add N Queens (51.cpp)

Author: PriyanshVerma

leetcode/cpp/backtracking/51.cpp

@@ -0,0 +1,52 @@
+#define f first
+#define s second
+class Solution {
+private:
+	int n;
+	vector<string> board;
+	vector<vector<string>> res;
+	
+	void solve(int row) {
+		if (row == n) {
+			res.push_back(board);
+			return;
+		}
+
+		for (int col = 0; col < n; ++col)
+		{
+			board[row][col] = 'Q';
+			if (valid(row, col)) {
+				solve(row+1);
+			} 
+			board[row][col] = '.';
+		}
+	}
+
+	bool valid(int ROW, int COL) {
+		vector<pair<int,int>> dirs = 
+                    {{-1,-1}, {-1,0}, {-1,1},
+									   {0, -1}, 		     {0,1},
+									   {1, -1}, {1, 0}, {1,1}};
+		for (auto d: dirs) {
+			int k = 1;
+			int nr = ROW + k*d.f, nc = COL + k*d.s;
+			while (nr < n && nc < n && nr >= 0 && nc >= 0) {
+				if (board[nr][nc] == 'Q')
+					return false;
+				k++;
+				nr = ROW + k*d.f;
+				nc = COL + k*d.s;
+			}
+		}
+
+		return true;
+	}
+
+public:
+	vector<vector<string>> solveNQueens(int n) {
+		this->n = n;
+		this->board = vector<string> (n, string (n, '.'));
+		solve(0);
+		return res;
+	}
+};