feat: Implement N-Queens problem solution using backtracking

n_queens.py

@@ -0,0 +1,46 @@
+def is_safe(board, row, col, N):
+    # Check if there's a queen in the same column
+    for i in range(row):
+        if board[i][col] == 1:
+            return False
+
+    # Check upper-left diagonal
+    for i, j in zip(range(row, -1, -1), range(col, -1, -1)):
+        if board[i][j] == 1:
+            return False
+
+    # Check upper-right diagonal
+    for i, j in zip(range(row, -1, -1), range(col, N)):
+        if board[i][j] == 1:
+            return False
+
+    return True
+
+def solve_n_queens(N):
+    board = [[0 for _ in range(N)] for _ in range(N)]
+    if solve_util(board, 0, N) is False:
+        print("No solution exists")
+    else:
+        print_solution(board)
+
+def solve_util(board, row, N):
+    if row == N:
+        return True
+
+    for col in range(N):
+        if is_safe(board, row, col, N):
+            board[row][col] = 1
+
+            if solve_util(board, row + 1, N):
+                return True
+
+            board[row][col] = 0  # Backtrack
+
+    return False
+
+def print_solution(board):
+    for row in board:
+        print(" ".join(["Q" if cell == 1 else "." for cell in row]))
+
+N = 8  # Change N to solve for different board sizes
+solve_n_queens(N)