[LeetCode] N-Queens II

[Problem]

Follow up for N-Queens problem.

Now, instead outputting board configurations, return the total number of distinct solutions.

[Solution]

class Solution {
public:
    // is the new Queen valid
    bool valid(int row, int column, vector<pair<int, int> > &located){
        for(int i = 0; i < located.size(); ++i){
            if(located[i].first + located[i].second == row + column || located[i].second - located[i].first == column - row){
                return false;
            }
        }
        return true;
    }
   
    // search location
    int search(bool column[], int n, int mth, vector<pair<int, int> > &located){
        int res = 0;
   
        // the last row
        if(mth == n - 1){
            for(int i = 0; i < n; ++i){
                if(column[i] == false && valid(mth, i, located)){
                    res++;
                }
            }
        }
        else{
            for(int i = 0; i < n; ++i){
                // valid in the ith column
                if(column[i] == false && valid(mth, i, located)){
   
                    // locate a Queen in (mth, i)
                    column[i] = true;
                    located.push_back(make_pair(mth, i));
   
                    // search in the next row
                    int r = search(column, n, mth+1, located);
                    res += r;
   
                    // back
                    column[i] = false;
                    located.pop_back();
                }
            }
        }
        return res;
    }
   
    // n queen
    int totalNQueens(int n) {
        // Start typing your C/C++ solution below
        // DO NOT write int main() function
       
        // the columns with Queen
        bool column[n];
        memset(column, false, sizeof(column));
   
        // located Queens
        vector<pair<int, int> > located;
   
        // search
        return search(column, n, 0, located);
    }
};

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