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解数独 #51

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louzhedong opened this issue Sep 6, 2018 · 0 comments
Open

解数独 #51

louzhedong opened this issue Sep 6, 2018 · 0 comments

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@louzhedong
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习题

出处:LeetCode 算法第37题

编写一个程序,通过已填充的空格来解决数独问题。

一个数独的解法需遵循如下规则

  1. 数字 1-9 在每一行只能出现一次。
  2. 数字 1-9 在每一列只能出现一次。
  3. 数字 1-9 在每一个以粗实线分隔的 3x3 宫内只能出现一次。

空白格用 '.' 表示。

img

一个数独。

img

答案被标成红色。

Note:

  • 给定的数独序列只包含数字 1-9 和字符 '.'
  • 你可以假设给定的数独只有唯一解。
  • 给定数独永远是 9x9 形式的。

思路

采用回溯法,遍历所有可能性,找出满足条件的解

解答

/**
 * @param {character[][]} board
 * @return {void} Do not return anything, modify board in-place instead.
 */

// 判断一行内是否可以放置
var isRowSafe = function (board, row, value) {
  for (var i = 0; i < 9; i  ) {
    if (board[row][i] == value) {
      return false;
    }
  }
  return true;
}

// 判断一列内是否可以放置
var isColumnSafe = function (board, column, value) {
  for (var i = 0; i < 9; i  ) {
    if (board[i][column] == value) {
      return false;
    }
  }
  return true;
}

// 判断九宫格内是否可以放置
var isBoardSafe = function (board, row, column, value) {
  var rowOffset = Math.floor(row / 3) * 3;
  var columnOffset = Math.floor(column / 3) * 3;
  for (var i = 0; i < 3; i  ) {
    for (var j = 0; j < 3; j  ) {
      if (board[rowOffset   i][columnOffset   j] == value) {
        return false;
      }
    }
  }
  return true;
}

var isSafe = function (board, row, column, value) {
  return isRowSafe(board, row, value) && isColumnSafe(board, column, value) && isBoardSafe(board, row, column, value);
}

function solve(board, row, column) {
  if (column == 9 && row == 8) {
    return true;
  }
  if (column == 9) {
    column = 0;
    row  ;
  }

  if (board[row][column] != '.') {
    return solve(board, row, column   1);
  }

  for (var i = 1; i <= 9; i  ) {
    if (isSafe(board, row, column, i)) {
      board[row][column] = i.toString();
      if (solve(board, row, column   1)) {
        return true;
      }
    }
  }

  board[row][column] = '.';
  return false;
}


var solveSudoku = function (board) {
  solve(board, 0, 0);
};
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