auto merge of #10478 : TeXitoi/rust/shootout-meteor, r=brson

This implementation of the meteor contest implements:
 - insertion check with bit trick;
 - pregenetation of every feasible placement of the pieces on the
   board;
 - filtering of placement that implies unfeasible board
 - central symetry breaking

related to #2776

Author: bors

src/test/bench/shootout-meteor.rs

@@ -0,0 +1,281 @@
+// Copyright 2013 The Rust Project Developers. See the COPYRIGHT
+// file at the top-level directory of this distribution and at
+// http://rust-lang.org/COPYRIGHT.
+//
+// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
+// http://www.apache.org/licenses/LICENSE-2.0> or the MIT license
+// <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your
+// option. This file may not be copied, modified, or distributed
+// except according to those terms.
+
+//
+// Utilities.
+//
+
+// returns an infinite iterator of repeated applications of f to x,
+// i.e. [x, f(x), f(f(x)), ...], as haskell iterate function.
+fn iterate<'a, T>(x: T, f: &'a fn(&T) -> T) -> Iterate<'a, T> {
+    Iterate {f: f, next: x}
+}
+struct Iterate<'self, T> {
+    priv f: &'self fn(&T) -> T,
+    priv next: T
+}
+impl<'self, T> Iterator<T> for Iterate<'self, T> {
+    fn next(&mut self) -> Option<T> {
+        let mut res = (self.f)(&self.next);
+        std::util::swap(&mut res, &mut self.next);
+        Some(res)
+    }
+}
+
+// a linked list using borrowed next.
+enum List<'self, T> {
+    Nil,
+    Cons(T, &'self List<'self, T>)
+}
+struct ListIterator<'self, T> {
+    priv cur: &'self List<'self, T>
+}
+impl<'self, T> List<'self, T> {
+    fn iter(&'self self) -> ListIterator<'self, T> {
+        ListIterator{cur: self}
+    }
+}
+impl<'self, T> Iterator<&'self T> for ListIterator<'self, T> {
+    fn next(&mut self) -> Option<&'self T> {
+        match *self.cur {
+            Nil => None,
+            Cons(ref elt, next) => {
+                self.cur = next;
+                Some(elt)
+            }
+        }
+    }
+}
+
+//
+// preprocess
+//
+
+// Takes a pieces p on the form [(y1, x1), (y2, x2), ...] and returns
+// every possible transformations (the 6 rotations with their
+// corresponding mirrored piece), with, as minimum coordinates, (0,
+// 0).  If all is false, only generate half of the possibilities (used
+// to break the symetry of the board).
+fn transform(piece: ~[(int, int)], all: bool) -> ~[~[(int, int)]] {
+    let mut res =
+        // rotations
+        iterate(piece, |rot| rot.iter().map(|&(y, x)| (x + y, -y)).collect())
+        .take(if all {6} else {3})
+        // mirror
+        .flat_map(|cur_piece| {
+            iterate(cur_piece, |mir| mir.iter().map(|&(y, x)| (x, y)).collect())
+            .take(2)
+        }).to_owned_vec();
+
+    // translating to (0, 0) as minimum coordinates.
+    for cur_piece in res.mut_iter() {
+        let (dy, dx) = *cur_piece.iter().min_by(|e| *e).unwrap();
+        for &(ref mut y, ref mut x) in cur_piece.mut_iter() {
+            *y -= dy; *x -= dx;
+        }
+    }
+
+    res
+}
+
+// A mask is a piece somewere on the board.  It is represented as a
+// u64: for i in the first 50 bits, m[i] = 1 if the cell at (i/5, i%5)
+// is occuped.  m[50 + id] = 1 if the identifier of the piece is id.
+
+// Takes a piece with minimum coordinate (0, 0) (as generated by
+// transform).  Returns the corresponding mask if p translated by (dy,
+// dx) is on the board.
+fn mask(dy: int, dx: int, id: uint, p: &[(int, int)]) -> Option<u64> {
+    let mut m = 1 << (50 + id);
+    for &(y, x) in p.iter() {
+        let x = x + dx + (y + (dy % 2)) / 2;
+        if x < 0 || x > 4 {return None;}
+        let y = y + dy;
+        if y < 0 || y > 9 {return None;}
+        m |= 1 << (y * 5 + x);
+    }
+    Some(m)
+}
+
+// Makes every possible masks.  masks[id][i] correspond to every
+// possible masks for piece with identifier id with minimum coordinate
+// (i/5, i%5).
+fn make_masks() -> ~[~[~[u64]]] {
+    let pieces = ~[
+        ~[(0,0),(0,1),(0,2),(0,3),(1,3)],
+        ~[(0,0),(0,2),(0,3),(1,0),(1,1)],
+        ~[(0,0),(0,1),(0,2),(1,2),(2,1)],
+        ~[(0,0),(0,1),(0,2),(1,1),(2,1)],
+        ~[(0,0),(0,2),(1,0),(1,1),(2,1)],
+        ~[(0,0),(0,1),(0,2),(1,1),(1,2)],
+        ~[(0,0),(0,1),(1,1),(1,2),(2,1)],
+        ~[(0,0),(0,1),(0,2),(1,0),(1,2)],
+        ~[(0,0),(0,1),(0,2),(1,2),(1,3)],
+        ~[(0,0),(0,1),(0,2),(0,3),(1,2)]];
+    let mut res = ~[];
+    for (id, p) in pieces.move_iter().enumerate() {
+        // To break the central symetry of the problem, every
+        // transformation must be taken except for one piece (piece 3
+        // here).
+        let trans = transform(p, id != 3);
+        let mut cur_piece = ~[];
