LeetCode 51 N-Queens

转载：递归算法学习系列之八皇后问题

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.."]
]

java解法如下所示：

public class Solution {
public void dfs(List<List<String>> res, List<String> list, Set<Integer> col, Set<Integer> diag1, Set<Integer> diag2, int row, int n){
if(row==n){
res.add(new ArrayList<String>(list));
return;
}
//遍历该行的所有列
for(int i=0;i<n;i++){
if(col.contains(i)||diag1.contains(row+i)||diag2.contains(row-i))
continue;
col.add(i);
diag1.add(row+i);
diag2.add(row-i);
char[] rowChar = new char
;
Arrays.fill(rowChar, '.');
rowChar[i] = 'Q';
String rowString = new String(rowChar);
list.add(rowString);
//继续搜索下一行
dfs(res, list, col, diag1, diag2, row+1, n);
//搜索完成后释放所用资源
list.remove(list.size()-1);
col.remove(i);
diag1.remove(row+i);
diag2.remove(row-i);
}
}
public List<List<String>> solveNQueens(int n) {
List<List<String>> res = new ArrayList<List<String>>();
if(n==0)
return res;
Set<Integer> col = new HashSet<Integer>(); //列集
Set<Integer> diag1 = new HashSet<Integer>(); //正对角线集
Set<Integer> diag2 = new HashSet<Integer>(); //副对角线集
List<String> list = new ArrayList<String>(); //用于存放每一种情况
dfs(res, list, col, diag1, diag2, 0, n);
return res;
}
}