From 07bce9d905980b94d240d159b7eeff3f1f66c014 Mon Sep 17 00:00:00 2001
From: vivekgogi <114925625+vivekgogi@users.noreply.github.com>
Date: Wed, 25 Oct 2023 20:29:23 +0530
Subject: [PATCH] Create N Queen

---
 N Queen | 114 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 114 insertions(+)
 create mode 100644 N Queen

diff --git a/N Queen b/N Queen
new file mode 100644
index 0000000..5430c69
--- /dev/null
+++ b/N Queen	
@@ -0,0 +1,114 @@
+// C++ program to solve N Queen Problem using backtracking
+
+#include <bits/stdc++.h>
+#define N 4
+using namespace std;
+
+// A utility function to print solution
+void printSolution(int board[N][N])
+{
+	for (int i = 0; i < N; i++) {
+		for (int j = 0; j < N; j++)
+		if(board[i][j])
+			cout << "Q ";
+		else cout<<". ";
+		printf("\n");
+	}
+}
+
+// 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
+bool isSafe(int board[N][N], int row, int col)
+{
+	int i, j;
+
+	// Check this row on left side
+	for (i = 0; i < col; i++)
+		if (board[row][i])
+			return false;
+
+	// Check upper diagonal on left side
+	for (i = row, j = col; i >= 0 && j >= 0; i--, j--)
+		if (board[i][j])
+			return false;
+
+	// Check lower diagonal on left side
+	for (i = row, j = col; j >= 0 && i < N; i++, j--)
+		if (board[i][j])
+			return false;
+
+	return true;
+}
+
+// A recursive utility function to solve N
+// Queen problem
+bool solveNQUtil(int board[N][N], int 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 (int i = 0; i < N; i++) {
+		
+		// Check if the queen can be placed on
+		// board[i][col]
+		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))
+				return true;
+
+			// If placing queen in board[i][col]
+			// doesn't lead to a solution, then
+			// remove queen from board[i][col]
+			board[i][col] = 0; // BACKTRACK
+		}
+	}
+
+	// If the queen cannot be placed in any row in
+	// this column 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
+// prints placement of queens in the form of 1s.
+// Please note that there may be more than one
+// solutions, this function prints one of the
+// feasible solutions.
+bool solveNQ()
+{
+	int board[N][N] = { { 0, 0, 0, 0 },
+						{ 0, 0, 0, 0 },
+						{ 0, 0, 0, 0 },
+						{ 0, 0, 0, 0 } };
+
+	if (solveNQUtil(board, 0) == false) {
+		cout << "Solution does not exist";
+		return false;
+	}
+
+	printSolution(board);
+	return true;
+}
+
+// Driver program to test above function
+int main()
+{
+	solveNQ();
+	return 0;
+}
+
+// This code is contributed by Aditya Kumar (adityakumar129)