DP problem: Queens on Chessboard

[Priyank-Gaur]

Your task is to place eight queens on a chessboard so that no two queens are attacking each other. As an additional challenge, each square is either free (
.
.) or reserved (
∗
∗), and you can only place queens on the free squares. However, the reserved squares do not prevent queens from attacking each other.

How many possible ways are there to place the queens?

[github-actions]

💎 Code Quality Check Results

❌ Missing Complexity Analysis

These files don't include time/space complexity:

• Python/dynamic_programming/Queens_on_Chessboard.py

Required: Add comments explaining time and space complexity (e.g., Time: O(n log n), Space: O(n))

❌ Missing Algorithm Description

These files don't explain what the algorithm does:

• Python/dynamic_programming/Queens_on_Chessboard.py

Required: Add a description explaining the algorithm, its purpose, and how it works

⚠️ Insufficient Comments

These files have very few comments:

• Python/dynamic_programming/Queens_on_Chessboard.py

Recommended: Add inline comments explaining the logic and key steps

📚 Quality Standards

To maintain high quality, every contribution should include:

1. ✍️ Algorithm Description

   • Explain what the algorithm does
   • Describe the approach and methodology
   • Include use cases or applications

2. 📊 Complexity Analysis

   • Time complexity (e.g., O(n log n))
   • Space complexity (e.g., O(n))
   • Brief explanation of why

3. 💬 Meaningful Comments

   • Explain complex logic
   • Document function parameters
   • Add inline comments for clarity

4. ✅ Test Cases/Examples

   • Demonstrate the code works
   • Show different input scenarios
   • Include edge cases

💡 Example Template

"""
Binary Search Algorithm

Description: Searches for a target value in a sorted array using divide-and-conquer

Time Complexity: O(log n) - halves search space each iteration
Space Complexity: O(1) - only uses constant extra space
"""

def binary_search(arr, target):
    # Initialize pointers
    left, right = 0, len(arr) - 1

    while left <= right:
        mid = (left + right) // 2

        # Check if target found
        if arr[mid] == target:
            return mid
        # Search right half
        elif arr[mid] < target:
            left = mid + 1
        # Search left half
        else:
            right = mid - 1

    return -1  # Not found

# Test cases
if __name__ == "__main__":
    test_arr = [1, 3, 5, 7, 9]
    print(binary_search(test_arr, 5))  # Output: 2
    print(binary_search(test_arr, 6))  # Output: -1

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2. Add the missing documentation
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[github-actions]

🎉 Welcome to Hacktoberfest 2025, @Priyank-Gaur! 🎃

Thank you for your first contribution to our DSA repository! Here's what happens next:

🔍 Automatic Checks

• ✅ Code Validation: Passed
• 🧪 Compilation Tests: Passed

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• Add comments explaining your algorithm
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Welcome to the community! 🚀

[github-actions]

🤖 Automated PR Status

🔍 Code Validation

✅ Passed - File naming and structure look good!

🧪 Compilation Tests

✅ Passed - All code compiles successfully!

📋 Overall Status

🎉 Ready for Review - Your PR has passed all automated checks!
👥 Maintainers have been notified for review.

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