adding ch12-8 eight queens problem for cpp"

chapter-8-recursion-and-Dynamic-Programming/8-12-Eight-Queens.cpp

@@ -0,0 +1,81 @@
+#include <vector>
+#include <iostream>
+#include <cmath>
+
+using namespace std;
+
+int GRID_SIZE = 8;
+
+bool checkValid(vector<int> columns, int row1, int col1) {
+
+	for (int row2 = 0; row2 < row1; row2++) {
+		int col2 = columns[row2];
+
+		// check if they are in the same column
+		// we don't need to check rows since always row2 < row1
+		if (col1 == col2) {
+			return false;
+		}
+
+		// check if they are in the same diaganol
+		if (abs(col2 - col1) == abs(row1 - row2)) {
+			return false;
+		}
+	}
+
+	return true;
+}
+
+void placeQueens(int row, vector<int> &columns, vector<vector<int> > &results) {
+	if (row == GRID_SIZE) {
+		results.push_back(columns);
+	}
+	else {
+		for (int col = 0; col < GRID_SIZE; col++) {
+			if (checkValid(columns, row, col)) {
+				columns[row] = col;
+				placeQueens(row + 1, columns, results);
+			}
+		}
+
+	}
+}
+
+void drawLine() {
+	for (int i = 0; i < GRID_SIZE * 2 + 1; i++)
+		cout << '-';
+	cout << endl;
+}
+
+void printBoard(vector<int> columns) {
+	drawLine();
+	for (int i = 0; i < GRID_SIZE; i++) {
+		cout << "|" ;
+		for (int j = 0; j < GRID_SIZE; j++) {
+			if (columns[i] == j) {
+				cout << "Q|" ;
+			}
+			else {
+				cout << " |";
+			}
+		}
+		cout << endl;
+		drawLine();
+	}
+	cout << endl;
+}
+
+void printBoards(vector<vector<int >> columns) {
+	int numSolutions = columns.size();
+	for (int i = 0; i < numSolutions; i++) {
+		printBoard(columns[i]);
+	}
+}
+
+int main() {
+	vector<int> columns(GRID_SIZE, -1);
+	vector<vector<int> > results;
+	placeQueens(0, columns, results);
+	printBoards(results);
+	return 0;
+}