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//! Library for back tracking with customizable search for possible moves. //! //! [Back tracking](https://en.wikipedia.org/wiki/Backtracking) is a general algorithm to find //! solution for constraint satisfaction problems. //! //! The performance of finding a solution can vary greatly with the algorithm used to look for //! the best position to set a value next. For example, a sodoku puzzle with many missing numbers //! can take 59 iterations when picking an empty slot with minimum number of options, //! but it takes 295 992 iterations to solve when looking for the first empty slot. //! //! One can explain this difference in performance using probability theory. //! If a slot can contain 2 correct out of N possible values, the odds are 2:N. //! When this slot is tangled through constraints with another slot with odds 1:M, //! the total odds become 2*1:N*M. //! To maximize the chance of finding a correct solution, one must maximize the odds for the //! remaining moves or fail to satisfy the constraints as early as possible. //! Fewer choices reduces the chances of being wrong, increases the chance of failing constraints //! early and therefore increases the chance of finding a solution more quickly. //! //! By making the search customizable, one can easier experiment with different algorithms //! to pick the next best guess and see which has the best performance on a given problem. //! This library is designed to assist with this kind of exploration. //! //! ### Solving simple moves //! //! In some constraint problems, there are lots of steps that are trivial once a choice is made. //! For example, in Sudoku a lot of numbers can be filled in once a number is selected for a slot. //! //! By solving simple moves separately, one can improve performance and reduce the debugging //! output significantly. //! //! ### Debugging //! //! The relationship between the structure of a puzzle and an efficient algorithm to pick the //! next best guess can be non-trivial, so understanding what happens is essential for finding //! an efficient algorithm. //! //! When the setting `SolveSettings::debug(true)` is enabled, the solver prints out the steps //! to standard output while solving. //! //! The solver prints "Guess" when making a new move, and "Try" when changing an earlier move. //! Number of iterations are printed at the end when the puzzle is solved. //! //! You can slow down the solving by setting `SolveSettings::sleep_ms(1000)`. //! This makes the solver wait one second (1000 milliseconds) before continuing to the next step. #![deny(missing_docs)] use std::fmt::Debug; /// Implemented by puzzles. /// /// A puzzle stores the state of the problem, and can be modified by inserting a value at a /// position within the puzzle. The solver does not understand the internal structure of the /// puzzle, but is still able to find a solution (if any exists). /// /// The initial state does not have to empty, and you can get the difference at the end /// by setting `SolveSettings::difference(true)`. pub trait Puzzle: Clone { /// The type of position. type Pos: Copy + Debug; /// The type of values stored in the puzzle. type Val: Copy + Debug + PartialEq; /// Solve simple stuff faster. /// This will reduce the number of steps in solution. /// If you do not know how to solve this, leave it empty. fn solve_simple(&mut self); /// Sets a value at position. fn set(&mut self, pos: Self::Pos, val: Self::Val); /// Print puzzle out to standard output. fn print(&self); /// Whether puzzle is solved. fn is_solved(&self) -> bool; /// Removes values from other puzzle to show changes. fn remove(&mut self, other: &Self); } /// Stores settings for solver. /// /// Default settings: /// /// - solve_simple: `true` /// - debug: `false` /// - difference: `false` /// - sleep_ms: `None` pub struct SolveSettings { solve_simple: bool, debug: bool, difference: bool, sleep_ms: Option<u64>, max_iterations: Option<u64>, } impl SolveSettings { /// Creates new solve settings. pub fn new() -> SolveSettings { SolveSettings { solve_simple: true, debug: false, difference: false, sleep_ms: None, max_iterations: None, } } /// Sets wheter to solve simple moves between each step. pub fn set_solve_simple(&mut self, val: bool) { self.solve_simple = val; } /// Whether to solve simple moves between each step. pub fn solve_simple(mut self, val: bool) -> Self { self.set_solve_simple(val); self } /// Sets whether to debug by printing out to standard output. pub