为什么 return 语句不会破坏 Javascript 中的递归循环

Question

Please i am trying to build a Sudoku solver in JavaScript but i face a problem when i get to the solve function , the recursive loop doesn't stop when the board is full. It executes till the end even after finding the solution. Please I'll be grateful if i can get some help. Here is what i tried doing:

class SudokuSolver {

  // convert puzzle string to 2D array
  boardParser(puzzleString) {
    var board = [];
    var i, j;

    for (i = 0; i < 81; i += 9) {
      var boardRow = [];
      for (j = 0; j < 9; j++) {
        boardRow.push(puzzleString.charAt(i + j));
      }
      board.push(boardRow)
    }

    // console.log(board);
    return board;
  }

  // Look for empty space on board (empty space = ".")
  // return [row, col] if empty space found
  // return [-1,-1] if no empty space found (board is full)
  getDot(board) {
    var i, j;

    for (i = 0; i < 9; i++) {
      for (j = 0; j < 9; j++) {
        if (board[i][j] == ".") {
          return [i, j];
        }
      }
    }
    return [-1, -1];
  }

  checkRowPlacement(board, row, column, value) {
    var i;
    for (i = 0; i < 9; i++) {
      if (board[row][i] == value) {
        // console.log("row check false");
        return {
          valid: false
        };
      }
    }
    // console.log("row check true");
    return {
      valid: true
    }
  }

  checkColPlacement(board, row, column, value) {
    var i;

    for (i = 0; i < 9; i++) {
      if (board[i][column] == value) {
        // console.log("col check false")
        return {
          valid: false
        }
      }
    }
    // console.log("col check true")
    return {
      valid: true
    };
  }

  checkRegionPlacement(board, row, column, value) {
    var i, j;
    var regRow = Math.floor(row / 3) * 3;
    var regCol = Math.floor(column / 3) * 3;

    for (i = 0; i < 3; i++) {
      for (j = 0; j < 3; j++) {
        if (board[regRow + i][regCol + j] == value) {
          // console.log("reg check false")
          return {
            valid: false
          }
        }
      }
    }
    // console.log("reg check true");
    return {
      valid: true
    }
  }

  checkvalue(board, row, column, value) {
    var rowCheck = this.checkRowPlacement(board, row, column, value).valid
    var colCheck = this.checkColPlacement(board, row, column, value).valid
    var regCheck = this.checkRegionPlacement(board, row, column, value).valid
    // console.log(rowCheck, colCheck, regCheck);

    if (rowCheck && colCheck && regCheck) {
      // console.log(true)
      return true;
    }
    // console.log(false)
    return false;
  }

  // convert 2D array back to string
  stringifyBoard(board) {
    var string = ""
    var i, j;

    for (i = 0; i < 9; i++) {
      for (j = 0; j < 9; j++) {
        string += board[i][j];
      }
    }

    // console.log(string);
    return string;
  }

  // check for any more empty spaces
  solved(board) {
    var i, j;

    if (this.getDot(board)[0] == -1) {
      return true
    }
    return false
  }

  solve(puzzleString) {
    var board = this.boardParser(puzzleString)
    var emptySpot = this.getDot(board);
    var row = emptySpot[0];
    var column = emptySpot[1];

    // full board condition
    if (this.solved(board)) {
      return puzzleString;
    }

    for (var i = 1; i <= 9; i++) {
      if (this.checkvalue(board, row, column, i)) {
        board[row][column] = i;
        var boardString = this.stringifyBoard(board);
        this.solve(boardString);
      }
    }

    // if board is unsolvable return false
    return false;
  }
}

const input = '5..91372.3...8.5.9.9.25..8.68.47.23...95..46.7.4.....5.2.......4..8916..85.72...3';

console.log(new SudokuSolver().solve(input));

it returns false, but the puzzle string is valid and also when i console log in the full board condition it shows the solved string but doesn't return it.

Answer 1

So once the board is solved and if this.solved(board) returns true, you are returning the solved board. But this is only at the last level of recursion chain. You need to check at every level of recursion if this particular move reaches a solved board state. Hence, validate the result of the next level and if it returns a solved board, return the solved board from the current level too. I have made appropriate changes in the solve function-

solve(puzzleString) {
    var board = this.boardParser(puzzleString)
    var emptySpot = this.getDot(board);
    var row = emptySpot[0];
    var column = emptySpot[1];

    // full board condition
    if (this.solved(board)) {
      return puzzleString;
    }

    for (var i = 1; i <= 9; i++) {
      if (this.checkvalue(board, row, column, i)) {
        board[row][column] = i;
        var boardString = this.stringifyBoard(board);
        var result = this.solve(boardString);
        if(result !== false){
            return result;
        }
      }
    }

    // if board is unsolvable return false
    return false;
  }

Answer 2

for (var i = 1; i <= 9; i++) {
   if (this.checkvalue(board, row, column, i)) {
     board[row][column] = i;
     var boardString = this.stringifyBoard(board);
     
     if(this.solve(boardString)) return true; //I've a modification here
   }
 }

Answer 3

You didn't write any code to stop the function when the solution is found. Here is my solution:

for (var i = 1; i <= 9; i++) {
  if (this.checkvalue(board, row, column, i)) {
    board[row][column] = i;
    var boardString = this.stringifyBoard(board);
    var sol = this.solve(boardString); // change
    if (sol) return sol // change
  }
}

I have done a similar one in python a while ago. Check it here if you are interested: https://onlinegdb.com/SJt2PQrjP