--description--

All real numbers form the uncountable set ℝ. Among its subsets, relatively simple are the convex sets, each expressed as a range between two real numbers a and b where a ≤ b. There are actually four cases for the meaning of "between", depending on open or closed boundary:

Note that if a = b, of the four only [a, a] would be non-empty.

Task

<ul> <li>Devise a way to represent any set of real numbers, for the definition of "any" in the implementation notes below.</li> <li>Provide methods for these common set operations (x is a real number; A and B are sets):</li> <ul> <li> x ∈ A: determine if x is an element of A

  example: 1 is in [1, 2), while 2, 3, ... are not.
</li>
<li>
  <i>A</i> ∪ <i>B</i>: union of <i>A</i> and <i>B</i>, i.e. {<i>x</i> | <i>x</i> ∈ <i>A</i> or <i>x</i> ∈ <i>B</i>}

  example: [0, 2) ∪ (1, 3) = [0, 3); [0, 1) ∪ (2, 3] = well, [0, 1) ∪ (2, 3]
</li>
<li>
  <i>A</i> ∩ <i>B</i>: intersection of <i>A</i> and <i>B</i>, i.e. {<i>x</i> | <i>x</i> ∈ <i>A</i> and <i>x</i> ∈ <i>B</i>}

  example: [0, 2) ∩ (1, 3) = (1, 2); [0, 1) ∩ (2, 3] = empty set
</li>
<li>
  <i>A</i> - <i>B</i>: difference between <i>A</i> and <i>B</i>, also written as <i>A</i> \ <i>B</i>, i.e. {<i>x</i> | <i>x</i> ∈ <i>A</i> and <i>x</i> ∉ <i>B</i>}

  example: [0, 2) − (1, 3) = [0, 1]
</li>

</ul> </ul>

--instructions--

Write a function that takes 2 objects, a string and an array as parameters. The objects represents the set and have attributes: low, high and rangeType.

The rangeType can have values 0, 1, 2 and 3 for CLOSED, BOTH_OPEN, LEFT_OPEN and RIGHT_OPEN, respectively. The function should implement a set using this information.

The string represents the operation to be performed on the sets. It can be: "union", "intersect" and "subtract" (difference).

After performing the operation, the function should check if the values in the array are present in the resultant set and store a corresponding boolean value to an array. The function should return this array.

--hints--

realSet should be a function.

assert(typeof realSet == 'function');

realSet({"low":0, "high":1, "rangeType":2}, {"low":0, "high":2, "rangeType":3}, "union", [1, 2, 3]) should return a array.

assert(
  Array.isArray(
    realSet(
      { low: 0, high: 1, rangeType: 2 },
      { low: 0, high: 2, rangeType: 3 },
      'union',
      [1, 2, 3]
    )
  )
);

realSet({"low":0, "high":1, "rangeType":2}, {"low":0, "high":2, "rangeType":3}, "union", [1, 2, 3]) should return [true, false, false].

assert.deepEqual(
  realSet(
    { low: 0, high: 1, rangeType: 2 },
    { low: 0, high: 2, rangeType: 3 },
    'union',
    [1, 2, 3]
  ),
  [true, false, false]
);

realSet({"low":0, "high":2, "rangeType":3}, {"low":1, "high":2, "rangeType":2}, "intersect", [0, 1, 2]) should return [false, false, false].

assert.deepEqual(
  realSet(
    { low: 0, high: 2, rangeType: 3 },
    { low: 1, high: 2, rangeType: 2 },
    'intersect',
    [0, 1, 2]
  ),
  [false, false, false]
);

realSet({"low":0, "high":3, "rangeType":3}, {"low":0, "high":1, "rangeType":1}, "subtract", [0, 1, 2]) should return [true, true, true].

assert.deepEqual(
  realSet(
    { low: 0, high: 3, rangeType: 3 },
    { low: 0, high: 1, rangeType: 1 },
    'subtract',
    [0, 1, 2]
  ),
  [true, true, true]
);

realSet({"low":0, "high":3, "rangeType":3}, {"low":0, "high":1, "rangeType":0}, "subtract", [0, 1, 2]) should return [false, false, true].

assert.deepEqual(
  realSet(
    { low: 0, high: 3, rangeType: 3 },
    { low: 0, high: 1, rangeType: 0 },
    'subtract',
    [0, 1, 2]
  ),
  [false, false, true]
);

realSet({"low":0, "high":33, "rangeType":1}, {"low":30, "high":31, "rangeType":0}, "intersect", [30, 31, 32]) should return [true, true, false].

assert.deepEqual(
  realSet(
    { low: 0, high: 33, rangeType: 1 },
    { low: 30, high: 31, rangeType: 0 },
    'intersect',
    [30, 31, 32]
  ),
  [true, true, false]
);

--seed--

--seed-contents--

function realSet(set1, set2, operation, values) {

}

--solutions--

function realSet(set1, set2, operation, values) {
  const RangeType = {
    CLOSED: 0,
    BOTH_OPEN: 1,
    LEFT_OPEN: 2,
    RIGHT_OPEN: 3
  };

  function Predicate(test) {
    this.test = test;
    this.or = function(other) {
      return new Predicate(t => this.test(t) || other.test(t));
    };
    this.and = function(other) {
      return new Predicate(t => this.test(t) && other.test(t));
    };
    this.negate = function() {
      return new Predicate(t => !this.test(t));
    };
  }

  function RealSet(start, end, rangeType, predF) {
    this.low = start;
    this.high = end;

    if (predF) {
      this.predicate = new Predicate(predF);
    } else {
      this.predicate = new Predicate(d => {
        switch (rangeType) {
          case RangeType.CLOSED:
            return start <= d && d <= end;
          case RangeType.BOTH_OPEN:
            return start < d && d < end;
          case RangeType.LEFT_OPEN:
            return start < d && d <= end;
          case RangeType.RIGHT_OPEN:
            return start <= d && d < end;
        }
      });
    }

    this.contains = function(d) {
      return this.predicate.test(d);
    };

    this.union = function(other) {
      var low2 = Math.min(this.low, other.low);
      var high2 = Math.max(this.high, other.high);
      return new RealSet(low2, high2, null, d =>
        this.predicate.or(other.predicate).test(d)
      );
    };

    this.intersect = function(other) {
      var low2 = Math.min(this.low, other.low);
      var high2 = Math.max(this.high, other.high);
      return new RealSet(low2, high2, null, d =>
        this.predicate.and(other.predicate).test(d)
      );
    };

    this.subtract = function(other) {
      return new RealSet(this.low, this.high, null, d =>
        this.predicate.and(other.predicate.negate()).test(d)
      );
    };
  }
  set1 = new RealSet(set1.low, set1.high, set1.rangeType);
  set2 = new RealSet(set2.low, set2.high, set2.rangeType);
  var result = [];
  values.forEach(function(value) {
    result.push(set1[operation](set2).contains(value));
  });
  return result;
}