LeetCode 52. N-Queens II

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本文介绍了一种解决N皇后问题的有效算法。该算法通过跟踪三个数组（水平、垂直和对角线）来确保皇后之间的不冲突放置。利用深度优先搜索（DFS）策略递归地放置皇后，并计算可行方案的数量。

Get the idea from this post: https://developers.google.com/optimization/puzzles/queens

We only to track three arrays. One is horizontally, one is vertically, one is diagonally.

Horizontally is main[2 * n - 1], Vertically is col[n], diagonally is anti[2 * n - 1];

int totalNQueens(int n) {
    vector<bool> col(n, true);
    vector<bool> anti(2*n-1, true);
    vector<bool> main(2*n-1, true);
    int count = 0;
    dfs(0, col, main, anti, count);
    return count;
}
void dfs(int i, vector<bool> &col, vector<bool>& main, vector<bool> &anti, int &count) {
        if (i == col.size()) {
            count++;
            return;
        }
       for (int j = 0; j < col.size(); j++) {
         if (col[j] && main[i+j] && anti[i+col.size()-1-j]) {
             col[j] = main[i+j] = anti[i+col.size()-1-j] = false;
             dfs(i+1, col, main, anti, count);
             col[j] = main[i+j] = anti[i+col.size()-1-j] = true;
      }
    }
}