// Copyright 2013-2014 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.

#![feature(phase)]
#[phase(syntax)] extern crate green;
extern crate sync;

use sync::Arc;

green_start!(main)

//
// 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: |&T|: 'a -> T) -> Iterate<'a, T> {
    Iterate {f: f, next: x}
}
struct Iterate<'a, T> {
    f: |&T|: 'a -> T,
    next: T
}
impl<'a, T> Iterator<T> for Iterate<'a, T> {
    fn next(&mut self) -> Option<T> {
        let mut res = (self.f)(&self.next);
        std::mem::swap(&mut res, &mut self.next);
        Some(res)
    }
}

// a linked list using borrowed next.
enum List<'a, T> {
    Nil,
    Cons(T, &'a List<'a, T>)
}
struct ListIterator<'a, T> {
    cur: &'a List<'a, T>
}
impl<'a, T> List<'a, T> {
    fn iter(&'a self) -> ListIterator<'a, T> {
        ListIterator{cur: self}
    }
}
impl<'a, T> Iterator<&'a T> for ListIterator<'a, T> {
    fn next(&mut self) -> Option<&'a 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: Vec<(int, int)> , all: bool) -> Vec<Vec<(int, int)>> {
    let mut res: Vec<Vec<(int, int)>> =
        // 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)
        }).collect();

    // 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: &Vec<(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[i][id] correspond to every
// possible masks for piece with identifier id with minimum coordinate
// (i/5, i%5).
fn make_masks() -> Vec<Vec<Vec<u64> > > {
    let pieces = vec!(
        vec!((0,0),(0,1),(0,2),(0,3),(1,3)),
        vec!((0,0),(0,2),(0,3),(1,0),(1,1)),
        vec!((0,0),(0,1),(0,2),(1,2),(2,1)),
        vec!((0,0),(0,1),(0,2),(1,1),(2,1)),
        vec!((0,0),(0,2),(1,0),(1,1),(2,1)),
        vec!((0,0),(0,1),(0,2),(1,1),(1,2)),
        vec!((0,0),(0,1),(1,1),(1,2),(2,1)),
        vec!((0,0),(0,1),(0,2),(1,0),(1,2)),
        vec!((0,0),(0,1),(0,2),(1,2),(1,3)),
        vec!((0,0),(0,1),(0,2),(0,3),(1,2)));

    // To break the central symetry of the problem, every
    // transformation must be taken except for one piece (piece 3
    // here).
    let transforms: Vec<Vec<Vec<(int, int)>>> =
        pieces.move_iter().enumerate()
        .map(|(id, p)| transform(p, id != 3))
        .collect();

    range(0, 50).map(|yx| {
        transforms.iter().enumerate().map(|(id, t)| {
            t.iter().filter_map(|p| mask(yx / 5, yx % 5, id, p)).collect()
        }).collect()
    }).collect()
}

// 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: &Vec<Vec<Vec<u64>>>) -> bool {
    let mut coverable = board;
    for (i, masks_at) in masks.iter().enumerate() {
        if board & 1 << i != 0 { continue; }
        for (cur_id, pos_masks) in masks_at.iter().enumerate() {
            if board & 1 << (50 + cur_id) != 0 { continue; }
            for &cur_m in pos_masks.iter() {
                if cur_m & board != 0 { continue; }
                coverable |= cur_m;
                // if every coordinates can be covered and every
                // piece can be used.
                if coverable == (1 << 60) - 1 { return false; }
            }
        }
        if coverable & 1 << i == 0 { return true; }
    }
    true
}

// Filter the masks that we can prove to result to unfeasible board.
fn filter_masks(masks: &mut Vec<Vec<Vec<u64>>>) {
    for i in range(0, masks.len()) {
        for j in range(0, masks.get(i).len()) {
            *masks.get_mut(i).get_mut(j) =
                masks.get(i).get(j).iter().map(|&m| m)
                .filter(|&m| !is_board_unfeasible(m, masks))
                .collect();
        }
    }
}

// Gets the identifier of a mask.
fn get_id(m: u64) -> u8 {
    for id in range(0u8, 10) {
        if m & (1 << (id + 50)) != 0 {return id;}
    }
    fail!("{:016x} does not have a valid identifier", m);
}

// Converts a list of mask to a StrBuf.
fn to_vec(raw_sol: &List<u64>) -> Vec<u8> {
    let mut sol = Vec::from_elem(50, '.' as u8);
    for &m in raw_sol.iter() {
        let id = '0' as u8 + get_id(m);
        for i in range(0u, 50) {
            if m & 1 << i != 0 {
                *sol.get_mut(i) = id;
            }
        }
    }
    sol
}

// Prints a solution in StrBuf form.
fn print_sol(sol: &Vec<u8>) {
    for (i, c) in sol.iter().enumerate() {
        if (i) % 5 == 0 { println!(""); }
        if (i + 5) % 10 == 0 { print!(" "); }
        print!("{} ", *c as char);
    }
    println!("");
}

// The data managed during the search
struct Data {
    // Number of solution found.
    nb: int,
    // Lexicographically minimal solution found.
    min: Vec<u8>,
    // Lexicographically maximal solution found.
    max: Vec<u8>
}
impl Data {
    fn new() -> Data {
        Data {nb: 0, min: vec!(), max: vec!()}
    }
    fn reduce_from(&mut self, other: Data) {
        self.nb += other.nb;
        let Data { min: min, max: max, ..} = other;
        if min < self.min { self.min = min; }
        if max > self.max { self.max = max; }
    }
}

// Records a new found solution.  Returns false if the search must be
// stopped.
fn handle_sol(raw_sol: &List<u64>, data: &mut Data) {
    // 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_vec(raw_sol);
    let sol2: Vec<u8> = sol1.iter().rev().map(|x| *x).collect();

    if data.nb == 2 {
        data.min = sol1.clone();
        data.max = sol1.clone();
    }

    if sol1 < data.min {data.min = sol1;}
    else if sol1 > data.max {data.max = sol1;}
    if sol2 < data.min {data.min = sol2;}
    else if sol2 > data.max {data.max = sol2;}
}

fn search(
    masks: &Vec<Vec<Vec<u64>>>,
    board: u64,
    mut i: uint,
    cur: List<u64>,
    data: &mut Data)
{
    // 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);}
    let masks_at = masks.get(i);

    // for every unused piece
    for id in range(0u, 10).filter(|id| board & (1 << (id + 50)) == 0) {
        // for each mask that fits on the board
        for &m in masks_at.get(id).iter().filter(|&m| board & *m == 0) {
            // This check is too costy.
            //if is_board_unfeasible(board | m, masks) {continue;}
            search(masks, board | m, i + 1, Cons(m, &cur), data);
        }
    }
}

fn par_search(masks: Vec<Vec<Vec<u64>>>) -> Data {
    let masks = Arc::new(masks);
    let (tx, rx) = channel();

    // launching the search in parallel on every masks at minimum
    // coordinate (0,0)
    for &m in masks.get(0).iter().flat_map(|masks_pos| masks_pos.iter()) {
        let masks = masks.clone();
        let tx = tx.clone();
        spawn(proc() {
            let mut data = Data::new();
            search(&*masks, m, 1, Cons(m, &Nil), &mut data);
            tx.send(data);
        });
    }

    // collecting the results
    drop(tx);
    let mut data = rx.recv();
    for d in rx.iter() { data.reduce_from(d); }
    data
}

fn main () {
    let mut masks = make_masks();
    filter_masks(&mut masks);
    let data = par_search(masks);
    println!("{} solutions found", data.nb);
    print_sol(&data.min);
    print_sol(&data.max);
    println!("");
}