LeetCode 50 N-Queens

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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.."]]

思路：回溯法，使用ArrayList<Integer> al来存储某个皇后的列，而它在ArrayList的索引就是其行数。

public class Solution {public List<String[]> solveNQueens(int n) {List<String[]> result = new LinkedList<String[]>();search(result, n, new ArrayList<Integer>(), 1);return result;}private boolean isValid(List<Integer> list) {int column = list.get(list.size() - 1);for (int i = 0; i < list.size() - 1; i++) {if (column == list.get(i)|| Math.abs(column - list.get(i)) == Math.abs(list.size() - 1- i)) {return false;}}return true;}private void search(List<String[]> result, int n, List<Integer> list,int col) {if (col > n) {char[] temp = new char[n];Arrays.fill(temp, '.');String[] str = new String[n];for (int i = 0; i < list.size(); i++) {StringBuilder sb = new StringBuilder(String.valueOf(temp));sb.setCharAt(list.get(i), 'Q');str[i] = sb.toString();}result.add(str);} else {for (int j = 0; j < n; j++) {list.add(j);if (isValid(list)) {search(result, n, list, col + 1);}list.remove(list.size() - 1);}}}}

思路2：回溯法，只不过使用了位移操作，更快，剪枝剪得更厉害，详细分析见http://blog.csdn.net/mlweixiao/article/details/40984589

public class Solution {static int upperlim = 1;private void search(int l, int ld, int rd, List<Integer> list,List<String[]> result) {if (l != upperlim) {int pos = upperlim & (~(l | ld | rd));while (pos != 0) {int p = pos & -pos;int temp = p;int index = 0;while (temp != 1) {temp = temp >> 1;index++;}list.add(index);// 从0开始的pos ^= p;search(l | p, (ld | p) << 1, (rd | p) >> 1, list, result);list.remove(list.size() - 1);}} else {char[] temp = new char[list.size()];Arrays.fill(temp, '.');String[] str = new String[list.size()];for (int i = 0; i < list.size(); i++) {StringBuilder sb = new StringBuilder(String.valueOf(temp));sb.setCharAt(list.get(i), 'Q');str[i] = sb.toString();}result.add(str);}}public List<String[]> solveNQueens(int n) {upperlim = (1 << n) - 1;List<String[]> result = new LinkedList<String[]>();search(0, 0, 0, new LinkedList<Integer>(), result);return result;}}

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