[LeetCode]N-Queens

最新推荐文章于 2020-07-10 00:48:29 发布

原创最新推荐文章于 2020-07-10 00:48:29 发布 · 1.8k 阅读

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本文提供了一种使用深度优先搜索（DFS）解决N皇后问题的方法，包括检查位置优化、皇后放置逻辑以及验证棋盘状态的函数。

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class Solution {
//using DFS
//CheckPosition part may can be optimized
public:
	vector<vector<string> > solveNQueens(int n) {
		// Start typing your C/C++ solution below
		// DO NOT write int main() function
		if(0 == n) return vector<vector<string> >();
		string emptyStr(n, '.');
		vector<vector<string> > ans;
		vector<string> path(n, emptyStr);
		vector<bool> colOccupied(n, false);
		solveNQueens_aux(n, 0, colOccupied, path, ans);
		return ans;
	}

	void solveNQueens_aux( int n, int row, vector<bool>& colOccupied, vector<string>& path, vector<vector<string> >& ans ) 
	{
		//throw std::exception("The method or operation is not implemented.");
		if(row == n) 
		{
			ans.push_back(path);
			return;
		}
		for (int i = 0; i < n; ++i)
		{
			if (false == colOccupied[i] && CheckPosition(path, row, i))
			{
				colOccupied[i] = true;
				path[row][i] = 'Q';
				solveNQueens_aux(n, row+1, colOccupied, path, ans);
				colOccupied[i] = false;
				path[row][i] = '.';
			}
		}
	}

	bool CheckPosition( vector<string>& path, int row, int col ) 
	{
		//throw std::exception("The method or operation is not implemented.");
		int right = col;
		int step = 0;
		int n = path.size();
		while (true)
		{
			int nowRow = row-step;
			int rightCol = col+step;
			int leftCol = col-step;
			if(nowRow < 0) return true;
			if(rightCol < n && path[nowRow][rightCol] == 'Q')
				return false;
			if (leftCol >= 0 && path[nowRow][leftCol] == 'Q')
				return false;
			step++;
		}
	}

};

second time

class Solution {
public:
    bool checkBoard(int curRow, vector<int>& path)
    {
        for(int i = 0; i < curRow; ++i)
        {
            int num1 = path[i];
            int num2 = path[curRow];
            if(num2&num1 || num2&num1<<(curRow-i) || num2&num1>>(curRow-i)) return false;
        }
        return true;
    }
    vector<string> convert2Board(int n, vector<int>& curPath)
    {
        map<int, int> posMap;
        for(int i = 0; i < n; ++i) posMap[1<<i] = n-1-i;
        vector<string> str(n);
        for(int i = 0; i < n; ++i)
        {
            str[i].resize(n, '.');
            int pos = posMap[curPath[i]];
            str[i][pos] = 'Q';
        }
        return str;
    }
    void solveNQueensUtil(int n, int curRow, vector<int>& curPath, vector<vector<string> >& allPath)
    {
        if(curRow == n)
        {
            vector<string> curBoard = convert2Board(n, curPath);
            allPath.push_back(curBoard);
        }
        
        for(int j = 0; j < n; ++j)
        {
            int curNum = 1<<j;
            curPath.push_back(curNum);
            if(checkBoard(curRow, curPath)) solveNQueensUtil(n, curRow+1, curPath, allPath);
            curPath.pop_back();
        }
    }
    vector<vector<string> > solveNQueens(int n) {
        // Start typing your C/C++ solution below
        // DO NOT write int main() function
        vector<vector<string> > allPath;
        vector<int> curPath;
        solveNQueensUtil(n, 0, curPath, allPath);
        return allPath;
    }
};