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N-Queens.cpp
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N-Queens.cpp
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/**
* The n-queens puzzle is the problem of placing n queens on
* an n¡Án 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.."]
* ]
*/
class Solution {
vector<string> generate(vector<int> &placement) {
int N = placement.size();
vector<string> ret;
for (int i = 0; i < N; i++) {
string s;
for (int j = 0; j < N; j++) {
s += (placement[i] == j) ? 'Q' : '.';
}
ret.push_back(s);
}
return ret;
}
bool valid(vector<int> &placement, int row, int col) {
for (int i = 0; i < row; i++) {
int j = placement[i];
if (j == col || i - row == j - col || i - row == col - j) {
return false;
}
}
return true;
}
void solve(vector<vector<string> > &ret, vector<int> &placement, int cur_row, const int N) {
if (cur_row == N) {
ret.push_back(generate(placement));
return;
}
for (int col = 0; col < N; col++) {
if (valid(placement, cur_row, col)) {
placement[cur_row] = col;
solve(ret, placement, cur_row + 1, N);
}
}
}
public:
vector<vector<string> > solveNQueens(int n) {
vector<vector<string> > ret;
if (n <= 0) {
return ret;
}
vector<int> placement(n);
solve(ret, placement, 0, n);
return ret;
}
};