N-Queens II Problem

Description

LeetCode Problem 52.

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.

Example 1:

``````1
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Input: n = 4
Output: 2
Explanation: There are two distinct solutions to the 4-queens puzzle as shown.
``````

Example 2:

``````1
2
Input: n = 1
Output: 1
``````

Constraints:

• 1 <= n <= 9

Sample C++ Code

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class Solution {
public:
int cnt;
int N;

void dfs(vector<int>& col2row, int row) {
if (row == N) {
cnt ++;
return;
}

int r, c;
bool place;
vector<vector<int>> dir = { {-1,-1}, {1,1}, {-1,1}, {1,-1} };
for (int col = 0; col < N; col ++) {
if (col2row[col] == -1) {
place = true;
for (int j = 0; j < 4; j ++) {
r = row + dir[j][0], c = col + dir[j][1];
while (r >= 0 && r < N && c >= 0 && c < N && place) {
if (col2row[c] == r) {
place = false;
break;
}
r += dir[j][0], c += dir[j][1];
}
if (!place)
break;
}
if (place) {
col2row[col] = row;
dfs(col2row, row+1);
col2row[col] = -1;
}
}
}
}

int totalNQueens(int n) {
cnt = 0, N = n;
vector<int> col2row(n, -1);
dfs(col2row, 0);
return cnt;
}
};
``````