build

en/docs/chapter_backtracking/n_queens_problem.md

@@ -101,9 +101,46 @@ Please note, in an $n$-dimensional matrix, the range of $row - col$ is $[-n + 1,
 === "C++"
 
     ```cpp title="n_queens.cpp"
-    [class]{}-[func]{backtrack}
+    /* Backtracking algorithm: n queens */
+    void backtrack(int row, int n, vector<vector<string>> &state, vector<vector<vector<string>>> &res, vector<bool> &cols,
+                   vector<bool> &diags1, vector<bool> &diags2) {
+        // When all rows are placed, record the solution
+        if (row == n) {
+            res.push_back(state);
+            return;
+        }
+        // Traverse all columns
+        for (int col = 0; col < n; col++) {
+            // Calculate the main and minor diagonals corresponding to the cell
+            int diag1 = row - col + n - 1;
+            int diag2 = row + col;
+            // Pruning: do not allow queens on the column, main diagonal, or minor diagonal of the cell
+            if (!cols[col] && !diags1[diag1] && !diags2[diag2]) {
+                // Attempt: place the queen in the cell
+                state[row][col] = "Q";
+                cols[col] = diags1[diag1] = diags2[diag2] = true;
+                // Place the next row
+                backtrack(row + 1, n, state, res, cols, diags1, diags2);
+                // Retract: restore the cell to an empty spot
+                state[row][col] = "#";
+                cols[col] = diags1[diag1] = diags2[diag2] = false;
+            }
+        }
+    }
 
-    [class]{}-[func]{nQueens}
+    /* Solve n queens */
+    vector<vector<vector<string>>> nQueens(int n) {
+        // Initialize an n*n size chessboard, where 'Q' represents the queen and '#' represents an empty spot
+        vector<vector<string>> state(n, vector<string>(n, "#"));
+        vector<bool> cols(n, false);           // Record columns with queens
+        vector<bool> diags1(2 * n - 1, false); // Record main diagonals with queens
+        vector<bool> diags2(2 * n - 1, false); // Record minor diagonals with queens
+        vector<vector<vector<string>>> res;
+
+        backtrack(0, n, state, res, cols, diags1, diags2);
+
+        return res;
+    }
     ```
 
 === "Java"