N-Queens II
The n-queens puzzle is the problem of placing n queens on an n x 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.
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Example 1:
Input: n = 4
Output: 2
Explanation: There are two distinct solutions to the 4-queens puzzle as shown.
Example 2:
Input: n = 1
Output: 1
Constraints:
1 <= n <= 9
Solution
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class Solution {
private:
vector<vector<string>> res;
unordered_set<int> colSet;
unordered_set<int> diag1Set;
unordered_set<int> diag2Set;
public:
bool checkVec(int row, int col) {
// Check column conflicts
if (colSet.count(col) > 0) {
return false;
}
// Check diagonal conflicts
if (diag1Set.count(row + col) > 0 || diag2Set.count(row - col) > 0) {
return false;
}
return true;
}
void solveNQueensImpl(int row, int n, vector<int> board) {
if (row == n) {
vector<string> tmpVec;
for (int i = 0; i < n; i++) {
string tmp(n, '.');
tmp[board[i]] = 'Q';
tmpVec.push_back(tmp);
}
res.push_back(tmpVec);
return;
}
for (int col = 0; col < n; col++) {
if (checkVec(row, col)) {
board[row] = col;
colSet.insert(col);
diag1Set.insert(row + col);
diag2Set.insert(row - col);
solveNQueensImpl(row + 1, n, board);
colSet.erase(col);
diag1Set.erase(row + col);
diag2Set.erase(row - col);
}
}
}
vector<vector<string>> solveNQueens(int n) {
vector<int> board(n, 0);
solveNQueensImpl(0, n, board);
return res;
}
int totalNQueens(int n) {
return solveNQueens(n).size();
}
};
