0051. N-Queens

Author: coderbean

markdown/0051. N-Queens.md

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+### [51\. N-Queens](https://leetcode.com/problems/n-queens/)
+
+Difficulty: **Hard**
+
+
+The _n_-queens puzzle is the problem of placing _n_ queens on an _n_×_n_ chessboard such that no two queens attack each other.
+
+![](https://assets.leetcode.com/uploads/2018/10/12/8-queens.png)
+
+Given an integer _n_, return all distinct solutions to the _n_-queens puzzle.
+
+Each solution contains a distinct board configuration of the _n_-queens' placement, where `'Q'` and `'.'` both indicate a queen and an empty space respectively.
+
+**Example:**
+
+```
+Input: 4
+Output: [
+ [".Q..",  // Solution 1
+  "...Q",
+  "Q...",
+  "..Q."],
+
+ ["..Q.",  // Solution 2
+  "Q...",
+  "...Q",
+  ".Q.."]
+]
+Explanation: There exist two distinct solutions to the 4-queens puzzle as shown above.
+```
+
+
+#### Solution
+
+Language: **Java**
+
+```java
+class Solution {
+    public List<List<String>> solveNQueens(int n) {
+        List<List<String>> result = new ArrayList<>();
+        if (n <= 0) {
+            return result;
+        }
+        LinkedList<Integer> column = new LinkedList<>();
+        LinkedList<Integer> pie = new LinkedList<>();
+        LinkedList<Integer> na = new LinkedList<>();
+        this.DFS(column, pie, na,
+                0, n, result, new ArrayList<>());
+        return result;
+    }
+​
+    private void DFS(LinkedList<Integer> column, LinkedList<Integer> pie, LinkedList<Integer> na,
+                     int row, int n, List<List<String>> result, List<String> currStat) {
+        if (row >= n) {
+            result.add(currStat);
+            return;
+        }
+        for (int i = 0; i < n; i++) {
+            if (column.contains(i) || pie.contains(i + row) || na.contains(row - i)) {
+                continue;
+            }
+            // 记录皇后可以攻击的点
+            column.add(i);
+            pie.add(i + row);
+            na.add(row - i);
+​
+            StringBuilder stringBuilder = new StringBuilder();
+            for (int j = 0; j < n; j++) {
+                if (j == i) {
+                    stringBuilder.append("Q");
+                } else {
+                    stringBuilder.append(".");
+                }
+            }
+            this.DFS(column, pie, na, row + 1, n, result, new ArrayList<String>(currStat) {{
+                add(stringBuilder.toString());
+            }});
+            // 移除，便于下一次回溯
+            column.pollLast();
+            pie.pollLast();
+            na.pollLast();
+        }
+    }
+}
+```
+![pic](https://gitee.com/jacobchang/PicBed/raw/master/2019-07-23-f66Gm8.png)

src/main/java/leetcode/_51_/Main.java

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+package leetcode._51_;
+
+import leetcode.common.Printer;
+
+import java.util.List;
+
+/**
+ * Created by zhangbo54 on 2019-03-04.
+ */
+public class Main {
+    public static void main(String[] args) {
+        Solution solution = new Solution();
+        List<List<String>> lists = solution.solveNQueens(1);
+        System.out.println(lists);
+    }
+}
+

