矩阵乘法递归求解

Posted 2022-02-13 shqhdmr

给定两个N×N的矩阵，求乘积

如下图所示，乘法执行过程如下：

1.矩阵1先拿出一行，矩阵2先拿出一列

2.行与列相乘得到value1

3.行与剩下矩阵2相乘得到value2（递归过程）

4.剩下矩阵1与列相乘得到value3（递归过程）

5.剩下矩阵1与剩下矩阵2相乘得到value4（递归过程）

6.将value1~value4合并成结果数组

写代码时注意约定，value1一定是数值，value2、value3、value4是数值、空数组或者非空的二维数组

由php实现，大体思路不难，但是要非常注意合并结果的细节：

  1 <?php
  2 
  3 class MatrixProduct
  4 
  5     protected $matrix1, $matrix2;
  6     protected $result;
  7 
  8     public function __construct($matrix1, $matrix2)
  9     
 10         $this->matrix1 = $matrix1;
 11         $this->matrix2 = $matrix2;
 12         $this->result = $this->matrixProduction($this->matrix1, $this->matrix2);
 13     
 14 
 15     public function show()
 16     
 17         foreach ($this->result as $row) 
 18             foreach ($row as $data) 
 19                 printf(‘%5d‘, $data);
 20             
 21             echo PHP_EOL;
 22         
 23     
 24 
 25     protected function popRow(&$matrix)
 26     
 27         return empty($matrix) ? [] : [array_shift($matrix)];
 28     
 29 
 30     protected function popColumn(&$matrix)
 31     
 32         $column = [];
 33         foreach ($matrix as $key => &$row) 
 34             $data = array_shift($row);
 35             if (empty($data) || empty($row)) 
 36                 unset($matrix[$key]);
 37             
 38             $column[] = [$data];
 39         
 40         return $column;
 41     
 42 
 43     protected function countProduction($row, $column)
 44     
 45         for ($i = 0, $sum = 0; $i < count($row[0]); $i++) 
 46             $sum += $row[0][$i] * $column[$i][0];
 47         
 48         return $sum;
 49     
 50 
 51     protected function merger($value1, $value2, $value3, $value4)
 52     
 53         if (empty($value2) && empty($value3)) 
 54             return $value1;
 55          else 
 56             $array12 = array_merge([$value1], !is_array($value2) ? [$value2] : $value2[0] ?? []);
 57             if (!is_array($value3)) 
 58                 $array34 = array_merge([$value3], !is_array($value4) ? [$value4] : $value4[0] ?? []);
 59                 return [$array12, $array34];
 60              else 
 61                 for ($i = 0, $array34 = []; $i < count($value3); $i++) 
 62                     $array34[] = array_merge($value3[$i], $value4[$i] ?? []);
 63                 
 64                 return array_merge([$array12], $array34);
 65             
 66         
 67     
 68 
 69     protected function matrixProduction($matrix1, $matrix2)
 70     
 71         $row = $this->popRow($matrix1);
 72         $column = $this->popColumn($matrix2);
 73         if (empty($row) || empty($column)) 
 74             return [];
 75         
 76 
 77         $value1 = $this->countProduction($row, $column);
 78         $value2 = $this->matrixProduction($row, $matrix2);
 79         $value3 = $this->matrixProduction($matrix1, $column);
 80         $value4 = $this->matrixProduction($matrix1, $matrix2);
 81 
 82         return $this->merger($value1, $value2, $value3, $value4);
 83     
 84 
 85 
 86 $matrix1 = [
 87     [1, 2, 3, 4],
 88     [1, 2, 3, 4],
 89     [1, 2, 3, 4],
 90     [1, 2, 3, 4],
 91 ];
 92 
 93 $matrix2 = [
 94     [1, 2, 3, 4],
 95     [5, 6, 7, 8],
 96     [9, 10, 11, 12],
 97     [13, 14, 15, 16]
 98 ];
 99 
100 $production = new MatrixProduct($matrix1, $matrix2);
101 $production->show();