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// Sudoku Solver
// 11 Nov 2012

package main

import (
	"bytes"
	"fmt"
	"time"
)

type Board [9][9]byte

func (b Board) String() string {
	var buf bytes.Buffer
	for _, row := range b {
		buf.WriteString("[ ")
		for _, digit := range row {
			buf.WriteString(string('0'+digit) + " ")
		}
		buf.WriteString("]\n")
	}
	return buf.String()
}

func (b Board) Check() bool {

	// Check rows (and valid numbers)
	for y := 0; y < 9; y++ {
		var found [10]bool
		for x := 0; x < 9; x++ {
			num := b[y][x]
			if num < 0 || num > 9 {
				return false
			}

			if num != 0 {
				if !found[num] {
					found[num] = true
				} else {
					return false
				}
			}
		}
	}

	// Check columns
	for x := 0; x < 9; x++ {
		var found [10]bool
		for y := 0; y < 9; y++ {
			num := b[y][x]
			if num == 0 {
				continue
			}

			if num != 0 {
				if !found[num] {
					found[num] = true
				} else {
					return false
				}
			}
		}
	}

	// Check squares
	for m := 0; m < 9; m += 3 {
		for n := 0; n < 9; n += 3 {
			var found [10]bool
			for i := 0; i < 9; i++ {
				num := b[m+i/3][n+i%3]
				if num == 0 {
					continue
				}
				if num != 0 {
					if !found[num] {
						found[num] = true
					} else {
						return false
					}
				}
			}
		}
	}

	return true
}

// Return viable candidates for position [y, x]
func (b Board) Viable(y, x int) []byte {
	var found uint

	ySquare := y / 3 * 3
	xSquare := x / 3 * 3

	for i := 0; i < 9; i++ {

		// Check row
		found |= uint(1) << b[y][i]

		// Check column
		found |= uint(1) << b[i][x]

		// Check square
		m := ySquare + i/3
		n := xSquare + i%3
		found |= uint(1) << b[m][n]
	}

	result := make([]byte, 0, 6)
	for i := byte(1); i <= 9; i++ {
		if ((found >> i) & 1) == 0 {
			result = append(result, i)
		}
	}

	return result
}

// Solver setup and launch
func (b *Board) Solve() bool {

	// Make sure the board is solvable before we bother
	if b.Check() {
		solved, success := _solve(*b)
		if success {
			*b = solved
			return true
		}
	}

	return false
}

// Recursive solving function
func _solve(board Board) (b Board, success bool) {
	least_index := -1
	var least_candidates []byte
	for i := 0; i < 81; i++ {
		if board[i/9][i%9] == 0 {
			candidates := board.Viable(i/9, i%9)
			if least_index == -1 || len(least_candidates) > len(candidates) {
				least_index = i
				least_candidates = candidates
				if len(least_candidates) <= 1 {
					break
				}
			}
		}
	}

	// If the entire board is filled, we're done here!
	if least_index == -1 {
		return board, true
	}

	// If we find a spot with no candidates, we can't do anything
	if len(least_candidates) == 0 {
		return
	}

	// See if any of the candidates lead to the promised land
	for _, num := range least_candidates {
		trial := board
		trial[least_index/9][least_index%9] = num
		trial, success = _solve(trial)
		if success {
			return trial, true
		}
	}

	return
}

func main() {

	var board Board
	board = sudoku_difficult
	fmt.Println("Solving board:")
	fmt.Println(board)

	start := time.Now()
	success := board.Solve()
	end := time.Since(start)

	if success {
		fmt.Println("Solved:")
		fmt.Println(board)
		fmt.Println("Time taken:", end)
	} else {
		fmt.Println("No solution found.")
	}

