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.
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[
[".Q..", // Solution 1
"...Q",
"Q...",
"..Q."],
["..Q.", // Solution 2
"Q...",
"...Q",
".Q.."]
]
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Code
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private boolean[] column;
private boolean[] diagonal1;
private boolean[] diagonal2;
private int result = 0;
public int (int n) {
column = new boolean[n];
diagonal1 = new boolean[2 * n - 1];
diagonal2 = new boolean[2 * n - 1];
helper(n, 0);
return result;
}
private void helper(int n, int x) {
if (x == n) {
result++;
return;
}
for (int y = 0; y < n; y++) {
if (!isValid(n, x, y))
continue;
update(n, x, y, true);
helper(n, x + 1);
update(n, x, y, false);
}
}
private boolean isValid(int n, int x, int y) {
return !column[y] && !diagonal1[x + y] && !diagonal2[y - x + n - 1];
}
private void update(int n, int x, int y, boolean put) {
column[y] = put;
diagonal1[x + y] = put;
diagonal2[y - x + n - 1] = put;
}
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