51. N 皇后
为保证权益，题目请参考 51. N 皇后(From LeetCode).
解决方案1
CPP
C++
#include <iostream>
#include <string>
#include <algorithm>
#include <vector>
using namespace std;
// class Solution
// {
// public:
// char chars[10][10];
// bool could_use[10][10];
// int end;
// vector<vector<string>> res;
// vector<vector<string>> solveNQueens(int n)
// {
// this->end = n;
// for (int i = 0; i < n; ++i)
// {
// fill(chars[i], chars[i] + n, '.');
// fill(could_use[i], could_use[i] + n, true);
// }
// dfs(0);
// return res;
// }
// void dfs(int dim)
// {
// if (dim == this->end)
// {
// vector<string> tmp;
// for (int i = 0; i < this->end; ++i)
// {
// string tmp2 = "";
// for (int j = 0; j < this->end; ++j)
// {
// tmp2 = tmp2 + this->chars[i][j];
// }
// tmp.push_back(tmp2);
// }
// this->res.push_back(tmp);
// }
// else
// {
// for (int i = 0; i < this->end; ++i)
// {
// if (this->could_use[dim][i])
// {
// this->could_use[dim][i] = false;
// this->chars[dim][i] = 'Q';
// for (int j = dim + 1; j < this->end; ++j)
// {
// this->could_use[j][i] = false;
// if ((i - (j - dim) >= 0))
// {
// this->could_use[j][i - (j - dim)] = false;
// }
// if ((i + (j - dim) < this->end))
// {
// this->could_use[j][i + (j - dim)] = false;
// }
// }
// dfs(dim + 1);
// this->could_use[dim][i] = true;
// this->chars[dim][i] = '.';
// for (int j = dim + 1; j < this->end; ++j)
// {
// this->could_use[j][i] = true;
// if ((i - (j - dim) >= 0))
// {
// this->could_use[j][i - (j - dim)] = true;
// }
// if ((i + (j - dim) < this->end))
// {
// this->could_use[j][i + (j - dim)] = true;
// }
// }
// }
// }
// }
// }
// };
class Solution
{
public:
vector<vector<char>> chars;
vector<vector<char>> could_use;
int end;
vector<vector<string>> res;
vector<vector<string>> solveNQueens(int n)
{
this->end = n;
for (int i = 0; i < n; ++i)
{
vector<char> chars2;
vector<char> could_use2;
for (int j = 0; j < n; ++j)
{
chars2.push_back('.');
could_use2.push_back(true);
}
chars.push_back(chars2);
could_use.push_back(could_use2);
}
dfs(0);
return res;
}
void dfs(int dim)
{
if (dim == this->end)
{
vector<string> tmp;
for (int i = 0; i < this->end; ++i)
{
string tmp2 = "";
for (int j = 0; j < this->end; ++j)
{
tmp2 = tmp2 + this->chars[i][j];
}
tmp.push_back(tmp2);
}
this->res.push_back(tmp);
}
else
{
for (int i = 0; i < this->end; ++i)
{
if (this->could_use[dim][i])
{
this->could_use[dim][i] = false;
this->chars[dim][i] = 'Q';
for (int j = dim + 1; j < this->end; ++j)
{
this->could_use[j][i] = false;
if ((i - (j - dim) >= 0))
{
this->could_use[j][i - (j - dim)] = false;
}
if ((i + (j - dim) < this->end))
{
this->could_use[j][i + (j - dim)] = false;
}
}
dfs(dim + 1);
this->could_use[dim][i] = true;
this->chars[dim][i] = '.';
for (int j = dim + 1; j < this->end; ++j)
{
this->could_use[j][i] = true;
if ((i - (j - dim) >= 0))
{
this->could_use[j][i - (j - dim)] = true;
}
if ((i + (j - dim) < this->end))
{
this->could_use[j][i + (j - dim)] = true;
}
}
}
}
}
}
};
int main()
{
Solution so;
so.solveNQueens(4);
return 0;
}1
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Python
python
from typing import List
class Solution:
def solveNQueens(self, n: int) -> List[List[str]]:
self.n = n
self.cols = set()
self.diag = set()
self.bdiag = set()
self.queens = [-1] * n
self.ans: List[List[str]] = []
self.dfs(0)
return self.ans
def dfs(self, row_idx: int):
if row_idx == self.n:
ans = []
tmp = ["."] * self.n
for q in self.queens:
tmp[q] = "Q"
ans.append("".join(tmp))
tmp[q] = "."
self.ans.append(ans)
else:
for col_idx in range(self.n):
if col_idx in self.cols:
continue
diag_idx = row_idx - col_idx + (self.n - 1)
if diag_idx in self.diag:
continue
bdiag_idx = row_idx + col_idx
if bdiag_idx in self.bdiag:
continue
self.cols.add(col_idx)
self.diag.add(diag_idx)
self.bdiag.add(bdiag_idx)
self.queens[row_idx] = col_idx
self.dfs(row_idx + 1)
self.cols.remove(col_idx)
self.diag.remove(diag_idx)
self.bdiag.remove(bdiag_idx)
self.queens[row_idx] = -11
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