编写一个程序，要求用蛮力法，回溯法，分支限界法来求解01背包问题，三种方法要求为同一组由随机数组成的数据，物品的数量由输入决定，物品重量和价值取随机数，背包大小为物品总重量的一半，并且输出三种方法分别的运行时间

好的，我可以帮你编写这个程序。首先，我会使用 Python 编程语言来实现三种求解 01背包问题的方法：蛮力法、回溯法和分支限界法。然后，我会生成随机的测试数据，根据输入的物品数量来确定物品的重量和价值，并将背包大小设为物品总重量的一半。最后，我会输出三种方法分别的运行时间。

下面是程序的实现：

import random
import time

# 蛮力法求解01背包问题
def brute_force(items, max_weight):
    n = len(items)
    max_value = 0
    best_subset = []

    for i in range(2**n):
        subset = []
        value = 0
        weight = 0

        for j in range(n):
            if (i >> j) & 1:
                subset.append(j)
                value += items[j][0]
                weight += items[j][1]

        if weight <= max_weight and value > max_value:
            max_value = value
            best_subset = subset

    return max_value, best_subset


# 回溯法求解01背包问题
def backtracking(items, max_weight):
    n = len(items)
    max_value = 0
    best_subset = []

    def backtrack(i, subset, value, weight):
        nonlocal max_value, best_subset

        if weight > max_weight:
            return

        if i == n:
            if value > max_value:
                max_value = value
                best_subset = subset
            return

        subset.append(i)
        backtrack(i+1, subset, value+items[i][0], weight+items[i][1])
        subset.pop()
        backtrack(i+1, subset, value, weight)

    backtrack(0, [], 0, 0)
    return max_value, best_subset


# 分支限界法求解01背包问题
def branch_and_bound(items, max_weight):
    n = len(items)
    max_value = 0
    best_subset = []

    def bound(i, value, weight):
        if weight > max_weight:
            return 0

        bound_value = value
        bound_weight = weight

        while i < n and bound_weight + items[i][1] <= max_weight:
            bound_value += items[i][0]
            bound_weight += items[i][1]
            i += 1

        if i < n:
            bound_value += (max_weight - bound_weight) * (items[i][0] / items[i][1])

        return bound_value

    def branch(i, value, weight):
        nonlocal max_value, best_subset

        if weight > max_weight:
            return

        if value > max_value:
            max_value = value
            best_subset = subset[:]

        if i == n:
            return

        if bound(i, value, weight) >= max_value:
            subset.append(i)
            branch(i+1, value+items[i][0], weight+items[i][1])
            subset.pop()
            branch(i+1, value, weight)

    subset = []
    branch(0, 0, 0)
    return max_value, best_subset


# 生成随机测试数据
def generate_test_data(num_items):
    items = []

    for _ in range(num_items):
        value = random.randint(1, 100)
        weight = random.randint(1, 100)
        items.append((value, weight))

    max_weight = sum(weight for _, weight in items) // 2

    return items, max_weight


# 主函数
def main():
    num_items = int(input("请输入物品数量："))
    items, max_weight = generate_test_data(num_items)

    start_time = time.time()
    brute_force_result = brute_force(items, max_weight)
    brute_force_time = time.time() - start_time

    start_time = time.time()
    backtracking_result = backtracking(items, max_weight)
    backtracking_time = time.time() - start_time

    start_time = time.time()
    branch_and_bound_result = branch_and_bound(items, max_weight)
    branch_and_bound_time = time.time() - start_time

    print("蛮力法结果：")
    print("总价值：", brute_force_result[0])
    print("选取的物品：", brute_force_result[1])
    print("运行时间：", brute_force_time)

    print("回溯法结果：")
    print("总价值：", backtracking_result[0])
    print("选取的物品：", backtracking_result[1])
    print("运行时间：", backtracking_time)

    print("分支限界法结果：")
    print("总价值：", branch_and_bound_result[0])
    print("选取的物品：", branch_and_bound_result[1])
    print("运行时间：", branch_and_bound_time)


if __name__ == "__main__":
    main()

你可以运行这个程序，输入物品数量，然后它会输出蛮力法、回溯法和分支限界法三种方法分别的运行结果和时间。希望对你有帮助！