Task: Pentomino tiling




Go: package main

import (
    "fmt"
    "math/rand"
    "time"
)

var F = [][]int{
    {1, -1, 1, 0, 1, 1, 2, 1}, {0, 1, 1, -1, 1, 0, 2, 0},
    {1, 0, 1, 1, 1, 2, 2, 1}, {1, 0, 1, 1, 2, -1, 2, 0},
    {1, -2, 1, -1, 1, 0, 2, -1}, {0, 1, 1, 1, 1, 2, 2, 1},
    {1, -1, 1, 0, 1, 1, 2, -1}, {1, -1, 1, 0, 2, 0, 2, 1},
}

var I = [][]int{{0, 1, 0, 2, 0, 3, 0, 4}, {1, 0, 2, 0, 3, 0, 4, 0}}

var L = [][]int{
    {1, 0, 1, 1, 1, 2, 1, 3}, {1, 0, 2, 0, 3, -1, 3, 0},
    {0, 1, 0, 2, 0, 3, 1, 3}, {0, 1, 1, 0, 2, 0, 3, 0}, {0, 1, 1, 1, 2, 1, 3, 1},
    {0, 1, 0, 2, 0, 3, 1, 0}, {1, 0, 2, 0, 3, 0, 3, 1}, {1, -3, 1, -2, 1, -1, 1, 0},
}

var N = [][]int{
    {0, 1, 1, -2, 1, -1, 1, 0}, {1, 0, 1, 1, 2, 1, 3, 1},
    {0, 1, 0, 2, 1, -1, 1, 0}, {1, 0, 2, 0, 2, 1, 3, 1}, {0, 1, 1, 1, 1, 2, 1, 3},
    {1, 0, 2, -1, 2, 0, 3, -1}, {0, 1, 0, 2, 1, 2, 1, 3}, {1, -1, 1, 0, 2, -1, 3, -1},
}

var P = [][]int{
    {0, 1, 1, 0, 1, 1, 2, 1}, {0, 1, 0, 2, 1, 0, 1, 1},
    {1, 0, 1, 1, 2, 0, 2, 1}, {0, 1, 1, -1, 1, 0, 1, 1}, {0, 1, 1, 0, 1, 1, 1, 2},
    {1, -1, 1, 0, 2, -1, 2, 0}, {0, 1, 0, 2, 1, 1, 1, 2}, {0, 1, 1, 0, 1, 1, 2, 0},
}

var T = [][]int{
    {0, 1, 0, 2, 1, 1, 2, 1}, {1, -2, 1, -1, 1, 0, 2, 0},
    {1, 0, 2, -1, 2, 0, 2, 1}, {1, 0, 1, 1, 1, 2, 2, 0},
}

var U = [][]int{
    {0, 1, 0, 2, 1, 0, 1, 2}, {0, 1, 1, 1, 2, 0, 2, 1},
    {0, 2, 1, 0, 1, 1, 1, 2}, {0, 1, 1, 0, 2, 0, 2, 1},
}

var V = [][]int{
    {1, 0, 2, 0, 2, 1, 2, 2}, {0, 1, 0, 2, 1, 0, 2, 0},
    {1, 0, 2, -2, 2, -1, 2, 0}, {0, 1, 0, 2, 1, 2, 2, 2},
}

var W = [][]int{
    {1, 0, 1, 1, 2, 1, 2, 2}, {1, -1, 1, 0, 2, -2, 2, -1},
    {0, 1, 1, 1, 1, 2, 2, 2}, {0, 1, 1, -1, 1, 0, 2, -1},
}

var X = [][]int{{1, -1, 1, 0, 1, 1, 2, 0}}

var Y = [][]int{
    {1, -2, 1, -1, 1, 0, 1, 1}, {1, -1, 1, 0, 2, 0, 3, 0},
    {0, 1, 0, 2, 0, 3, 1, 1}, {1, 0, 2, 0, 2, 1, 3, 0}, {0, 1, 0, 2, 0, 3, 1, 2},
    {1, 0, 1, 1, 2, 0, 3, 0}, {1, -1, 1, 0, 1, 1, 1, 2}, {1, 0, 2, -1, 2, 0, 3, 0},
}

var Z = [][]int{
    {0, 1, 1, 0, 2, -1, 2, 0}, {1, 0, 1, 1, 1, 2, 2, 2},
    {0, 1, 1, 1, 2, 1, 2, 2}, {1, -2, 1, -1, 1, 0, 2, -2},
}

var shapes = [][][]int{F, I, L, N, P, T, U, V, W, X, Y, Z}

var symbols = []byte("FILNPTUVWXYZ-")

const (
    nRows = 8
    nCols = 8
    blank = 12
)

var grid [nRows][nCols]int
var placed [12]bool

func tryPlaceOrientation(o []int, r, c, shapeIndex int) bool {
    for i := 0; i < len(o); i += 2 {
        x := c + o[i+1]
        y := r + o[i]
        if x < 0 || x >= nCols || y < 0 || y >= nRows || grid[y][x] != -1 {
            return false
        }
    }
    grid[r][c] = shapeIndex
    for i := 0; i < len(o); i += 2 {
        grid[r+o[i]][c+o[i+1]] = shapeIndex
    }
    return true
}

