52. N-Queens II

[Lakshya182005]

PR Title Format: 52. N-Queens II.cpp

Intuition

Row-by-Row Safe Placement

• The N-Queens problem is fundamentally a constraint satisfaction problem.
• Each queen attacks its column, main diagonal, and anti-diagonal.
• By keeping track of these attacked positions, we can efficiently check if placing a queen is safe.
• Backtracking allows us to explore all possible configurations row by row.
• The key insight is that each queen placement depends only on columns and diagonals already occupied, so we don’t need to check the entire board each time.

Approach

Backtracking with Row-by-Row Placement

Initialization

• Initialize a variable count to 0 to store the number of valid solutions.
• Create three sets (or arrays) to keep track of attacks:
  1. cols – columns where a queen is already placed.
  2. diag – main diagonals under attack (row + col).
  3. anti_diag – anti-diagonals under attack (row - col).

Iteration (Row-by-Row Backtracking)

1. Start from the first row (row = 0).
2. For each column in the current row, check if placing a queen is valid (not in cols, diag, or anti_diag).
3. If valid:
   • Add the column to cols.
   • Add row + col to diag.
   • Add row - col to anti_diag.
   • Recursively place a queen in the next row.
   • After recursion, backtrack by removing the queen from cols, diag, and anti_diag.
4. If row == n, all queens are placed safely. Increment count.

Termination
Return the total count of valid N-Queens solutions.

Code Solution (C++)

class Solution {
public:
    int totalNQueens(int n) {
        int count = 0; 

        unordered_set<int> cols;      
        unordered_set<int> diag;      
        unordered_set<int> anti_diag; 

 
        function<void(int)> bckt = [&](int row) {
            if(row == n){ /
                count++;
                return;
            }

            
            for(int col = 0; col < n; col++){
                if(cols.count(col) || diag.count(row + col) || anti_diag.count(row - col))
                    continue; 

           
                cols.insert(col);
                diag.insert(row + col);
                anti_diag.insert(row - col);

                bckt(row + 1); 

       
                cols.erase(col);
                diag.erase(row + col);
                anti_diag.erase(row - col);
            }
        };

        bckt(0);
        return count; 
    }
};
    

Related Issues

Closes #242

By submitting this PR, I confirm that:

• [ x] This is my original work not totally AI generated
• [x ] I have tested the solution thoroughly on leetcode
• [ x] I have maintained proper PR description format
• [x ] This is a meaningful contribution, not spam

Summary by Sourcery

New Features:

• Implement Solution::totalNQueens to count all valid N-Queens configurations using recursive backtracking and sets for columns, main diagonals, and anti-diagonals attacks.

[sourcery-ai]

Reviewer's Guide

Implement N-Queens II solution using backtracking to explore row-by-row placements and track attacked columns and diagonals, supplemented with detailed approach and complexity comments.

Class diagram for the Solution class in N-Queens II

classDiagram
class Solution {
  +int totalNQueens(int n)
}
Solution : -int count
Solution : -unordered_set<int> cols
Solution : -unordered_set<int> diag
Solution : -unordered_set<int> anti_diag
Solution : -void backtrack(int row)

Loading

File-Level Changes

Change	Details	Files
Implement totalNQueens solution with backtracking	Define and manage cols, diag, anti_diag sets Implement recursive backtracking lambda Add safety checks before placing queens Insert and remove set entries for placement and backtracking Handle base case to increment solution count	52. N-Queens II.cpp
Document approach and complexity analysis	Add detailed approach description before the code Include time and space complexity comments	52. N-Queens II.cpp

Assessment against linked issues

Issue	Objective	Addressed	Explanation
#242	Provide a working C++ solution for LeetCode Problem 52 (N-Queens II) that counts the number of valid N-Queens arrangements using backtracking.	✅
#242	Include an explanation of the approach and intuition for the solution, describing the use of sets to track attacks and the backtracking process.	✅
#242	Ensure the filename follows the convention '[Number]. [Problem Title].cpp' (i.e., '52. N-Queens II.cpp').	✅

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[github-actions]

Thanks for raising the PR, the owner will be review it soon' keep patience, keep contributing>>>!!! make sure you have star ⭐ the repo

[sourcery-ai]

Hey there - I've reviewed your changes and they look great!

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[SjxSubham]

@Lakshya182005 Star the repo as well...⭐

[Lakshya182005]

thank you!
could you please add hacktoberfest accepted to this pull request and merge it.