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