src/main/java/leetcode/_51_/Solution.java

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+package leetcode._51_;
+
+import java.util.ArrayList;
+import java.util.LinkedList;
+import java.util.List;
+
+class Solution {
+    public List<List<String>> solveNQueens(int n) {
+        List<List<String>> result = new ArrayList<>();
+        if (n <= 0) {
+            return result;
+        }
+        LinkedList<Integer> column = new LinkedList<>();
+        LinkedList<Integer> pie = new LinkedList<>();
+        LinkedList<Integer> na = new LinkedList<>();
+        this.DFS(column, pie, na,
+                0, n, result, new ArrayList<>());
+        return result;
+    }
+
+    private void DFS(LinkedList<Integer> column, LinkedList<Integer> pie, LinkedList<Integer> na,
+                     int row, int n, List<List<String>> result, List<String> currStat) {
+        if (row >= n) {
+            result.add(currStat);
+            return;
+        }
+        for (int i = 0; i < n; i++) {
+            if (column.contains(i) || pie.contains(i + row) || na.contains(row - i)) {
+                continue;
+            }
+            // 记录皇后可以攻击的点
+            column.add(i);
+            pie.add(i + row);
+            na.add(row - i);
+
+            StringBuilder stringBuilder = new StringBuilder();
+            for (int j = 0; j < n; j++) {
+                if (j == i) {
+                    stringBuilder.append("Q");
+                } else {
+                    stringBuilder.append(".");
+                }
+            }
+            this.DFS(column, pie, na, row + 1, n, result, new ArrayList<String>(currStat) {{
+                add(stringBuilder.toString());
+            }});
+            // 移除，便于下一次回溯
+            column.pollLast();
+            pie.pollLast();
+            na.pollLast();
+            // currStat.remove(stringBuilder.toString());
+        }
+    }
+}

src/main/java/leetcode/_51_/solution.md

@@ -0,0 +1,86 @@
+### [51\. N-Queens](https://leetcode.com/problems/n-queens/)
+
+Difficulty: **Hard**
+
+
+The _n_-queens puzzle is the problem of placing _n_ queens on an _n_×_n_ chessboard such that no two queens attack each other.
+
+![](https://assets.leetcode.com/uploads/2018/10/12/8-queens.png)
+
+Given an integer _n_, return all distinct solutions to the _n_-queens puzzle.
+
+Each solution contains a distinct board configuration of the _n_-queens' placement, where `'Q'` and `'.'` both indicate a queen and an empty space respectively.
+
+**Example:**
+
+```
+Input: 4
+Output: [
+ [".Q..",  // Solution 1
+  "...Q",
+  "Q...",
+  "..Q."],
+
+ ["..Q.",  // Solution 2
+  "Q...",
+  "...Q",
+  ".Q.."]
+]
+Explanation: There exist two distinct solutions to the 4-queens puzzle as shown above.
+```
+
+
+#### Solution
+
+Language: **Java**
+
+```java
+class Solution {
+    public List<List<String>> solveNQueens(int n) {
+        List<List<String>> result = new ArrayList<>();
+        if (n <= 0) {
+            return result;
+        }
+        LinkedList<Integer> column = new LinkedList<>();
+        LinkedList<Integer> pie = new LinkedList<>();
+        LinkedList<Integer> na = new LinkedList<>();
+        this.DFS(column, pie, na,
+                0, n, result, new ArrayList<>());
+        return result;
+    }
+​
+    private void DFS(LinkedList<Integer> column, LinkedList<Integer> pie, LinkedList<Integer> na,
+                     int row, int n, List<List<String>> result, List<String> currStat) {
+        if (row >= n) {
+            result.add(currStat);
+            return;
+        }
+        for (int i = 0; i < n; i++) {
+            if (column.contains(i) || pie.contains(i + row) || na.contains(row - i)) {
+                continue;
+            }
+            // 记录皇后可以攻击的点
+            column.add(i);
+            pie.add(i + row);
+            na.add(row - i);
+​
+            StringBuilder stringBuilder = new StringBuilder();
+            for (int j = 0; j < n; j++) {
+                if (j == i) {
+                    stringBuilder.append("Q");
+                } else {
+                    stringBuilder.append(".");
+                }
+            }
+            this.DFS(column, pie, na, row + 1, n, result, new ArrayList<String>(currStat) {{
+                add(stringBuilder.toString());
+            }});
+            // 移除，便于下一次回溯
+            column.pollLast();
+            pie.pollLast();
+            na.pollLast();
+        }
+    }
+}
+```
+![pic](https://gitee.com/jacobchang/PicBed/raw/master/2019-07-23-f66Gm8.png)