Merge pull request #683 from harshita9621/master

N-Queen Problem using C++

Author: smv1999

Backtracking/N-Queen Problem.cpp

@@ -0,0 +1,108 @@
+/* N-Queen Problem
+
+
+You have to place n queens on an nxn chessboard.
+Idea: Try all the possible positions for the queen. isSafe functions check whether
+the current position is safe or not
+
+*/
+
+#include<iostream>
+using namespace std;
+
+	
+bool isSafe(int board[][10], int i, int j, int n){
+	//Check in col
+		
+	for(int row=0;row<i;row++){
+		if(board[row][j] == 1){
+			return false;
+		}
+	}
+	//Left diagonal
+	int x=i;
+	int y=j;
+		
+	while(x>=0 && y>=0){
+		if(board[x][y]==1){
+			return false;
+		}
+		x--;
+		y--;
+	}
+	//Right diagonal
+	x=i;
+	y=j;
+		
+	while(x>=0 && y>=0){
+		if(board[x][y]==1){
+			return false;
+		}
+		x--;
+		y++;
+	}
+	//The position is safe
+	return true;
+	
+	
+}
+
+bool nQueen(int board[][10], int i,int n){
+	if(i==n){//base case
+	// Place Queeen in n rows (0..n-1)
+	//print the board
+	for(int i=0;i<n;i++){
+		for(int j=0;j<n;j++){
+			if(board[i][j]==1){
+				cout<<"Q ";
+			}
+			else{
+				cout<<"_ ";
+			}
+		}
+		cout<<endl;
+	}
+		return true;
+	}
+	//Recursive case
+	
+	for(int j=0;j<n;j++){
+		//Check i,j th position is safe to place the queen or not.
+		if(isSafe(board,i,j,n)){
+			//Place the Queen ,i, j in the right position
+			board[i][j]=1;
+			
+			if(nQueen(board,i+1,n)){
+				return true;
+			}
+			//Means i,j is not the right position
+			board[i][j]=0; //backtracking
+		}
+	}
+	//coudln't place the queen in current position.
+	return false;
+}
+		
+	
+int main(){
+	int n;
+	cin>>n;
+	
+	int board[10][10]={0};
+	nQueen(board,0,n);
+	
+	return 0;
+	
+}
+
+/* Input:
+4
+
+Output:
+
+_ Q _ _
+_ _ _ Q
+Q _ _ _
+_ _ Q _
+
+*/