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// File: n_queens.go
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// Created Time: 2023-05-09
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// Author: Reanon (793584285@qq.com)
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package chapter_backtracking
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/* 回溯演算法：n 皇后 */
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func backtrack(row, n int, state *[][]string, res *[][][]string, cols, diags1, diags2 *[]bool) {
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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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newState := make([][]string, len(*state))
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for i, _ := range newState {
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newState[i] = make([]string, len((*state)[0]))
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copy(newState[i], (*state)[i])
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}
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*res = append(*res, newState)
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return
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}
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// 走訪所有列
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for col := 0; col < n; col++ {
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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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diag1 := row - col + n - 1
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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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(*cols)[col], (*diags1)[diag1], (*diags2)[diag2] = true, true, true
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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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(*cols)[col], (*diags1)[diag1], (*diags2)[diag2] = false, false, false
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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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func nQueens(n int) [][][]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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state := make([][]string, n)
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for i := 0; i < n; i++ {
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row := make([]string, n)
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for i := 0; i < n; i++ {
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row[i] = "#"
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}
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state[i] = row
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}
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// 記錄列是否有皇后
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cols := make([]bool, n)
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diags1 := make([]bool, 2*n-1)
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diags2 := make([]bool, 2*n-1)
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res := make([][][]string, 0)
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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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