Implement N Queens Solution Dart

[rrbharath]

Pull Request Template

Description

This PR adds a solution for 51. N-Queens

Problem Description:

The n-queens puzzle is the problem of placing n queens on an n x n chessboard such that no two queens attack each other.

Given an integer n, return all distinct solutions to the n-queens puzzle. You may return the answer in any order.

Each solution contains a distinct board configuration of the n-queens' placement, where 'Q' and '.' both indicate a queen and an empty space, respectively.

Approach
Given its a N x N board we cant bruteforce all possible solutions since that may give us TLE. Instead what we can do is backtrack. We place a queen on each row and if it is safe, we continue otherwise we remove and move onto the next possible correct configuration

Dependencies:
Dart

Complexity
Time Complexity: O(N!)
Space Complexity: O(N)

Difficulty: Hard
Tags: Backtracking, Array

Put check marks:

Have you made changes in README file ?

• Added problem & solution under correct topic.
• Specified Space & Time complexity.
• Specified difficulty level, tag & Note(if any).

How Has This Been Tested?

This solution has been tested by using the following scenarios:

• Test A
  n = 4
  Output: [[".Q..","...Q","Q...","..Q."],["..Q.","Q...","...Q",".Q.."]]
• Test B
  n = 1
  Output: [["Q"]]

Make sure all below guidelines are followed else PR will get Reject:

• My code follows the style guidelines of this project
• I have performed a self-review of my own code
• I have commented my code so that it is easy to understand
• I have made corresponding changes to the documentation
• My changes generate no new warnings
• Any dependent changes have been merged and published in downstream modules