days = parseInt(days);
      var numerator1 = resolve(friends - 1);
      var numerator2 = resolve(friends);
      var numerator = numerator1.concat(numerator2);
      var denominator1 = resolve(friends + days - 1);
      var denominator2 = resolve(friends - days);
      var denominator = denominator1.concat(denominator2);
      $("#answer").empty().append(reduceCalculate(numerator, denominator));
    }

    function resolve(x) {
      var factArray = [];
      x = (x < 1) ? 1 : x;
      while (x > 0) {
        factArray.push(x--);
      }
      return factArray;
    }

    function primeFactorization(x) {
      var primeArray = [];
      var primeNumber = 2;
      while (primeNumber <= x) {
        var count = 0;
        while (x % primeNumber == 0) {
          x = x / primeNumber;
          count++;
        }
        if (count != 0) primeArray[primeNumber] = count;
        primeNumber++;
      }
      return primeArray;
    }

    function collectPrimeNumber(factArray) {
      var gatherArray = [];
      $.each(factArray, function() {
        var primeArray = primeFactorization(this);
        for (var key in primeArray) {
          if (gatherArray[key]) {
            gatherArray[key] += primeArray[key];
          } else {
            gatherArray[key] = primeArray[key];
          }
        }
      });
      return gatherArray;
    }

    function reduceCalculate(numeratorArray, denominatorArray) {
      var numeratorPrime = collectPrimeNumber(numeratorArray);
      var denominatorPrime = collectPrimeNumber(denominatorArray);
      for (var key in numeratorPrime) {
        if (denominatorPrime[key]) {
          var gap = numeratorPrime[key] - denominatorPrime[key];
          if (gap > 0) {
            numeratorPrime[key] = gap;
            delete denominatorPrime[key];
          } else if (gap == 0) {
            delete numeratorPrime[key];
            delete denominatorPrime[key];
          }
        }
      }
      for (var key in denominatorPrime) {
        if (numeratorPrime[key]) {
          var gap = denominatorPrime[key] - numeratorPrime[key];
          if (gap > 0) {denominatorPrime[key] = gap;
            delete numeratorPrime[key];
          }
        }
      }
      var numeratorElem = [];
      var denominatorElem = [];
      for (var key in numeratorPrime) {
        numeratorElem.push(Math.pow(key, numeratorPrime[key]));
      }
      for (var key in denominatorPrime) {
        denominatorElem.push(Math.pow(key, denominatorPrime[key]));
      }
      var answerArray = [];
      $.each(denominatorElem, function(i) {
        var numerator = numeratorElem[i];
        if (numerator) {
          answerArray.push((numerator / this).toFixed(20));
        } else {
          answerArray.push((1 / this).toFixed(20));
        }
      });
      var numElmLength = numeratorElem.length;
      var denElmLength = denominatorElem.length;
      if (numElmLength > denElmLength) {
        for (var i = 0; i <= numElmLength - denElmLength - 1; i++) {
          answerArray.push(numeratorElem[i + denElmLength]);
        }
      }
      var answer = 1;
      $.each(answerArray, function() {
        answer *= this;
      });
      return (answer * 100).toFixed(20) + " %";
    }
  });
})(jQuery);