[Leetcode] N-queens

N-queens

The n-queens Puzzle is the problem of placing N Queens on a nxn chessboard such that No, Queens attack.

Given an integer n, return all distinct solutions to the n-queens puzzle.

Each solution contains a distinct board configuration of the n-queens ' placement, where ‘Q‘ and ‘.‘ both Indi Cate a queen and an empty space respectively.

For example,
There exist-distinct solutions to the 4-queens puzzle:

[ [". Q.. ",  //solution 1  " ... Q ",  " Q ... ",".  . Q. "], ["]. Q. ",  //Solution 2  " Q ... ",  " ... Q ",  ". Q.. "]

Analysis:

Save the chessboard as an N-dimensional array a[n], the value of element I in the array represents the empress position of line I, so that the space size of the problem can be compressed dimension O (N), in judging whether conflict is also very simple, first each row only a queen, and in the array occupies only one element position, the row conflict does not exist, Next is the column conflict, judging whether there is a[i] and the current column J to place the Queen is equal. As for the slash conflict, it can be observed that all the queens that clash on the slash have a regular position, i.e. the ranks of each of them are equal in absolute terms, i.e. | Row–i | = | Col–a[i] |.

1 Const intN_queen = +;2 Const intINVALID =- +;3 4 classSolution5 {6 Private:7   BOOLIs_valid (Const intRowConst intColConst intN)8   {9      for(intI=0; i<n; ++i)Ten       if(A[i] = = Col | | abs (I-ROW) = = ABS (a[i]-col)) One         return false; A  -     return true; -   } the  -   voidShow (vector<vector<string> > &ret,intN) -   { -vector<string>temp; +     stringstr =""; -      for(intI=0; i<n; ++i) +     { Astr =""; at        for(intj=0; j<n; ++j) -       { -         if(A[i] = =j) -str + ="Q"; -         Else -str + ="."; in       } -  to temp.push_back (str); +     } -  the Ret.push_back (temp); *   } $ Panax Notoginseng   voidQueen (vector<vector<string> > &ret,intN) -   { the     intI=0, j=0; +  A      while(i<N) the     { +        while(j<N) -       { $         if(Is_valid (i, J, N)) $         { -A[i] =J; -j =0; the            Break; -         }Wuyi         Else theJ + +; -       } Wu  -       if(A[i] = =INVALID) About       { $         if(i = =0) -            Break; -         Else -         { Ai--; +j = A[i] +1; theA[i] =INVALID; -           Continue; $         } the       } the  the       if(i = = n1) the       { - Show (ret, n); inj = A[i] +1; theA[i] =INVALID; the         Continue; About       } thei++; the     } thecout <<"i ="<< I <<"ret.size () ="<< ret.size () <<Endl; +   } -  the  Public:Bayivector<vector<string> > Solvenqueens (intN) the   { the      for(intI=0; i<n; ++i) -A[i] =INVALID; -  thevector<vector<string> >ret; the Queen (ret, n); the  the     returnret; -   } the  the Private: the   intA[n_queen];94};

[Leetcode] N-queens