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/**
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* File: n_queens.kt
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* Created Time: 2024-01-25
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* Author: curtishd (1023632660@qq.com)
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*/
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package chapter_backtracking.n_queens
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/* 回溯演算法：n 皇后 */
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fun backtrack(
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row: Int,
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n: Int,
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state: MutableList<MutableList<String>>,
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res: MutableList<MutableList<MutableList<String>>?>,
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cols: BooleanArray,
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diags1: BooleanArray,
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diags2: BooleanArray
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) {
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// 當放置完所有行時，記錄解
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if (row == n) {
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val copyState = mutableListOf<MutableList<String>>()
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for (sRow in state) {
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copyState.add(sRow.toMutableList())
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}
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res.add(copyState)
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return
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}
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// 走訪所有列
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for (col in 0..<n) {
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// 計算該格子對應的主對角線和次對角線
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val diag1 = row - col + n - 1
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val diag2 = row + col
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// 剪枝：不允許該格子所在列、主對角線、次對角線上存在皇后
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if (!cols[col] && !diags1[diag1] && !diags2[diag2]) {
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// 嘗試：將皇后放置在該格子
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state[row][col] = "Q"
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diags2[diag2] = true
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diags1[diag1] = diags2[diag2]
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cols[col] = diags1[diag1]
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// 放置下一行
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backtrack(row + 1, n, state, res, cols, diags1, diags2)
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// 回退：將該格子恢復為空位
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state[row][col] = "#"
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diags2[diag2] = false
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diags1[diag1] = diags2[diag2]
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cols[col] = diags1[diag1]
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}
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}
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}
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/* 求解 n 皇后 */
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fun nQueens(n: Int): MutableList<MutableList<MutableList<String>>?> {
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// 初始化 n*n 大小的棋盤，其中 'Q' 代表皇后，'#' 代表空位
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val state = mutableListOf<MutableList<String>>()
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for (i in 0..<n) {
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val row = mutableListOf<String>()
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for (j in 0..<n) {
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row.add("#")
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}
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state.add(row)
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}
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val cols = BooleanArray(n) // 記錄列是否有皇后
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val diags1 = BooleanArray(2 * n - 1) // 記錄主對角線上是否有皇后
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val diags2 = BooleanArray(2 * n - 1) // 記錄次對角線上是否有皇后
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val res = mutableListOf<MutableList<MutableList<String>>?>()
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backtrack(0, n, state, res, cols, diags1, diags2)
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return res
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}
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/* Driver Code */
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fun main() {
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val n = 4
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val res = nQueens(n)
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println("輸入棋盤長寬為 $n")
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println("皇后放置方案共有 ${res.size} 種")
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for (state in res) {
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println("--------------------")
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for (row in state!!) {
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println(row)
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}
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}
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} |
