分支定界python代码

分支定界是一种求解优化问题的算法，它通过不断划分问题空间并剪枝来寻找最优解。下面是一个简单的分支定界算法的Python代码示例：

import heapq

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

def branch_and_bound(items, capacity):
    n = len(items)
    items.sort(key=lambda x: x[1]/x[0], reverse=True)  # 按照价值重量比降序排序
    priority_queue = []
    max_value = 0

    root = Node(-1, 0, 0, 0)
    priority_queue.append((-root.bound, root))

    while priority_queue:
        _, node = heapq.heappop(priority_queue)

        if node.bound > max_value:
            continue

        if node.level == n-1:
            continue

        # 不选择当前物品
        without_item = Node(node.level+1, node.value, node.weight, node.bound)
        without_item.bound = calculate_bound(without_item, items, capacity)
        if without_item.bound > max_value:
            heapq.heappush(priority_queue, (-without_item.bound, without_item))

        # 选择当前物品
        with_item = Node(node.level+1, node.value+items[node.level+1][1], node.weight+items[node.level+1][0], node.bound)
        with_item.bound = calculate_bound(with_item, items, capacity)
        if with_item.weight <= capacity and with_item.bound > max_value:
            max_value = with_item.value
        if with_item.bound > max_value:
            heapq.heappush(priority_queue, (-with_item.bound, with_item))

    return max_value

def calculate_bound(node, items, capacity):
    bound = node.value
    total_weight = node.weight
    level = node.level + 1

    while level < len(items) and total_weight + items[level][0] <= capacity:
        bound += items[level][1]
        total_weight += items[level][0]
        level += 1

    if level < len(items):
        bound += (capacity - total_weight) * (items[level][1] / items[level][0])

    return bound

# 测试代码
items = [(2, 10), (3, 5), (5, 15), (7, 7), (1, 6), (4, 18), (1, 3)]
capacity = 15
max_value = branch_and_bound(items, capacity)
print("最大价值:", max_value)

这段代码实现了一个分支定界算法来解决背包问题。它通过优先队列来管理待扩展的节点，并根据节点的上界进行剪枝。在每个节点处，算法分别考虑选择当前物品和不选择当前物品两种情况，并计算相应的上界。算法会不断扩展节点，直到找到最优解或者队列为空。