Set of real numbers: Difference between revisions
→{{header|Julia}}
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(Note that this result is not exactly the same as the previous result. Determining why would be an interesting exercise in numerical analysis.)
=={{header|Java}}==
<lang java>import java.util.Objects;
import java.util.function.Predicate;
public class RealNumberSet {
public enum RangeType {
CLOSED,
BOTH_OPEN,
LEFT_OPEN,
RIGHT_OPEN,
}
public static class RealSet {
private Double low;
private Double high;
private Predicate<Double> predicate;
private double interval = 0.00001;
public RealSet(Double low, Double high, Predicate<Double> predicate) {
this.low = low;
this.high = high;
this.predicate = predicate;
}
public RealSet(Double start, Double end, RangeType rangeType) {
this(start, end, d -> {
switch (rangeType) {
case CLOSED:
return start <= d && d <= end;
case BOTH_OPEN:
return start < d && d < end;
case LEFT_OPEN:
return start < d && d <= end;
case RIGHT_OPEN:
return start <= d && d < end;
default:
throw new IllegalStateException("Unhandled range type encountered.");
}
});
}
public boolean contains(Double d) {
return predicate.test(d);
}
public RealSet union(RealSet other) {
double low2 = Math.min(low, other.low);
double high2 = Math.max(high, other.high);
return new RealSet(low2, high2, d -> predicate.or(other.predicate).test(d));
}
public RealSet intersect(RealSet other) {
double low2 = Math.min(low, other.low);
double high2 = Math.max(high, other.high);
return new RealSet(low2, high2, d -> predicate.and(other.predicate).test(d));
}
public RealSet subtract(RealSet other) {
return new RealSet(low, high, d -> predicate.and(other.predicate.negate()).test(d));
}
public double length() {
if (low.isInfinite() || high.isInfinite()) return -1.0; // error value
if (high <= low) return 0.0;
Double p = low;
int count = 0;
do {
if (predicate.test(p)) count++;
p += interval;
} while (p < high);
return count * interval;
}
public boolean isEmpty() {
if (Objects.equals(high, low)) {
return predicate.negate().test(low);
}
return length() == 0.0;
}
}
public static void main(String[] args) {
RealSet a = new RealSet(0.0, 1.0, RangeType.LEFT_OPEN);
RealSet b = new RealSet(0.0, 2.0, RangeType.RIGHT_OPEN);
RealSet c = new RealSet(1.0, 2.0, RangeType.LEFT_OPEN);
RealSet d = new RealSet(0.0, 3.0, RangeType.RIGHT_OPEN);
RealSet e = new RealSet(0.0, 1.0, RangeType.BOTH_OPEN);
RealSet f = new RealSet(0.0, 1.0, RangeType.CLOSED);
RealSet g = new RealSet(0.0, 0.0, RangeType.CLOSED);
for (int i = 0; i <= 2; i++) {
Double dd = (double) i;
System.out.printf("(0, 1] ∪ [0, 2) contains %d is %s\n", i, a.union(b).contains(dd));
System.out.printf("[0, 2) ∩ (1, 2] contains %d is %s\n", i, b.intersect(c).contains(dd));
System.out.printf("[0, 3) − (0, 1) contains %d is %s\n", i, d.subtract(e).contains(dd));
System.out.printf("[0, 3) − [0, 1] contains %d is %s\n", i, d.subtract(f).contains(dd));
System.out.println();
}
System.out.printf("[0, 0] is empty is %s\n", g.isEmpty());
System.out.println();
RealSet aa = new RealSet(
0.0, 10.0,
x -> (0.0 < x && x < 10.0) && Math.abs(Math.sin(Math.PI * x * x)) > 0.5
);
RealSet bb = new RealSet(
0.0, 10.0,
x -> (0.0 < x && x < 10.0) && Math.abs(Math.sin(Math.PI * x)) > 0.5
);
RealSet cc = aa.subtract(bb);
System.out.printf("Approx length of A - B is %f\n", cc.length());
}
}</lang>
{{out}}
<pre>(0, 1] ∪ [0, 2) contains 0 is true
[0, 2) ∩ (1, 2] contains 0 is false
[0, 3) − (0, 1) contains 0 is true
[0, 3) − [0, 1] contains 0 is false
(0, 1] ∪ [0, 2) contains 1 is true
[0, 2) ∩ (1, 2] contains 1 is false
[0, 3) − (0, 1) contains 1 is true
[0, 3) − [0, 1] contains 1 is false
(0, 1] ∪ [0, 2) contains 2 is false
[0, 2) ∩ (1, 2] contains 2 is false
[0, 3) − (0, 1) contains 2 is true
[0, 3) − [0, 1] contains 2 is true
[0, 0] is empty is false
Approx length of A - B is 2.075870</pre>
=={{header|Julia}}==
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