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package solutions
import (
"github.com/01-edu/z01"
)
const size = 8
// board is a chessboard composed of boolean squares, a true square means a queen is on it
// a false square means it is a free square
var board [size][size]bool
// goodDirection check that there is no queen on the segment that starts at (x, y)
// coordinates, points into the direction vector (vx, vy) and ends at the edge of the board
func goodDirection(x, y, vx, vy int) bool {
// x and y are still on board
for 0 <= x && x < size &&
0 <= y && y < size {
if board[x][y] {
// Not a good line : the square is already occupied
return false
}
x = x + vx // Move x in the right direction
y = y + vy // Move y in the right direction
}
// All clear
return true
}
// goodSquare makes all the necessary line checks for the queens movements
func goodSquare(x, y int) bool {
return goodDirection(x, y, +0, -1) &&
goodDirection(x, y, +1, -1) &&
goodDirection(x, y, +1, +0) &&
goodDirection(x, y, +1, +1) &&
goodDirection(x, y, +0, +1) &&
goodDirection(x, y, -1, +1) &&
goodDirection(x, y, -1, +0) &&
goodDirection(x, y, -1, -1)
}
func printQueens() {
x := 0
for x < size {
y := 0
for y < size {
if board[x][y] {
// We have found a queen, let's print her y
z01.PrintRune(rune(y) + '1')
}
y++
}
x++
}
z01.PrintRune('\n')
}
// tryX tries, for a given x (column) to find a y (row) so that the queen on (x, y) is a part
// of the solution to the problem
func tryX(x int) {
y := 0
for y < size {
if goodSquare(x, y) {
// Since the square is good for the queen, let's put one on it:
board[x][y] = true
if x == size-1 {
// x is the biggest possible x, it means that we just placed the last
// queen on the board, so the solution is complete and we can print it
printQueens()
} else {
// let's try to put another queen on the next empty x (column)
tryX(x + 1)
}
// remove the queen of the board, to try other y values
board[x][y] = false
}
y++
}
}
func EightQueens() {
// try the first column
tryX(0)
}