From 939cf083ef8c6bd0095a2f7c5ae20d02d381f6fa Mon Sep 17 00:00:00 2001
From: Akshad Kolhatkar <52818443+AkshadK7@users.noreply.github.com>
Date: Sun, 31 Oct 2021 02:57:33 +0530
Subject: [PATCH] Added the implementation of N_Queens_Algorithm

An Optimized Backtracking Solution
---
 Algorithms/N_Queens_Algorithm | 92 +++++++++++++++++++++++++++++++++++
 1 file changed, 92 insertions(+)
 create mode 100644 Algorithms/N_Queens_Algorithm

diff --git a/Algorithms/N_Queens_Algorithm b/Algorithms/N_Queens_Algorithm
new file mode 100644
index 0000000..aa09ab3
--- /dev/null
+++ b/Algorithms/N_Queens_Algorithm
@@ -0,0 +1,92 @@
+# Python3 program to solve N Queen
+# Problem using backtracking
+global N
+N = 4
+
+def printSolution(board):
+	for i in range(N):
+		for j in range(N):
+			print (board[i][j], end = " ")
+		print()
+
+# A utility function to check if a queen can
+# be placed on board[row][col]. Note that this
+# function is called when "col" queens are
+# already placed in columns from 0 to col -1.
+# So we need to check only left side for
+# attacking queens
+def isSafe(board, row, col):
+
+	# Check this row on left side
+	for i in range(col):
+		if board[row][i] == 1:
+			return False
+
+	# Check upper diagonal on left side
+	for i, j in zip(range(row, -1, -1),
+					range(col, -1, -1)):
+		if board[i][j] == 1:
+			return False
+
+	# Check lower diagonal on left side
+	for i, j in zip(range(row, N, 1),
+					range(col, -1, -1)):
+		if board[i][j] == 1:
+			return False
+
+	return True
+
+def solveNQUtil(board, col):
+	
+	# base case: If all queens are placed
+	# then return true
+	if col >= N:
+		return True
+
+	# Consider this column and try placing
+	# this queen in all rows one by one
+	for i in range(N):
+
+		if isSafe(board, i, col):
+			
+			# Place this queen in board[i][col]
+			board[i][col] = 1
+
+			# recur to place rest of the queens
+			if solveNQUtil(board, col + 1) == True:
+				return True
+
+			# If placing queen in board[i][col
+			# doesn't lead to a solution, then
+			# queen from board[i][col]
+			board[i][col] = 0
+
+	# if the queen can not be placed in any row in
+	# this colum col then return false
+	return False
+
+# This function solves the N Queen problem using
+# Backtracking. It mainly uses solveNQUtil() to
+# solve the problem. It returns false if queens
+# cannot be placed, otherwise return true and
+# placement of queens in the form of 1s.
+# note that there may be more than one
+# solutions, this function prints one of the
+# feasible solutions.
+def solveNQ():
+	board = [ [0, 0, 0, 0],
+			[0, 0, 0, 0],
+			[0, 0, 0, 0],
+			[0, 0, 0, 0] ]
+
+	if solveNQUtil(board, 0) == False:
+		print ("Solution does not exist")
+		return False
+
+	printSolution(board)
+	return True
+
+# Driver Code
+solveNQ()
+
+# This code is contributed by Divyanshu Mehta