N-Queens

Author: Shikha-code36

Backtracking/51-N-Queens.py

@@ -0,0 +1,52 @@
+'''Leetcode- https://leetcode.com/problems/n-queens/ '''
+'''
+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.
+
+Example 1:
+
+Input: n = 4
+Output: [[".Q..","...Q","Q...","..Q."],["..Q.","Q...","...Q",".Q.."]]
+'''
+
+
+def solveNQueens(n):
+
+    cols = set()
+    pos = set()
+    neg = set()
+
+    res = []
+    board = [["."] * n for i in range(n)]
+
+    def backtrack(r):
+        if r == n:
+            copy = ["".join(row) for row in board]
+            res.append(copy)
+            return
+
+        for c in range(n):
+            if c in cols or (r + c) in pos or (r - c) in neg:
+                continue
+
+            cols.add(c)
+            pos.add(r+c)
+            neg.add(r-c)
+            board[r][c] = "Q"
+
+            backtrack(r+1)
+
+            cols.remove(c)
+            pos.remove(r+c)
+            neg.remove(r-c)
+            board[r][c] = "."
+
+    backtrack(0)
+
+    return res
+
+#T:O(n!)
+#S:O(N^2)

README.md

@@ -20,5 +20,6 @@ Check the notes for the explaination - [Notes](https://stingy-shallot-4ea.notion
     - [x] [Palindrome Partitioning](Backtracking/131-Palindrome-Partitioning.py)
     - [x] [Letter Combinations of a Phone Number](Backtracking/17-Letter-Combinations-of-a-Phone-Number.py)
     - [x] [Generalized Abbreviation](Backtracking/320-Generalized-Abbreviation.py)
+    - [x] [N-Queens](Backtracking/51-N-Queens.py)