Create N-queen.java

src/main/java/com/thealgorithms/backtracking/N-queen.java

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+//Question - The n-queens puzzle is the problem of placing n queens on an n x n chessboard such that no two queens attack each other. 
+//Given an integer n, return all distinct solutions to the n-queens puzzle. You may return the answer in any order. 
+//Each solution contains a distinct board configuration of the n-queens' placement, where 'Q' and '.' both indicate a queen and an empty space, respectively.
+
+class Solution {
+    public boolean isSafe(int row, int col, char[][] board) {
+        // horizontal
+        for (int j = 0; j < board.length; j++) {
+            if (board[row][j] == 'Q') {
+                return false;
+            }
+        }
+
+        // vertical
+        for (int i = 0; i < board.length; i++) {
+            if (board[i][col] == 'Q') {
+                return false;
+            }
+        }
+
+        // upper left
+        int r = row;
+        for (int c = col; c >= 0 && r >= 0; c--, r--) {
+            if (board[r][c] == 'Q') {
+                return false;
+            }
+        }
+
+        // upper right
+        r = row;
+        for (int c = col; c < board.length && r >= 0; r--, c++) {
+            if (board[r][c] == 'Q') {
+                return false;
+            }
+        }
+
+        // lower left
+        r = row;
+        for (int c = col; c >= 0 && r < board.length; r++, c--) {
+            if (board[r][c] == 'Q') {
+                return false;
+            }
+        }
+        // lower right
+        for (int c = col; c < board.length && r < board.length; c++, r++) {
+            if (board[r][c] == 'Q') {
+                return false;
+            }
+        }
+        return true;
+    }
+
+    public void saveBoard(char[][] board, List<List<String>> allBoards) {
+        String row = "";
+        List<String> newBoard = new ArrayList<>();
+        for (int i = 0; i < board.length; i++) { // loop run on BOARD
+            row = ""; // value of row is equal to EMPTY String;
+            for (int j = 0; j < board[0].length; j++) {
+                if (board[i][j] == 'Q')
+                    row += 'Q';
+                else
+                    row += '.';
+            }
+            newBoard.add(row);
+        }
+        allBoards.add(newBoard);
+    }
+
+    public void helper(char[][] board, List<List<String>> allBoards, int col) {
+        if (col == board.length) {
+            saveBoard(board, allBoards);
+            return;
+        }
+        for (int row = 0; row < board.length; row++) {
+            if (isSafe(row, col, board)) {
+                board[row][col] = 'Q';
+                helper(board, allBoards, col + 1);
+                board[row][col] = '.';
+            }
+        }
+    }
+
+    public List<List<String>> solveNQueens(int n) {
+        List<List<String>> allBoards = new ArrayList<>();
+        char[][] board = new char[n][n];
+
+        helper(board, allBoards, 0);
+        return allBoards;
+    }
+}