javascript - 使用 JavaScript/jQuery 的杯子分数

Question

假设 1 杯等于 2.36 dl。我想要一个函数，它可以在 dl 中输入代表杯子的小数，并将杯子的数量输出为分数。

到目前为止，这是我得到的结果:

  var dl = 2.36;

  cupToFraction(.78);  // 1/3 cup
  cupToFraction(2.36); // 1 cup      
  cupToFraction(4.72); // 2 cups
  cupToFraction(8.26); // 3 1/2 cups

  function cupToFraction (cup) {
    var deci = (cup / dl);
    alert(deci);
  }

Answer 1

一种选择是使用连分数来获得有理近似值:

var dl = 2.36;
function cupToFraction (cup) {
    var deci = (cup / dl);
    var integerPart = Math.floor(deci);
    deci -= integerPart;
    deci = 1 / deci;
    var c = [];
    // Tune these parameters for how far you want the continued fraction to go
    // 3 means at most 3 terms; 10 means no terms higher than 10.
    for (let i = 0; i < 3 && deci < 10; ++i) {
      let f = Math.floor(deci);
      c.push(f);
      deci -= f;
      deci = 1/deci;
    }
    if (c.length === 0) return [integerPart, 0, 1];
    var p = 1, q = c.pop();
    while (c.length > 0) {
      var int = c.pop();
      p = q*int + p;
      [p, q] = [q, p];
    }
    // Handle case like cupToFraction(2.35)
    if (p === q) { p = 0; integerPart++; }
    return [integerPart, p, q];
}

它返回一个数组，其元素是integerPart, numerator, denominator。例如，cupToFraction(8.26) 给出 [3, 1, 2] for 3 1/2。我确信这个算法可以更优化，但现在必须这样做。