Create N Queens.cpp

N Queens.cpp

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+#include <bits/stdc++.h>
+using namespace std;
+
+// A utility function to print solution
+void printSolution(vector<vector<int>>& board) {
+    int n = board.size();
+    for (int i = 0; i < n; i++) {
+        for (int j = 0; j < n; j++)
+            if(board[i][j])
+                cout << "Q ";
+            else
+                cout << ". ";
+        cout << "\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(vector<vector<int>>& board, 
+                    int row, int col) {
+    int n = board.size();
+    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(vector<vector<int>>& board, int col) {
+    int n = board.size();
+
+    // 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 n) {
+    vector<vector<int>> board(n, vector<int>(n, 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() {
+    int n = 4;
+    solveNQ(n);
+    return 0;
+}