php求解数独

<?php
/*
    php数独求解，时间大约在1分钟
*/
$nums[0] = array(0, 5, 0, 0, 1, 0, 0, 0, 9, );
$nums[1] = array(0, 1, 0, 0, 0, 0, 6, 0, 0, );
$nums[2] = array(2, 0, 0, 0, 9, 0, 0, 0, 0, );
$nums[3] = array(0, 4, 0, 0, 0, 3, 7, 0, 0, );
$nums[4] = array(0, 2, 0, 0, 0, 0, 0, 8, 0, );
$nums[5] = array(0, 0, 5, 7, 0, 0, 0, 2, 0, );
$nums[6] = array(0, 0, 0, 0, 5, 0, 0, 0, 1, );
$nums[7] = array(0, 0, 3, 0, 0, 0, 0, 4, 0, );
$nums[8] = array(9, 0, 0, 0, 8, 0, 0, 3, 0, );

findShuDu($nums);
exit;

function findShuDu($arr)
{
  $paramArray = array($arr);
  //向$paramArray增加数组, 参数用引用传递
  cycleArray($paramArray);

  $resultArray = $paramArray[count($paramArray) - 1];
  echo "\n";
  showArray($arr);
  echo "\n";
  showArray($resultArray);
  if (calcArray($resultArray))
  {
    //echo 'success' . "\n";
  }
  else
  {
    echo 'fail' . "\n";
  }
}

//验证结果是否有效
function calcArray($arr)
{
  for($i = 0; $i < 9; $i ++)
  {
    $sum1 = 0;
    $sum2 = 0;
    for($j = 0; $j < 9; $j ++)
    {
      $sum1 += $arr[$i][$j];
      $sum2 += $arr[$j][$i];
    }

    if (
        $sum1 != 45 || $sum2 != 45
         )
    {
      echo 'check fail: ' . $i . ' ' . $j . "\n";
      return false;
    }
  }

  return true;
}

//显示结果数组
function showArray($arrLast)
{
  for($i = 0; $i < 9; $i ++)
  {
    //echo "array(";
    for($j = 0; $j < 9; $j ++)
    {
      echo $arrLast[$i][$j];
      echo ', ';
    }
    echo "\n";
    //echo "),\n";
  }
}

//获取一个位置有效的可选数字的数组
function getPositionAvailArray($arr)
{
  $arrNew = array();
  for($i = 0; $i < 9; $i ++)
  {
    for($j = 0; $j < 9; $j ++)
    {
      //不为0的位置跳过
      if ($arr[$i][$j] > 0)
      {
        continue;
      }

      //可用数字
      $hv = array(1, 2, 3, 4, 5, 6, 7, 8, 9);

      //取消行已有数字
      for($k = 0; $k < 9; $k ++)
      {
        $a = $arr[$i][$k];
        if ($a > 0)
        {
          $key = array_search($a, $hv);

          if (false !== $key)
          {
            //$key 为false时不能用unset，不然会出错
            unset($hv[$key]);
          }
        }
      }

      //取消列已有数字
      for($k = 0; $k < 9; $k ++)
      {

        $a = $arr[$k][$j];
        if ($a > 0)
        {
          $key = array_search($a, $hv);
          if (false !== $key)
          {
            unset($hv[$key]);
          }
        }
      }

      //取消小方块中已有数字
      $otherI1 = intval($i / 3);
      $otherJ1 = intval($j / 3);
      $otherI = $otherI1 * 3;
      $otherJ = $otherJ1 * 3;
      for ($ii = $otherI; $ii<$otherI + 3; $ii ++)
      {
        for ($jj = $otherJ; $jj<$otherJ + 3; $jj ++)
        {
          $a = $arr[$ii][$jj];
          if ($a > 0)
          {
            $key = array_search($a, $hv);
            if (false !== $key)
            {
              unset($hv[$key]);
            }
          }
        }
      }
      if (empty($hv))
      {
        /*
             echo '出现无效数字 ';
             echo sprintf("行: %s列: %s\n", $i + 1, $j + 1);
             showArray($arr);
         */
        return false;
      }
      $arrNew[$i][$j] = $hv;
    }
  }

  return $arrNew;
}

//递归循环得到有效数组,参数用引用传递，每次得到有效数组后增加到最后
function cycleArray(&$numArray)
{
  //取最后一个数组
  $arr = $numArray[count($numArray) - 1];
  $info = getPositionAvailArray($arr);
  if (false === $info)
  {
    return false;
  }

  $positionI = -1;
  $positionJ = -1;
  $availCountMin = 9;

  //找出可选数字最少的位置
  for($i = 0; $i < 9; $i ++)
  {
    for($j = 0; $j < 9; $j ++)
    {
      $availCount = count($info[$i][$j]);
      if ($availCount > 0 && $availCount < $availCountMin)
      {
        $positionI = $i;
        $positionJ = $j;

        $availCountMin = $availCount;
      }
    }
  }

  if ($positionI >= 0 && $positionJ >= 0)
  {
    $newInfo = $info[$positionI][$positionJ];

    foreach ($newInfo as $key => $value)
    {
      echo sprintf("[%s][%s]: %s;\t", $positionI, $positionJ, $value);
      $arr[$positionI][$positionJ] = $value;
      //unset的bug存在的地方, 如果用[]构建数组, 同时之前用unset取消一些元素，那么key值可能并不是按顺序递增，所以用count()得到数组元素个数来作为key值.被注释的代码是有问题的代码.
      //var_dump(array_keys($numArray));
      //$numArray[] = $arr;
      //var_dump(array_keys($numArray));
      //------------------------------
      $numArray[count($numArray)] = $arr;

      $ret = cycleArray($numArray);
      if ($ret)
      {
        return true;
      }
      else
      {
        //取消最后一个数组元素
        unset($numArray[count($numArray) - 1]);
      }
    }

    return false;
  }

  return true;
}