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.."]
]
Solution: 1. Recursion.
2. Recursion + bit version. (fast)
The idea is from http://www.matrix67.com/blog/archives/266 (in chinese).
3. Iteration.
1 class Solution { 2 public: 3 int totalNQueens(int n) { 4 int res = 0; 5 totalNQueensRe(n, 0, 0, 0, res); 6 return res; 7 } 8 9 void totalNQueensRe(int n, int row, int ld, int rd, int &total) 10 { 11 if(row == (1 << n) - 1) { 12 total++; 13 return; 14 } 15 16 int valid = ~(row | ld | rd); 17 for(int i = n - 1; i >= 0; --i) { 18 int pos = 1 << i; 19 if (valid & pos) 20 totalNQueensRe(n, row | pos, (ld | pos) << 1, (rd | pos) >> 1, total); 21 } 22 } 23 };