leetcode 51: N-Queens

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DFS method:

class Solution {public:    vector<vector<string>> solveNQueens(int n) {        vector<vector<string> > res;        vector<string> board;        for(int i=0;i<n;i++)        {            string s;            for(int j=0;j<n;j++)                s+='.';            board.push_back(s);        }        solver(res,board,0,n);        return res;    }    void solver(vector<vector<string> >& res, vector<string> board, int row, int n)    {        if(row==n)            res.push_back(board);        for(int j=0;j<n;j++)        {            if(isValid(board,row,j,n))            {                board[row][j]='Q';                solver(res,board,row+1,n);                board[row][j]='.';            }        }    }    bool isValid(vector<string> board, int row, int col, int n)    {        int i,j;        for(i=0;i<row;i++)            if(board[i][col]=='Q')                return false;        for(i=row-1,j=col-1;i>=0&&j>=0;i--,j--)            if(board[i][j]=='Q')                return false;        for(i=row-1,j=col+1;i>=0&&j<n;i--,j++)            if(board[i][j]=='Q')                return false;        return true;    }};

Updated version, using 3 arrays to check the validation. The three arrays are for the column, 45 degree line and 135 degree line.

class Solution {public:    vector<vector<string>> solveNQueens(int n) {        vector<vector<string> > res;        vector<string> board(n,string(n,'.'));        vector<bool> v_col(n,0);        vector<bool> v_45(2*n-1,0),v_135(2*n-1,0);        helper(n,0,res,board,v_col,v_45,v_135);        return res;    }    void helper(int n,int row,vector<vector<string> >& res,vector<string>& board,vector<bool>& v_col,vector<bool>& v_45,vector<bool>& v_135)    {        if(row==n)            res.push_back(board);        for(int i=0;i<n;i++)        {            int idx_col=i,idx_45=n-1-row+i,idx_135=row+i;            if(v_col[idx_col]==0&&v_45[idx_45]==0&&v_135[idx_135]==0)            {                board[row][i]='Q';                v_col[idx_col]=1;                v_45[idx_45]=1;                v_135[idx_135]=1;                helper(n,row+1,res,board,v_col,v_45,v_135);                board[row][i]='.';                v_col[idx_col]=0;                v_45[idx_45]=0;                v_135[idx_135]=0;            }        }    }};

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