Python 背包分支定界法

Question

我花了一周的时间编写背包问题的分支定界代码，并且阅读了很多关于该主题的文章和书籍。但是，当我运行我的代码时，我没有得到我期望的结果。从文本文件接收输入，例如:

12
4 1
1 1
3 2
2 3

其中第一行是容量，随后的每一行都是值/权重对。我使用这个文件得到的结果是“8”而不是“10”(除非我弄错了，背包里放不下所有元素)。这是我的代码:

#!/usr/bin/python
# -*- coding: utf-8 -*-

import Queue
from collections import namedtuple
Item = namedtuple("Item", ['index', 'value', 'weight', 'level', 'bound', 'contains'])

class Node:
    def __init__(self, level, value, weight, bound, contains):
         self.level = level
         self.value = value
         self.weight = weight
         self.bound = bound
         self.contains = contains

def upper_bound(u, k, n, v, w):
    if u.weight > k:
        return 0

    else:
        bound = u.value
        wt = u.weight
        j = u.level + 1

        while j < n and wt + w[j] <= k:
            bound += v[j]
            wt += w[j]
            j += 1

    # fill knapsack with fraction of a remaining item
            if j < n:
                bound += (k - wt) * (v[j] / w[j])

            return bound

def knapsack(items, capacity):
    item_count = len(items)
    v = [0]*item_count
    w = [0]*item_count

# sort items by value to weight ratio
    items = sorted(items, key=lambda k: k.value/k.weight, reverse = True)

    for i,item in enumerate(items, 0):
        v[i] = int(item.value)
        w[i] = int(item.weight)

    q = Queue.Queue()

    root = Node(0, 0, 0, 0.0, [])
    root.bound = upper_bound(root, capacity, item_count, v, w)
    q.put(root)

    value = 0
    taken = [0]*item_count
    best = set()

    while not q.empty():
        c = q.get()

        if c.bound > value:
            level = c.level+1

    # check 'left' node (if item is added to knapsack)
        left = Node(c.value + v[level], c.weight + w[level], level, 0.0, c.contains[:])
        left.contains.append(level)

        if left.weight <= capacity and left.value > value:
            value = left.value
            best |= set(left.contains)

        left.bound = upper_bound(left, capacity, item_count, v, w)

        if left.bound > value:
            q.put(left)

        # check 'right' node (if items is not added to knapsack)
        right = Node(c.value, c.weight, level, 0.0, c.contains[:])
        right.contains.append(level)
        right.bound = upper_bound(right, capacity, item_count, v, w)

        if right.bound > value:
            q.put(right)

    for b in best:
        taken[b] = 1

    value = sum([i*j for (i,j) in zip(v,taken)])

    return str(value)

我的索引关闭了吗？我没有正确遍历树或计算边界吗？

Answer 1

def upper_bound(u, k, n, v, w):
        if u.weight > k:
            return 0
        else:
            bound = u.value
            wt = u.weight
            j = u.level 
            while j < n and wt + w[j] <= k:
                bound += v[j]
                wt += w[j]
                j += 1
            # fill knapsack with fraction of a remaining item
            if j < n:
                bound += (k - wt) * float(v[j])/ w[j]
            return bound


def knapsack(items, capacity):
        item_count = len(items)
        v = [0]*item_count
        w = [0]*item_count
        # sort items by value to weight ratio
        items = sorted(items, key=lambda k: float(k.value)/k.weight, reverse = True)
        for i,item in enumerate(items, 0):
            v[i] = int(item.value)
            w[i] = int(item.weight)
        q = Queue.Queue()
        root = Node(0, 0, 0, 0.0,[])
        root.bound = upper_bound(root, capacity, item_count, v, w)
        q.put(root)
        value = 0
        taken = [0]*item_count
        best = set()
        while not q.empty():
            c = q.get()
            if c.bound > value:
                level = c.level+1
            # check 'left' node (if item is added to knapsack)
            left = Node(level,c.value + v[level-1], c.weight + w[level-1], 0.0, c.contains[:])
            left.bound = upper_bound(left, capacity, item_count, v, w)
            left.contains.append(level)
            if left.weight <= capacity:
                if left.value > value:
                    value = left.value
                    best = set(left.contains)
                if left.bound > value:
                    q.put(left)
                # check 'right' node (if items is not added to knapsack)   
            right = Node(level,c.value, c.weight, 0.0, c.contains[:])
            right.bound = upper_bound(right, capacity, item_count, v, w)
            if right.weight <= capacity:
                if right.value > value:
                    value = right.value
                    best = set(right.contains)
                if right.bound > value:
                    q.put(right)
        for b in best:
            taken[b-1] = 1
        value = sum([i*j for (i,j) in zip(v,taken)])
        return str(value)