---
id: 5eb3e4b20aa93c437f9e9717
title: Set of real numbers
challengeType: 5
forumTopicId: 385322
dashedName: set-of-real-numbers
---
# --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:
- [a, b]: {x | a ≤ x and x ≤ b }
- (a, b): {x | a < x and x < b }
- [a, b): {x | a ≤ x and x < b }
- (a, b]: {x | a < x and x ≤ b }
Note that if *a* = *b*, of the four only \[*a*, *a*] would be non-empty.
**Task**
- Devise a way to represent any set of real numbers, for the definition of "any" in the implementation notes below.
- Provide methods for these common set operations (x is a real number; A and B are sets):
-
x ∈ A: determine if x is an element of A
example: 1 is in [1, 2), while 2, 3, ... are not.
-
A ∪ B: union of A and B, i.e. {x | x ∈ A or x ∈ B}
example: [0, 2) ∪ (1, 3) = [0, 3); [0, 1) ∪ (2, 3] = well, [0, 1) ∪ (2, 3]
-
A ∩ B: intersection of A and B, i.e. {x | x ∈ A and x ∈ B}
example: [0, 2) ∩ (1, 3) = (1, 2); [0, 1) ∩ (2, 3] = empty set
-
A - B: difference between A and B, also written as A \ B, i.e. {x | x ∈ A and x ∉ B}
example: [0, 2) − (1, 3) = [0, 1]
# --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.
```js
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.
```js
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]`.
```js
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]`.
```js
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]`.
```js
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]`.
```js
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]`.
```js
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--
```js
function realSet(set1, set2, operation, values) {
}
```
# --solutions--
```js
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;
}
```