網路通訊原理hw3-2

var f = function(n) {
  if (n <= 1) {
    return 1;
  } else {
    return n * f(n - 1);
  }
}

var getP0 = function(y) {
  var sum = 0;

  for (var i = 0; i <= y; i++) {
    sum += (Math.pow(7, i) / f(i));
  }

  for (var i = y + 1; i <= 20; i++) {
    sum += (Math.pow(7, y) * Math.pow(2, i - y) / f(i));
  }

  return 1 / sum;
};

var getPi = function(y, i, P0) {
  if (0 <= i  && i <= y) {
    return (Math.pow(7, i) / f(i)) * P0;
  } else if (y < i && i <= 20) {
    return (Math.pow(7, y) * Math.pow(2, i - y) / f(i)) * P0;
  }
};

var getBOplusBH = function(y) {
  var P0 = getP0(y);

  var BO = 0;
  for (var i = y; i <= 20; i++) {
    BO += getPi(y, i, P0);
  };
  var BH;
  BH = (Math.pow(7, y) * Math.pow(2, 20 - y) / f(20)) * P0;

  return BO + BH;
};

var min = 999999999;
var ymin;
for (var y = 1; y < 20; y++) {
  var BOplusBH = getBOplusBH(y);
  console.log('y = ' + y + '\t', 'BO + BH = ' + BOplusBH);
  if (BOplusBH < min) {
    min = BOplusBH;
    ymin = y;
  }
}

console.log('min y = ' + ymin);
console.log('min BO + BH = ' + min);