85 lines
2.6 KiB
Kotlin
85 lines
2.6 KiB
Kotlin
/**
|
|
* File: n_queens.kt
|
|
* Created Time: 2024-01-25
|
|
* Author: curtishd (1023632660@qq.com)
|
|
*/
|
|
|
|
package chapter_backtracking.n_queens
|
|
|
|
/* Backtracking algorithm: n queens */
|
|
fun backtrack(
|
|
row: Int,
|
|
n: Int,
|
|
state: MutableList<MutableList<String>>,
|
|
res: MutableList<MutableList<MutableList<String>>?>,
|
|
cols: BooleanArray,
|
|
diags1: BooleanArray,
|
|
diags2: BooleanArray
|
|
) {
|
|
// When all rows are placed, record the solution
|
|
if (row == n) {
|
|
val copyState = mutableListOf<MutableList<String>>()
|
|
for (sRow in state) {
|
|
copyState.add(sRow.toMutableList())
|
|
}
|
|
res.add(copyState)
|
|
return
|
|
}
|
|
// Traverse all columns
|
|
for (col in 0..<n) {
|
|
// Calculate the main and minor diagonals corresponding to the cell
|
|
val diag1 = row - col + n - 1
|
|
val diag2 = row + col
|
|
// Pruning: do not allow queens on the column, main diagonal, or minor diagonal of the cell
|
|
if (!cols[col] && !diags1[diag1] && !diags2[diag2]) {
|
|
// Attempt: place the queen in the cell
|
|
state[row][col] = "Q"
|
|
diags2[diag2] = true
|
|
diags1[diag1] = diags2[diag2]
|
|
cols[col] = diags1[diag1]
|
|
// Place the next row
|
|
backtrack(row + 1, n, state, res, cols, diags1, diags2)
|
|
// Retract: restore the cell to an empty spot
|
|
state[row][col] = "#"
|
|
diags2[diag2] = false
|
|
diags1[diag1] = diags2[diag2]
|
|
cols[col] = diags1[diag1]
|
|
}
|
|
}
|
|
}
|
|
|
|
/* Solve n queens */
|
|
fun nQueens(n: Int): MutableList<MutableList<MutableList<String>>?> {
|
|
// Initialize an n*n size chessboard, where 'Q' represents the queen and '#' represents an empty spot
|
|
val state = mutableListOf<MutableList<String>>()
|
|
for (i in 0..<n) {
|
|
val row = mutableListOf<String>()
|
|
for (j in 0..<n) {
|
|
row.add("#")
|
|
}
|
|
state.add(row)
|
|
}
|
|
val cols = BooleanArray(n) // Record columns with queens
|
|
val diags1 = BooleanArray(2 * n - 1) // Record main diagonals with queens
|
|
val diags2 = BooleanArray(2 * n - 1) // Record minor diagonals with queens
|
|
val res = mutableListOf<MutableList<MutableList<String>>?>()
|
|
|
|
backtrack(0, n, state, res, cols, diags1, diags2)
|
|
|
|
return res
|
|
}
|
|
|
|
/* Driver Code */
|
|
fun main() {
|
|
val n = 4
|
|
val res = nQueens(n)
|
|
|
|
println("Input chessboard dimensions as $n")
|
|
println("Total of ${res.size} queen placement solutions")
|
|
for (state in res) {
|
|
println("--------------------")
|
|
for (row in state!!) {
|
|
println(row)
|
|
}
|
|
}
|
|
} |