add: NQueens

Author: Jer3myYu

java/Backtracking/NQueens.java

@@ -0,0 +1,41 @@
+import java.util.HashSet;
+import java.util.Set;
+
+public class NQueens {
+    int res = 0;
+
+    public int nQueens(int n) {
+        dfs(0, new HashSet<>(), new HashSet<>(), new HashSet<>(), n);
+        return res;
+    }
+
+    private void dfs(int r, Set<Integer> diagonalsSet, Set<Integer> antiDiagonalsSet, Set<Integer> colsSet, int n) {
+        // Termination condition: If we have reached the end of the rows,
+        // we've placed all 'n' queens.
+        if (r == n) {
+            res++;
+            return;
+        }
+        for (int c = 0; c < n; c++) {
+            int currDiagonal = r - c;
+            int currAntiDiagonal = r + c;
+            // If there are queens on the current column, diagonal or
+            // anti-diagonal, skip this square.
+            if (colsSet.contains(c) || diagonalsSet.contains(currDiagonal) || antiDiagonalsSet.contains(currAntiDiagonal)) {
+                continue;
+            }
+            // Place the queen by marking the current column, diagonal, and
+            // anti−diagonal as occupied.
+            colsSet.add(c);
+            diagonalsSet.add(currDiagonal);
+            antiDiagonalsSet.add(currAntiDiagonal);
+            // Recursively move to the next row to continue placing queens.
+            dfs(r + 1, diagonalsSet, antiDiagonalsSet, colsSet, n);
+            // Backtrack by removing the current column, diagonal, and
+            // anti−diagonal from the hash sets.
+            colsSet.remove(c);
+            diagonalsSet.remove(currDiagonal);
+            antiDiagonalsSet.remove(currAntiDiagonal);
+        }
+    }
+}