Data Structures and Algorithms: N-Queens II (Count Solutions) 🎯

Welcome to this comprehensive lesson on the N-Queens II problem, a fascinating exercise in computer science that combines the understanding of Data Structures and Algorithms! This lesson is designed to be beginner-friendly, but will also provide enough depth for intermediate learners. Let's dive in!

Understanding the N-Queens II Problem 📝

The N-Queens II problem is a classic challenge in computer science where we aim to place N non-attacking queens on an N x N chessboard. Unlike the N-Queens I problem, our goal here is to find all possible solutions, not just one. 💡 Pro Tip: This problem is a great way to practice recursion and backtracking!

Breaking Down the Problem 📝

Initialize an empty list to store the solutions.
Start a recursive function that takes an N as an argument.
For each row (from 0 to N-1), we will place a queen in a non-attacking position.
If a queen cannot be placed due to attacks, the current placement is not a solution, and we backtrack (move back to the previous row).
If a queen is successfully placed, we store the solution (the current list of positions) and continue the recursion for the remaining rows.
When all rows are filled, we have found a solution, and the function returns.
Once the recursive call for all rows is complete, we have found all solutions, and the function returns the list of solutions.

Implementing the Solution 💡

Let's look at a Python example that solves the N-Queens II problem for an N of 4:

python

def find_n_queens_solutions(n):
    solutions = []

    def backtrack(row):
        if row == n:
            solutions.append(queens)
        else:
            for col in range(n):
                if is_safe(queens, row, col):
                    queens[row] = col
                    backtrack(row + 1)
                    queens[row] = None

    backtrack(0)
    return solutions

def is_safe(queens, row, col):
    for r in range(row):
        if queens[r] == col or abs(queens[r] - col) == abs(r - row):
            return False
    return True

n = 4
queens = [None] * n
solutions = find_n_queens_solutions(n)
print(solutions)

Quiz Time 🎯

That's it for this lesson! With a solid understanding of the N-Queens II problem, you're well on your way to mastering recursion and backtracking, two essential skills for any programmer. Happy coding, and remember: the journey to becoming a skilled developer is all about practice, practice, practice! 💡 Pro Tip: Try solving the N-Queens II problem for different values of N to deepen your understanding!