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-rw-r--r--rand/examples/monte-carlo.rs51
-rw-r--r--rand/examples/monty-hall.rs116
2 files changed, 167 insertions, 0 deletions
diff --git a/rand/examples/monte-carlo.rs b/rand/examples/monte-carlo.rs
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+// Copyright 2018 Developers of the Rand project.
+// Copyright 2013-2018 The Rust Project Developers.
+//
+// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
+// https://www.apache.org/licenses/LICENSE-2.0> or the MIT license
+// <LICENSE-MIT or https://opensource.org/licenses/MIT>, at your
+// option. This file may not be copied, modified, or distributed
+// except according to those terms.
+
+//! # Monte Carlo estimation of π
+//!
+//! Imagine that we have a square with sides of length 2 and a unit circle
+//! (radius = 1), both centered at the origin. The areas are:
+//!
+//! ```text
+//! area of circle = πr² = π * r * r = π
+//! area of square = 2² = 4
+//! ```
+//!
+//! The circle is entirely within the square, so if we sample many points
+//! randomly from the square, roughly π / 4 of them should be inside the circle.
+//!
+//! We can use the above fact to estimate the value of π: pick many points in
+//! the square at random, calculate the fraction that fall within the circle,
+//! and multiply this fraction by 4.
+
+#![cfg(feature="std")]
+
+
+extern crate rand;
+
+use rand::distributions::{Distribution, Uniform};
+
+fn main() {
+ let range = Uniform::new(-1.0f64, 1.0);
+ let mut rng = rand::thread_rng();
+
+ let total = 1_000_000;
+ let mut in_circle = 0;
+
+ for _ in 0..total {
+ let a = range.sample(&mut rng);
+ let b = range.sample(&mut rng);
+ if a*a + b*b <= 1.0 {
+ in_circle += 1;
+ }
+ }
+
+ // prints something close to 3.14159...
+ println!("π is approximately {}", 4. * (in_circle as f64) / (total as f64));
+}
diff --git a/rand/examples/monty-hall.rs b/rand/examples/monty-hall.rs
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+// Copyright 2018 Developers of the Rand project.
+// Copyright 2013-2018 The Rust Project Developers.
+//
+// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
+// https://www.apache.org/licenses/LICENSE-2.0> or the MIT license
+// <LICENSE-MIT or https://opensource.org/licenses/MIT>, at your
+// option. This file may not be copied, modified, or distributed
+// except according to those terms.
+
+//! ## Monty Hall Problem
+//!
+//! This is a simulation of the [Monty Hall Problem][]:
+//!
+//! > Suppose you're on a game show, and you're given the choice of three doors:
+//! > Behind one door is a car; behind the others, goats. You pick a door, say
+//! > No. 1, and the host, who knows what's behind the doors, opens another
+//! > door, say No. 3, which has a goat. He then says to you, "Do you want to
+//! > pick door No. 2?" Is it to your advantage to switch your choice?
+//!
+//! The rather unintuitive answer is that you will have a 2/3 chance of winning
+//! if you switch and a 1/3 chance of winning if you don't, so it's better to
+//! switch.
+//!
+//! This program will simulate the game show and with large enough simulation
+//! steps it will indeed confirm that it is better to switch.
+//!
+//! [Monty Hall Problem]: https://en.wikipedia.org/wiki/Monty_Hall_problem
+
+#![cfg(feature="std")]
+
+
+extern crate rand;
+
+use rand::Rng;
+use rand::distributions::{Distribution, Uniform};
+
+struct SimulationResult {
+ win: bool,
+ switch: bool,
+}
+
+// Run a single simulation of the Monty Hall problem.
+fn simulate<R: Rng>(random_door: &Uniform<u32>, rng: &mut R)
+ -> SimulationResult {
+ let car = random_door.sample(rng);
+
+ // This is our initial choice
+ let mut choice = random_door.sample(rng);
+
+ // The game host opens a door
+ let open = game_host_open(car, choice, rng);
+
+ // Shall we switch?
+ let switch = rng.gen();
+ if switch {
+ choice = switch_door(choice, open);
+ }
+
+ SimulationResult { win: choice == car, switch }
+}
+
+// Returns the door the game host opens given our choice and knowledge of
+// where the car is. The game host will never open the door with the car.
+fn game_host_open<R: Rng>(car: u32, choice: u32, rng: &mut R) -> u32 {
+ use rand::seq::SliceRandom;
+ *free_doors(&[car, choice]).choose(rng).unwrap()
+}
+
+// Returns the door we switch to, given our current choice and
+// the open door. There will only be one valid door.
+fn switch_door(choice: u32, open: u32) -> u32 {
+ free_doors(&[choice, open])[0]
+}
+
+fn free_doors(blocked: &[u32]) -> Vec<u32> {
+ (0..3).filter(|x| !blocked.contains(x)).collect()
+}
+
+fn main() {
+ // The estimation will be more accurate with more simulations
+ let num_simulations = 10000;
+
+ let mut rng = rand::thread_rng();
+ let random_door = Uniform::new(0u32, 3);
+
+ let (mut switch_wins, mut switch_losses) = (0, 0);
+ let (mut keep_wins, mut keep_losses) = (0, 0);
+
+ println!("Running {} simulations...", num_simulations);
+ for _ in 0..num_simulations {
+ let result = simulate(&random_door, &mut rng);
+
+ match (result.win, result.switch) {
+ (true, true) => switch_wins += 1,
+ (true, false) => keep_wins += 1,
+ (false, true) => switch_losses += 1,
+ (false, false) => keep_losses += 1,
+ }
+ }
+
+ let total_switches = switch_wins + switch_losses;
+ let total_keeps = keep_wins + keep_losses;
+
+ println!("Switched door {} times with {} wins and {} losses",
+ total_switches, switch_wins, switch_losses);
+
+ println!("Kept our choice {} times with {} wins and {} losses",
+ total_keeps, keep_wins, keep_losses);
+
+ // With a large number of simulations, the values should converge to
+ // 0.667 and 0.333 respectively.
+ println!("Estimated chance to win if we switch: {}",
+ switch_wins as f32 / total_switches as f32);
+ println!("Estimated chance to win if we don't: {}",
+ keep_wins as f32 / total_keeps as f32);
+}