fn set_debug(&mut self, val: bool) { self.debug = val; } /// Whether to debug by printing out to standard output. pub fn debug(mut self, val: bool) -> Self { self.set_debug(val); self } /// Sets whether to return the difference from initial puzzle. pub fn set_difference(&mut self, val: bool) { self.difference = val; } /// Whether to return the difference from initial puzzle. pub fn difference(mut self, val: bool) -> Self { self.set_difference(val); self } /// Sets how many milliseconds to sleep between each step, if any. pub fn set_maybe_sleep_ms(&mut self, val: Option<u64>) { self.sleep_ms = val; } /// Sets how many milliseconds to sleep between each step, if any. pub fn maybe_sleep_ms(mut self, val: Option<u64>) -> Self { self.set_maybe_sleep_ms(val); self } /// Sets how many milliseconds to sleep between each step. pub fn set_sleep_ms(&mut self, val: u64) { self.sleep_ms = Some(val); } /// How many milliseconds to sleep between each step. pub fn sleep_ms(mut self, val: u64) -> Self { self.set_sleep_ms(val); self } /// Sets the maximum number of iterations before giving up. pub fn set_maybe_max_iterations(&mut self, val: Option<u64>) { self.max_iterations = val; } /// The maximum number of iterations before giving up. pub fn maybe_max_iterations(mut self, val: Option<u64>) -> Self { self.set_maybe_max_iterations(val); self } /// Sets the maximum number of iterations before giving up. pub fn set_max_iterations(&mut self, val: u64) { self.max_iterations = Some(val); } /// The maximum number of iterations before giving up. pub fn max_iterations(mut self, val: u64) -> Self { self.set_max_iterations(val); self } } /// Contains solution. pub struct Solution<T> { /// The solved puzzle. pub puzzle: T, /// The number of iterations used to solve the puzzle. pub iterations: u64, } /// Solvees puzzles using back tracking. pub struct BackTrackSolver<T> where T: Puzzle { /// Stores the states. pub states: Vec<T>, /// Stores the choices for the states. pub choice: Vec<(T::Pos, Vec<T::Val>)>, /// Search for simple solutions. pub settings: SolveSettings, } impl<T> BackTrackSolver<T> where T: Puzzle { /// Creates a new solver. pub fn new(puzzle: T, settings: SolveSettings) -> BackTrackSolver<T> { BackTrackSolver { states: vec![puzzle], choice: vec![], settings: settings, } } /// Solves puzzle, using a closure to look for best position to set a value next, /// and a closure for picking options in preferred order. /// /// The second closure returns possible values at a given position. /// The last move in the list has highest priority, because the solver pops the values in turn. pub fn solve<F, G>(mut self, mut f: F, mut g: G) -> Option<Solution<T>> where F: FnMut(&T) -> Option<T::Pos>, G: FnMut(&T, T::Pos) -> Vec<T::Val> { use std::thread::sleep; use std::time::Duration; let mut iterations: u64 = 0; loop { if self.settings.debug { if let Some(ms) = self.settings.sleep_ms { sleep(Duration::from_millis(ms)); } } let n = self.states.len() - 1; let mut new = self.states[n].clone(); if self.settings.solve_simple { new.solve_simple(); } if self.settings.debug { new.print(); } iterations += 1; if let Some(max_iterations) = self.settings.max_iterations { if iterations > max_iterations { return None; } } if new.is_solved() { if self.settings.debug { println!("Solved! Iterations: {}", iterations); } if self.settings.difference { new.remove(&self.states[0]); } return Some(Solution { puzzle: new, iterations: iterations }); } let empty = f(&new); let mut possible = match empty { None => vec![], Some(x) => g(&new, x) }; if possible.len() == 0 { // println!("No possible at {:?}", empty); loop { if self.choice.len() == 0 { if self.settings.debug { // No more possible choices. println!("No more possible choices"); } return None; } let (pos, mut possible) = self.choice.pop().unwrap(); if let Some(new_val) = possible.pop() { // Try next choice. let n = self.states.len() - 1; self.states[n].set(pos, new_val); self.choice.push((pos, possible)); if self.settings.debug { println!("Try {:?}, {:?} depth {} {} (failed at {:?})", pos, new_val, self.choice.len(), self.states.len(), empty); } break; } else { if self.states.pop().is_none() { // No more possible choices. return None; } } } } else { let empty = empty.unwrap(); // Put in the first guess. let v = possible.pop().unwrap(); new.set(empty, v); self.choice.push((empty, possible)); self.states.push(new); if self.settings.debug { println!("Guess {:?}, {:?} depth {} {}", empty, v, self.choice.len(), self.states.len()); } } } } }