卡在数独回溯求解器中 (Java)

Question

三天来我一直在试图找出我在数独回溯求解器中的错误。题目出自leetcodeSudoku Solver。

我的求解器是根据附图推导的。问题是即使从根到叶的路径无效，我的板也会被更改。

换句话说，它经过无效路径后，它尝试的值在我的原始板中是固定的。但是，我只在 children returns 为真时更新我的原始板（请参阅辅助方法中的部分：// put a number and generate children）。

基本上，对于每个“.”，我生成从 1 到 9 的所有可能性，构建一个临时板来填充当前的“.”。有一种可能性，然后调用下一个 '.' 的助手带温度板。我知道由于 space 的成本，为每个可能的 child 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，为什么我的板子在所有 children 都无效的情况下仍在更改？

例如以初始板为基础

..9748...; 7.......; .2.1.9...;

..7...24.; .64.1.59.; .98...3..;

...8.3.2.; .........6; ...2759..;

我运行得到了最终结果：

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没有区别。 char[][] boardTemp = board 表示它们指向相同的内存...您在原始代码中遗漏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] = '.';
    }
}

卡在数独回溯求解器中 (Java)

Stuck in Sudoku backtracking solver (Java)

java

parameters

recursion

sudoku

backtracking