38 lines
1.1 KiB
Plaintext
38 lines
1.1 KiB
Plaintext
import 'dart:async';
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import 'dart:math' show Random;
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main() async {
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print('Compute π using the Monte Carlo method.');
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await for (var estimate in computePi().take(100)) {
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print('π ≅ $estimate');
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}
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}
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/// Generates a stream of increasingly accurate estimates of π.
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Stream<double> computePi({int batch: 100000}) async* {
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var total = 0;
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var count = 0;
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while (true) {
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var points = generateRandom().take(batch);
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var inside = points.where((p) => p.isInsideUnitCircle);
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total += batch;
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count += inside.length;
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var ratio = count / total;
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// Area of a circle is A = π⋅r², therefore π = A/r².
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// So, when given random points with x ∈ <0,1>,
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// y ∈ <0,1>, the ratio of those inside a unit circle
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// should approach π / 4. Therefore, the value of π
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// should be:
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yield ratio * 4;
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}
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}
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Iterable<Point> generateRandom([int seed]) sync* {
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final random = Random(seed);
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while (true) {
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yield Point(random.nextDouble(), random.nextDouble());
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}
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}
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class Point {
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final double x, y;
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const Point(this.x, this.y);
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bool get isInsideUnitCircle => x * x + y * y <= 1;
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}
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