算法练习第三十天|两道hard51. N 皇后、37. 解数独

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37. 解数独
51. N 皇后

解数独

class Solution {public void solveSudoku(char[][] board) {backTrace(board);}public boolean backTrace(char[][] board){//仅收集一个结果for(int i = 0;i<9;i++){for(int j = 0;j<9;j++){if(board[i][j] != '.') continue;for (char k = '1'; k <= '9'; k++){if (isValid(i, j, k, board)){board[i][j] = k;if (backTrace(board)) // 如果找到合适一组立刻返回return true;board[i][j] = '.';}}// 9个数都试完了，都不行，那么就返回falsereturn false;}}// 遍历完没有返回false，说明找到了合适棋盘位置了return true;}/*** 判断棋盘是否合法有如下三个维度:*     同行是否重复*     同列是否重复*     9宫格里是否重复*/private boolean isValid(int row, int col, char val, char[][] board){// 同行是否重复for (int i = 0; i < 9; i++){if (board[row][i] == val){return false;}}// 同列是否重复for (int j = 0; j < 9; j++){if (board[j][col] == val){return false;}}// 9宫格里是否重复int startRow = (row / 3) * 3;int startCol = (col / 3) * 3;for (int i = startRow; i < startRow + 3; i++){for (int j = startCol; j < startCol + 3; j++){if (board[i][j] == val){return false;}}}return true;}
}

N 皇后

class Solution {List<List<String>> res = new ArrayList();public List<List<String>> solveNQueens(int n) {char[][] chessboard = new char[n][n];for(char[] c : chessboard){Arrays.fill(c,'.');}backTrace(chessboard,n,0);return res;}public void backTrace(char[][] chessboard,int n,int row){if(row == n){res.add(arrays2String(chessboard));}//从0到第n列for(int i = 0;i<n;i++){if(!isValid(row,i,chessboard,n)) continue;chessboard[row][i] = 'Q';backTrace(chessboard,n,row+1);chessboard[row][i] = '.';}}public List<String> arrays2String(char[][] chessboard){List<String> list = new ArrayList<>();for (char[] c : chessboard) {list.add(String.copyValueOf(c));}return list;}public boolean isValid(int row,int col,char[][] chessboard,int n){//检查列for(int i = 0;i<row;i++){if(chessboard[i][col] == 'Q') return false;}// 检查45度对角线，从当前位置往左上for(int i = row-1,j=col-1; i>=0&&j>=0;i--,j--){if(chessboard[i][j] == 'Q') return false;}// 从当前位置往右上for (int i=row-1, j=col+1; i>=0 && j<=n-1; i--, j++) {if (chessboard[i][j] == 'Q') {return false;}}return true;}
}