PHP回溯法解决0-1背包问题实例分析

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

70

71

72

73

74

<?php

$v_arr = array(11,21,31,33,43,53,55,65);

$w_arr = array(1,11,21,23,33,43,45,55);

$n = count($w_arr );

//测试输出

var_dump(bknap1(110));

//var_dump(bound(139,89,7,110));

function bound($v,$w,$k,$W_total){

global $v_arr,$w_arr,$n;

$b = $v;

$c = $w;

//var_dump($W_total);var_dump($n);var_dump($k);var_dump($v);var_dump($w);

//die;

for($i=$k+1;$i<$n;$i++){

$c = $c + $w_arr[$i];

//var_dump($W_total);var_dump($c);

if($c<$W_total)

$b += $v_arr[$i];

else{

//var_dump((1-($c-$W_total)/$w_arr[$i])*$v_arr[$i]);

$b = $b+(1-($c-$W_total)/$w_arr[$i])*$v_arr[$i];

return $b;

}

}

/*var_dump('------bound head');

var_dump($k);

var_dump($b);

var_dump('------bound end');*/

return $b;

}

function bknap1($W_total){

global $v_arr,$w_arr,$n;

$cw = $cp = 0;

$k = 0;

$fp = -1;

while(true){

while($k<$n && $cw+$w_arr[$k]<=$W_total){

$cw += $w_arr[$k];

$cp += $v_arr[$k];

$Y_arr[$k] = 1;

$k +=1;

}

//var_dump($cw);var_dump($cp);var_dump($Y_arr);var_dump($k);var_dump($n);

if($k==$n){

$fp = $cp;

$fw = $cw;

$k = $n-1;

$X_arr = $Y_arr;

//bound($cp,$cw,$k,$W_total);

//var_dump(bound($cp,$cw,$k,$W_total),$fp,$k);die;

//var_dump($fp);var_dump($fw);var_dump($Y_arr);var_dump($k);var_dump($n);

}else{

$Y_arr[$k] = 0;

}

//var_dump($Y_arr);var_dump($k);var_dump($n);//die;

//var_dump(bound($cp,$cw,$k,$W_total),$fp);die;

while(bound($cp,$cw,$k,$W_total)<=$fp)

{

while($k>=0 && $Y_arr[$k]!=1){

$k -= 1;

}

if($k<0)

{

return $X_arr;

}

var_dump($k);

$Y_arr[$k] = 0;

$cw -= $w_arr[$k];

$cp -= $v_arr[$k];

}

$k += 1;

}

}

?>