+        for dy in range(0, 10) {
+            for dx in range(0, 5) {
+                let masks = 
+                    trans.iter()
+                    .filter_map(|t| mask(dy, dx, id, *t))
+                    .collect();
+                cur_piece.push(masks);
+            }
+        }
+        res.push(cur_piece);
+    }
+    res
+}
+
+// Check if all coordinates can be covered by an unused piece and that
+// all unused piece can be placed on the board.
+fn is_board_unfeasible(board: u64, masks: &[~[~[u64]]]) -> bool {
+    let mut coverable = board;
+    for i in range(0, 50).filter(|&i| board & 1 << i == 0) {
+        for (cur_id, pos_masks) in masks.iter().enumerate() {
+            if board & 1 << (50 + cur_id) != 0 {continue;}
+            for &cur_m in pos_masks[i].iter() {
+                if cur_m & board == 0 {coverable |= cur_m;}
+            }
+        }
+        if coverable & (1 << i) == 0 {return true;}
+    }
+    // check if every coordinates can be covered and every piece can
+    // be used.
+    coverable != (1 << 60) - 1
+}
+
+// Filter the masks that we can prove to result to unfeasible board.
+fn filter_masks(masks: &[~[~[u64]]]) -> ~[~[~[u64]]] {
+    masks.iter().map(
+        |p| p.iter().map(
+            |p| p.iter()
+                .map(|&m| m)
+                .filter(|&m| !is_board_unfeasible(m, masks))
+                .collect())
+            .collect())
+        .collect()
+}
+
+// Gets the identifier of a mask.
+fn get_id(m: u64) -> u8 {
+    for id in range(0, 10) {
+        if m & (1 << (id + 50)) != 0 {return id as u8;}
+    }
+    fail!("{:016x} does not have a valid identifier", m);
+}
+
+// Converts a list of mask to a ~str.
+fn to_utf8(raw_sol: &List<u64>) -> ~str {
+    let mut sol: ~[u8] = std::vec::from_elem(50, '.' as u8);
+    for &m in raw_sol.iter() {
+        let id = get_id(m);
+        for i in range(0, 50) {
+            if m & 1 << i != 0 {sol[i] = '0' as u8 + id;}
+        }
+    }
+    std::str::from_utf8_owned(sol)
+}
+
+// Prints a solution in ~str form.
+fn print_sol(sol: &str) {
+    for (i, c) in sol.iter().enumerate() {
+        if (i) % 5 == 0 {println("");}
+        if (i + 5) % 10 == 0 {print(" ");}
+        print!("{} ", c);
+    }
+    println("");
+}
+
+// The data managed during the search
+struct Data {
+    // If more than stop_after is found, stop the search.
+    stop_after: int,
+    // Number of solution found.
+    nb: int,
+    // Lexicographically minimal solution found.
+    min: ~str,
+    // Lexicographically maximal solution found.
+    max: ~str
+}
+
+// Records a new found solution.  Returns false if the search must be
+// stopped.
+fn handle_sol(raw_sol: &List<u64>, data: &mut Data) -> bool {
+    // because we break the symetry, 2 solutions correspond to a call
+    // to this method: the normal solution, and the same solution in
+    // reverse order, i.e. the board rotated by half a turn.
+    data.nb += 2;
+    let sol1 = to_utf8(raw_sol);
+    let sol2: ~str = sol1.iter().invert().collect();
+
+    if data.nb == 2 {
+        data.min = sol1.clone();
+        data.max = sol1.clone();
+    }
+
+    if sol1 < data.min {data.min = sol1.clone();}
+    if sol2 < data.min {data.min = sol2.clone();}
+    if sol1 > data.max {data.max = sol1;}
+    if sol2 > data.max {data.max = sol2;}
+    data.nb < data.stop_after
+}
+
+// Search for every solutions.  Returns false if the search was
+// stopped before the end.
+fn search(
+    masks: &[~[~[u64]]],
+    board: u64,
+    mut i: int,
+    cur: List<u64>,
+    data: &mut Data)
+    -> bool
+{
+    // Search for the lesser empty coordinate.
+    while board & (1 << i)  != 0 && i < 50 {i += 1;}
+    // the board is full: a solution is found.
+    if i >= 50 {return handle_sol(&cur, data);}
+
+    // for every unused piece
+    for id in range(0, 10).filter(|id| board & (1 << (id + 50)) == 0) {
+        // for each mask that fits on the board
+        for &m in masks[id][i].iter().filter(|&m| board & *m == 0) {
+            // This check is too costy.
+            //if is_board_unfeasible(board | m, masks) {continue;}
+            if !search(masks, board | m, i + 1, Cons(m, &cur), data) {
+                return false;
+            }
+        }
+    }
+    return true;
+}
+
+fn main () {
+    let args = std::os::args();
+    let stop_after = if args.len() <= 1 {
+        2098
+    } else {
+        from_str(args[1]).unwrap()
+    };
+    let masks = make_masks();
+    let masks = filter_masks(masks);
+    let mut data = Data {stop_after: stop_after, nb: 0, min: ~"", max: ~""};
+    search(masks, 0, 0, Nil, &mut data);
+    println!("{} solutions found", data.nb);
+    print_sol(data.min);
+    print_sol(data.max);
+    println("");
+}