}

// Sample boards
var sudoku_wrong = Board{
	{5, 3, 4, 6, 7, 8, 9, 1, 2},
	{6, 7, 2, 1, 9, 5, 3, 4, 8},
	{1, 9, 8, 3, 8, 2, 5, 6, 7},
	{8, 5, 9, 7, 6, 1, 4, 2, 3},
	{4, 2, 6, 8, 5, 3, 7, 9, 1},
	{7, 1, 3, 9, 2, 4, 8, 5, 6},
	{9, 6, 1, 5, 3, 7, 2, 8, 4},
	{2, 8, 7, 4, 1, 9, 6, 3, 5},
	{3, 4, 5, 2, 8, 6, 1, 7, 9},
}

var sudoku_easy = Board{
	{2, 9, 0, 0, 0, 0, 0, 7, 0},
	{3, 0, 6, 0, 0, 8, 4, 0, 0},
	{8, 0, 0, 0, 4, 0, 0, 0, 2},
	{0, 2, 0, 0, 3, 1, 0, 0, 7},
	{0, 0, 0, 0, 8, 0, 0, 0, 0},
	{1, 0, 0, 9, 5, 0, 0, 6, 0},
	{7, 0, 0, 0, 9, 0, 0, 0, 1},
	{0, 0, 1, 2, 0, 0, 3, 0, 6},
	{0, 3, 0, 0, 0, 0, 0, 5, 9},
}

var sudoku_hard = Board{
	{1, 0, 0, 0, 0, 7, 0, 9, 0},
	{0, 3, 0, 0, 2, 0, 0, 0, 8},
	{0, 0, 9, 6, 0, 0, 5, 0, 0},
	{0, 0, 5, 3, 0, 0, 9, 0, 0},
	{0, 1, 0, 0, 8, 0, 0, 0, 2},
	{6, 0, 0, 0, 0, 4, 0, 0, 0},
	{3, 0, 0, 0, 0, 0, 0, 1, 0},
	{0, 4, 0, 0, 0, 0, 0, 0, 7},
	{0, 0, 7, 0, 0, 0, 3, 0, 0},
}

var sudoku_superhard = Board{
	{8, 0, 0, 0, 0, 0, 0, 0, 0},
	{0, 0, 3, 6, 0, 0, 0, 0, 0},
	{0, 7, 0, 0, 9, 0, 2, 0, 0},
	{0, 5, 0, 0, 0, 7, 0, 0, 0},
	{0, 0, 0, 0, 4, 5, 7, 0, 0},
	{0, 0, 0, 1, 0, 0, 0, 3, 0},
	{0, 0, 1, 0, 0, 0, 0, 6, 8},
	{0, 0, 8, 5, 0, 0, 0, 1, 0},
	{0, 9, 0, 0, 0, 0, 4, 0, 0},
}

var sudoku_megahard = Board{
	{9, 8, 0, 7, 0, 0, 6, 0, 0},
	{5, 0, 0, 0, 8, 4, 0, 0, 0},
	{0, 0, 3, 0, 6, 0, 0, 0, 0},
	{6, 0, 0, 0, 0, 7, 9, 0, 0},
	{0, 7, 0, 0, 0, 0, 0, 2, 0},
	{0, 0, 5, 0, 0, 0, 0, 0, 3},
	{4, 0, 0, 0, 7, 0, 8, 0, 0},
	{0, 5, 0, 9, 0, 0, 0, 1, 0},
	{0, 0, 0, 0, 0, 8, 0, 0, 2},
}

var sudoku_difficult = Board{
	{0, 0, 0, 0, 0, 0, 0, 0, 0},
	{0, 0, 0, 0, 0, 3, 0, 8, 5},
	{0, 0, 1, 0, 2, 0, 0, 0, 0},
	{0, 0, 0, 5, 0, 7, 0, 0, 0},
	{0, 0, 4, 0, 0, 0, 1, 0, 0},
	{0, 9, 0, 0, 0, 0, 0, 0, 0},
	{5, 0, 0, 0, 0, 0, 0, 7, 3},
	{0, 0, 2, 0, 1, 0, 0, 0, 0},
	{0, 0, 0, 0, 4, 0, 0, 0, 9},
}