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NQueensIi.java
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NQueensIi.java
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// Link: https://leetcode.com/problems/n-queens-ii/
/*
* DFS
* 0ms, 100%
*
* The same idea of 51-N-Queens and this problem is easier. We don't need to store
* the solutions and instead just return the number of solutions
*/
class Solution {
public int totalNQueens(int n) {
// Three arrays used to check the three directions: column, 45-degree diagonal, and 135-degree diagonal
int[] col = new int[n];
int[] diagonal = new int[2 * n - 1];
int[] antiDiagonal = new int[2 * n - 1];
int[] ans = new int[1];
dfs(col, diagonal, antiDiagonal, ans, 0, n);
return ans[0];
}
private void dfs(int[] col, int[] diagonal, int[] antiDiagonal, int[] ans, int row, int n) {
if (row == n) {
ans[0]++;
return;
}
for (int i = 0; i < n; ++i) {
if (col[i] == 1 || diagonal[row + i] == 1 || antiDiagonal[row - i + n - 1] == 1) {
continue;
}
// Mark
col[i] = 1;
diagonal[row + i] = 1;
antiDiagonal[row - i + n - 1] = 1;
dfs(col, diagonal, antiDiagonal, ans, row + 1, n);
// Restore
col[i] = 0;
diagonal[row + i] = 0;
antiDiagonal[row - i + n - 1] = 0;
}
}
}
/*
* Time complexity:
*
* Space complexity: O(n)
*
* Notes:
*
*/