func removeOrientation(o []int, r, c int) {
    grid[r][c] = -1
    for i := 0; i < len(o); i += 2 {
        grid[r+o[i]][c+o[i+1]] = -1
    }
}

func solve(pos, numPlaced int) bool {
    if numPlaced == len(shapes) {
        return true
    }
    row := pos / nCols
    col := pos % nCols
    if grid[row][col] != -1 {
        return solve(pos+1, numPlaced)
    }

    for i := range shapes {
        if !placed[i] {
            for _, orientation := range shapes[i] {
                if !tryPlaceOrientation(orientation, row, col, i) {
                    continue
                }
                placed[i] = true
                if solve(pos+1, numPlaced+1) {
                    return true
                }
                removeOrientation(orientation, row, col)
                placed[i] = false
            }
        }
    }
    return false
}

func shuffleShapes() {
    rand.Shuffle(len(shapes), func(i, j int) {
        shapes[i], shapes[j] = shapes[j], shapes[i]
        symbols[i], symbols[j] = symbols[j], symbols[i]
    })
}

func printResult() {
    for _, r := range grid {
        for _, i := range r {
            fmt.Printf("%c ", symbols[i])
        }
        fmt.Println()
    }
}

func main() {
    rand.Seed(time.Now().UnixNano())
    shuffleShapes()
    for r := 0; r < nRows; r++ {
        for i := range grid[r] {
            grid[r][i] = -1
        }
    }
    for i := 0; i < 4; i++ {
        var randRow, randCol int
        for {
            randRow = rand.Intn(nRows)
            randCol = rand.Intn(nCols)
            if grid[randRow][randCol] != blank {
                break
            }
        }
        grid[randRow][randCol] = blank
    }
    if solve(0, 0) {
        printResult()
    } else {
        fmt.Println("No solution")
    }
}




Python: from itertools import product

minos = (((197123, 7, 6), (1797, 6, 7), (1287, 6, 7), (196867, 7, 6)),
        ((263937, 6, 6), (197126, 6, 6), (393731, 6, 6), (67332, 6, 6)),
        ((16843011, 7, 5), (2063, 5, 7), (3841, 5, 7), (271, 5, 7), (3848, 5, 7), (50463234, 7, 5), (50397441, 7, 5), (33686019, 7, 5)),
        ((131843, 7, 6), (1798, 6, 7), (775, 6, 7), (1795, 6, 7), (1543, 6, 7), (197377, 7, 6), (197378, 7, 6), (66307, 7, 6)),
        ((132865, 6, 6), (131846, 6, 6), (198146, 6, 6), (132611, 6, 6), (393986, 6, 6), (263938, 6, 6), (67330, 6, 6), (132868, 6, 6)),
        ((1039, 5, 7), (33751554, 7, 5), (16843521, 7, 5), (16974081, 7, 5), (33686274, 7, 5), (3842, 5, 7), (3844, 5, 7), (527, 5, 7)),
        ((1804, 5, 7), (33751297, 7, 5), (33686273, 7, 5), (16974338, 7, 5), (16843522, 7, 5), (782, 5, 7), (3079, 5, 7), (3587, 5, 7)),
        ((263683, 6, 6), (198148, 6, 6), (66310, 6, 6), (393985, 6, 6)),
        ((67329, 6, 6), (131591, 6, 6), (459266, 6, 6), (263940, 6, 6)),
        ((459780, 6, 6), (459009, 6, 6), (263175, 6, 6), (65799, 6, 6)),
        ((4311810305, 8, 4), (31, 4, 8)),
        ((132866, 6, 6),))

boxchar_double_width = ' ╶╺╵└┕╹┖┗╴─╼┘┴┶┚┸┺╸╾━┙┵┷┛┹┻╷┌┍│├┝╿┞┡┐┬┮┤┼┾┦╀╄┑┭┯┥┽┿┩╃╇╻┎┏╽┟┢┃┠┣┒┰┲┧╁╆┨╂╊┓┱┳┪╅╈┫╉╋'
boxchar_single_width = [c + ' ─━'[i%3] for i, c in enumerate(boxchar_double_width)]


patterns = boxchar_single_width

tiles = []
for row in reversed(minos):
    tiles.append([])
    for n, x, y in row:
        for shift in (b*8 + a for a, b in product(range(x), range(y))):
            tiles[-1].append(n << shift)

def img(seq):
    b = [[0]*10 for _ in range(10)]

    for i, s in enumerate(seq):
        for j, k in product(range(8), range(8)):
            if s & (1<<(j*8 + k)):
                b[j + 1][k + 1] = i + 1

    idices = [[0]*9 for _ in range(9)]
    for i, j in product(range(9), range(9)):
        n = (b[i+1][j+1], b[i][j+1], b[i][j], b[i+1][j], b[i+1][j+1])
        idices[i][j] = sum((a != b)*(1 + (not a or not b))*3**i for i, (a,b) in enumerate(zip(n, n[1:])))

    return '\n'.join(''.join(patterns[i] for i in row) for row in idices)

def tile(board=0, seq=tuple(), tiles=tiles):
    if not tiles:
        yield img(seq)
        return

    for c in tiles[0]:
        b = board | c

        tnext = [] 
        for t in tiles[1:]:
            tnext.append(tuple(n for n in t if not n&b))
            if not tnext[-1]: break 
        else:
            yield from tile(b, seq + (c,), tnext)

for x in tile():
    print(x)