78 lines
2.8 KiB
Java
78 lines
2.8 KiB
Java
/**
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* File: n_queens.java
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* Created Time: 2023-05-04
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* Author: krahets (krahets@163.com)
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*/
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package chapter_backtracking;
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import java.util.*;
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public class n_queens {
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/* 回溯演算法：n 皇后 */
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public static void backtrack(int row, int n, List<List<String>> state, List<List<List<String>>> res,
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boolean[] cols, boolean[] diags1, boolean[] diags2) {
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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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List<List<String>> copyState = new ArrayList<>();
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for (List<String> sRow : state) {
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copyState.add(new ArrayList<>(sRow));
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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 (int 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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int diag1 = row - col + n - 1;
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int 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.get(row).set(col, "Q");
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cols[col] = diags1[diag1] = diags2[diag2] = 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.get(row).set(col, "#");
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cols[col] = diags1[diag1] = diags2[diag2] = 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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public static List<List<List<String>>> nQueens(int n) {
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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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List<List<String>> state = new ArrayList<>();
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for (int i = 0; i < n; i++) {
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List<String> row = new ArrayList<>();
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for (int j = 0; j < n; j++) {
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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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boolean[] cols = new boolean[n]; // 記錄列是否有皇后
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boolean[] diags1 = new boolean[2 * n - 1]; // 記錄主對角線上是否有皇后
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boolean[] diags2 = new boolean[2 * n - 1]; // 記錄次對角線上是否有皇后
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List<List<List<String>>> res = new ArrayList<>();
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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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public static void main(String[] args) {
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int n = 4;
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List<List<List<String>>> res = nQueens(n);
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System.out.println("輸入棋盤長寬為 " + n);
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System.out.println("皇后放置方案共有 " + res.size() + " 種");
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for (List<List<String>> state : res) {
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System.out.println("--------------------");
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for (List<String> row : state) {
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System.out.println(row);
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}
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}
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}
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}
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