数独回溯算法中的递归（Java）

Question

三天来，我一直在努力找出我在数独回溯求解中的错误。问题来自leetcode Sudoku Solver

我的解算器基于附件中的推论。问题是，即使从根到叶的路径无效，我的电路板也会被更改

换句话说，在它通过一条无效路径后，它尝试的值在我的原始电路板中被固定。但是，我只在其子项返回true时更新原始板（请参阅helper method://put a number and generate children中的部分）

基本上，对于每个“.”，我生成从1到9的所有可能性，构造一个临时板，填充当前的“.”如果有一种可能性，请致电下一个的助手用临时板。我知道，由于空间成本的原因，为每个可能的孩子存储相同大小的boardTemp是不好的，但我现在主要关心的是在优化成本之前先解决问题

总而言之，为什么我的董事会在所有孩子都无效的情况下仍在变动

例如，基于初始板

。。9748...; 7.2.1.9...;

。。7.24.; .64.1.59.; .98...3..;

。。。8.3.2.; ........6.2759..;

跑步后我得到了最终结果：

139748652；745326189; 826159437;

35769.24。64.1.59.; .98...3..;

。。。8.3.2.; ........6.2759..;

public void sudokuSolver(char[][] board) {
    for (int i = 0 ; i < board.length ; i++) {
        for (int j = 0 ; j < board.length ; j++) {
            if (board[i][j] == '.') {
                // find the first '.' as root
                helper(i, j, board);
                return;
            }
        }
    }
}

private boolean helper(int row, int col, char[][] board) {
    // case 2. check if it has following '.' and store its position
    boolean hasNext = false;
    boolean nextSearching = false;
    int nextRow = row;
    int nextCol = col;
    for (int i = 0 ; i < board.length ; i++) {
        for (int j = 0; j < board.length ; j++) {
            if (nextSearching && !hasNext && board[i][j] == '.') {
                hasNext = true; // there is next!
                nextRow = i;
                nextCol = j;
            }
            if (i == row && j == col) {
                nextSearching = true;
            }
        }
    }

    // exit condition: last '.'
    if (!hasNext) {
        for (char put = '1' ; put <= '9' ; put ++) {
            if (isValid(row, col, board, put)) {
                return true;
            }
        }
        return false;
    }

    // put a number and generate children
    for (char put = '1' ; put <= '9' ; put ++) {
        if (isValid(row, col, board, put)) {
            char[][] boardTemp = board;
            boardTemp[row][col] = put;
            boolean valid = helper(nextRow, nextCol, boardTemp);
            if (valid) {
                // board is supposed to change only when valid is true.
                board[row][col] = put;
                return true;
            }
        }
    }
    return false;
}

private boolean isValid(int row, int col, char[][] board, char c) {
    // go through each row, column, and subblock to determine if c is a valid choice based on current board.
    for (int jCol = 0 ; jCol < 9 ; jCol ++) {
        if (board[row][jCol] == c) {
            return false;
        }
    }
    for (int iRow = 0 ; iRow < 9 ; iRow ++) {
        if (board[iRow][col] == c) {
            return false;
        }
    }
    for (int i = row/3*3 ; i < row/3*3 + 3 ; i++) {
        for (int j = col/3*3 ; j < col/3*3 + 3 ; j++) {
            if (board[i][j] == c) {
                return false;
            }
        }
    }
    return true;
}

Answer 1

使用boardTemp和board之间没有区别char[][] boardTemp = board意味着它们指向同一个内存。。。您在原始代码中漏掉的是输入无效数字后的else部分：

for (char put = '1' ; put <= '9' ; put ++) {
    if (isValid(row, col, board, put)) {
        char[][] boardTemp = board; // board and boardTemp are essentially the same thing
        boardTemp[row][col] = put;
        boolean valid = helper(nextRow, nextCol, boardTemp);
        if (valid) {
            // board is supposed to change only when valid is true.
            board[row][col] = put;
            return true;
        }
        // THIS IS WHAT YOU MISSED!!
        // if you don't reset the '.' back, your later backtrack will not work 
        // because you put an invalid number on your board and you will never find a solution
        boardTemp[row][col] = '.';
    }
}