113 lines
4 KiB
Java
113 lines
4 KiB
Java
import java.util.Objects;
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import java.util.function.Predicate;
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public class RealNumberSet {
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public enum RangeType {
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CLOSED,
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BOTH_OPEN,
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LEFT_OPEN,
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RIGHT_OPEN,
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}
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public static class RealSet {
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private Double low;
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private Double high;
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private Predicate<Double> predicate;
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private double interval = 0.00001;
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public RealSet(Double low, Double high, Predicate<Double> predicate) {
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this.low = low;
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this.high = high;
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this.predicate = predicate;
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}
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public RealSet(Double start, Double end, RangeType rangeType) {
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this(start, end, d -> {
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switch (rangeType) {
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case CLOSED:
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return start <= d && d <= end;
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case BOTH_OPEN:
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return start < d && d < end;
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case LEFT_OPEN:
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return start < d && d <= end;
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case RIGHT_OPEN:
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return start <= d && d < end;
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default:
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throw new IllegalStateException("Unhandled range type encountered.");
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}
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});
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}
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public boolean contains(Double d) {
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return predicate.test(d);
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}
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public RealSet union(RealSet other) {
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double low2 = Math.min(low, other.low);
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double high2 = Math.max(high, other.high);
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return new RealSet(low2, high2, d -> predicate.or(other.predicate).test(d));
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}
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public RealSet intersect(RealSet other) {
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double low2 = Math.min(low, other.low);
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double high2 = Math.max(high, other.high);
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return new RealSet(low2, high2, d -> predicate.and(other.predicate).test(d));
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}
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public RealSet subtract(RealSet other) {
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return new RealSet(low, high, d -> predicate.and(other.predicate.negate()).test(d));
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}
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public double length() {
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if (low.isInfinite() || high.isInfinite()) return -1.0; // error value
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if (high <= low) return 0.0;
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Double p = low;
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int count = 0;
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do {
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if (predicate.test(p)) count++;
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p += interval;
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} while (p < high);
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return count * interval;
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}
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public boolean isEmpty() {
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if (Objects.equals(high, low)) {
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return predicate.negate().test(low);
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}
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return length() == 0.0;
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}
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}
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public static void main(String[] args) {
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RealSet a = new RealSet(0.0, 1.0, RangeType.LEFT_OPEN);
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RealSet b = new RealSet(0.0, 2.0, RangeType.RIGHT_OPEN);
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RealSet c = new RealSet(1.0, 2.0, RangeType.LEFT_OPEN);
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RealSet d = new RealSet(0.0, 3.0, RangeType.RIGHT_OPEN);
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RealSet e = new RealSet(0.0, 1.0, RangeType.BOTH_OPEN);
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RealSet f = new RealSet(0.0, 1.0, RangeType.CLOSED);
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RealSet g = new RealSet(0.0, 0.0, RangeType.CLOSED);
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for (int i = 0; i <= 2; i++) {
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Double dd = (double) i;
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System.out.printf("(0, 1] ∪ [0, 2) contains %d is %s\n", i, a.union(b).contains(dd));
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System.out.printf("[0, 2) ∩ (1, 2] contains %d is %s\n", i, b.intersect(c).contains(dd));
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System.out.printf("[0, 3) − (0, 1) contains %d is %s\n", i, d.subtract(e).contains(dd));
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System.out.printf("[0, 3) − [0, 1] contains %d is %s\n", i, d.subtract(f).contains(dd));
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System.out.println();
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}
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System.out.printf("[0, 0] is empty is %s\n", g.isEmpty());
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System.out.println();
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RealSet aa = new RealSet(
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0.0, 10.0,
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x -> (0.0 < x && x < 10.0) && Math.abs(Math.sin(Math.PI * x * x)) > 0.5
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);
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RealSet bb = new RealSet(
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0.0, 10.0,
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x -> (0.0 < x && x < 10.0) && Math.abs(Math.sin(Math.PI * x)) > 0.5
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);
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RealSet cc = aa.subtract(bb);
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System.out.printf("Approx length of A - B is %f\n", cc.length());
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}
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}
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