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 the number of distinct solutions to the n-queens puzzle.
Example:
Input: 4
Output: 2
Explanation: There are two distinct solutions to the 4-queens puzzle as shown below.
[
[".Q..", // Solution 1
"...Q",
"Q...",
"..Q."],
["..Q.", // Solution 2
"Q...",
"...Q",
".Q.."]
]
題目鏈接：https://leetcode-cn.com/problems/n-queens-ii/
思路
法一：回溯法
思路和上一道n皇后問題用的一樣。
class Solution {
public:
vector<int> row;
vector<bool> col;
vector<bool> dir1;
vector<bool> dir2;
int res = 0;
int totalNQueens(int n) {
if(n<=0) return 0;
if(n==1) return 1;
row = vector<int>(n);
col = vector<bool>(n, false);
dir1 = vector<bool>(n*2-1, false);
dir2 = vector<bool>(n*2-1, false);
trace(n,0);
return res*2;
}
void trace(int n, int idx){
if(idx==n){
++res;
return;
}
for(int j=0; j<n; ++j){
if(idx==0 && j>=n/2) break;
if(!col[j] && !dir1[j-idx+n-1] && !dir2[idx+j]){
row[idx] = j;
col[j] = true;
dir1[j-idx+n-1] = true;
dir2[idx+j] = true;
trace(n, idx+1);
row[idx] = -1;
col[j] = false;
dir1[j-idx+n-1] = false;
dir2[idx+j] = false;
}
}
}
};
法二：位運算
這個是在沒看懂。。哭了
等我其他題刷上來了再解決這個可惡的位運算。。。
參考：https://leetcode-cn.com/problems/n-queens-ii/solution/nhuang-hou-ii-by-leetcode/