N-Queens

Author: mengli

NQueens.java

@@ -0,0 +1,77 @@
+/**
+ * The n-queens puzzle is the problem of placing n queens on an n×n chessboard such that no two queens attack each other.
+ * 
+ * Given an integer n, return all distinct solutions to the n-queens puzzle.
+ * 
+ * Each solution contains a distinct board configuration of the n-queens' placement, where 'Q' and '.' both indicate a queen and an empty space respectively.
+ * 
+ * For example,
+ * 
+ * There exist two distinct solutions to the 4-queens puzzle:
+ * 
+ * [
+ *  [".Q..",  // Solution 1
+ *   "...Q",
+ *   "Q...",
+ *   "..Q."],
+ *
+ *  ["..Q.",  // Solution 2
+ *   "Q...",
+ *   "...Q",
+ *   ".Q.."]
+ *  ]
+ */
+
+import java.util.ArrayList;
+
+public class NQueens {
+	public ArrayList<String[]> solveNQueens(int n) {
+		ArrayList<String[]> ret = new ArrayList<String[]>();
+		if (n == 0)
+			return ret;
+		StringBuffer line = new StringBuffer();
+		for (int i = 0; i < n; i++) {
+			line.append('.');
+		}
+		StringBuffer[] sol = new StringBuffer[n];
+		for (int i = 0; i < n; i++) {
+			sol[i] = new StringBuffer(line.toString());
+		}
+		boolean[] cols = new boolean[n];
+		int[] row = new int[n];
+		findSolutions(n, 0, ret, sol, row, cols);
+		return ret;
+	}
+
+	private void findSolutions(int n, int start, ArrayList<String[]> ret,
+			StringBuffer[] sol, int[] row, boolean[] cols) {
+		if (start == n) {
+			String[] newSol = new String[n];
+			for (int i = 0; i < n; i++) {
+				newSol[i] = sol[i].toString();
+			}
+			ret.add(newSol);
+		} else {
+			for (int i = 0; i < n; i++) {
+				if (cols[i])
+					continue;
+				boolean ok = true;
+				for (int j = 0; j < start; j++) {
+					if (Math.abs(start - j) == Math.abs(i - row[j])) {
+						ok = false;
+						break;
+					}
+				}
+				if (ok) {
+					cols[i] = true;
+					sol[start].setCharAt(i, 'Q');
+					row[start] = i;
+					findSolutions(n, start + 1, ret, sol, row, cols);
+					row[start] = 0;
+					sol[start].setCharAt(i, '.');
+					cols[i] = false;
+				}
+			}
+		}
+	}
+}