[Leetcode]51. N-QUEENSN Queen

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.

Example:

Input:4output: [[". Q.. ",  //solution 1  " ... Q ",  " Q ... ",".  . Q. "], ["]. Q. ",  //Solution 2  " Q ... ",  " ... Q ",  ". Q.. "] Explanation:there exist, distinct solutions to the 4-queens puzzle as shown above.

Topic

NxN chessboard pendulum n pieces, require not to peer, the same column, the same diagonal, the same counter-diagonal, return all pendulum method.

Ideas

Dfs:c[i] denotes the column number where the queen of the line I is located, i.e. a queen is placed on the position (I, c[i]) so that a one-dimensional array can be used to record the entire board.

Code

1 /* 2 Time:o (n!*n) n rows * per line from N to N-1 to n-2 ... 1 i.e. n!3 space:o (n)4 */5 6 classSolution {7        PublicList<list<string>> Solvenqueens (intN) {8list<list<string>> result =NewArraylist<>();9         int[] C =New int[n];//C[i] Represents the column number of the Queen I row, from two to one-dimensionalTenDFS (C, 0, result); One         returnresult; A     } -     Private Static voidDfsint[] C,intRow, list<list<string>>result) { -         intN =c.length; the         if(row = = N) {//The termination condition, also the convergence condition, means that a feasible solution has been found -List<string> solution =NewArraylist<>(); -             //line I -              for(inti = 0; i < N; ++i) { +                 Char[] Chararray =New Char[N]; -Arrays.fill (Chararray, '. ')); +                 //Column J A                  for(intj = 0; J < N; ++j) { at                     if(j = = C[i]) chararray[j] = ' Q '; -                 } -Solution.add (NewString (Chararray)); -             } - Result.add (solution); -             return; in         } -  to          for(intj = 0; J < N; ++J) {//extended status, one column of the test +             BooleanOK =isValid (C, Row, j); -             if(!ok)Continue;//pruning, if illegal, continue to try the next column the             //Perform extended actions *C[row] =J; $DFS (C, row + 1, result);Panax Notoginseng             //Undo Action -             //C[row] =-1; the         } +     } A  the     /** + * Can you put a queen in the (row, col) position? -      * $      * @paramC Chess $      * @paramRow is currently being processed, and the front row has been put to the Queen. -      * @paramCol Current Column -      * @returncan you put a queen ? the      */ -     Private Static BooleanIsValid (int[] C,intRowintCol) {Wuyi          for(inti = 0; i < row; ++i) { the             //in the same column -             if(C[i] = = col)return false; Wu             //on the same diagonal -             if(Math.Abs (i-row) = = Math.Abs (c[i]-col))return false; About         } $         return true; -     } -}

[Leetcode]51. N-QUEENSN Queen