2024第二届国际高校数学建模竞赛 A题:金字塔石块的运输 Chatgpt-4 详细思路和代码

import math
 
def calculate_min_transport_rounds_optimized(vehicles, capacities, distances, total_stones, strategy='max_capacity'):
    n = len(vehicles)
    if strategy == 'max_capacity':
        # 按承载能力降序排序
        vehicles_capacities = sorted(zip(vehicles, capacities), key=lambda x: x[1], reverse=True)
    elif strategy == 'longest_distance':
        # 按距离降序排序
        vehicles_distances = sorted(zip(vehicles, distances), key=lambda x: x[1], reverse=True)
    
    min_rounds = 0
    stones_left = total_stones
    
    while stones_left > 0:
        min_rounds += 1
        if strategy == 'max_capacity':
            # 每次尽可能多地运输石头
            capacity_used = 0
            for vehicle, capacity in vehicles_capacities:
                if stones_left <= 0:
                    break
                if capacity >= stones_left:
                    capacity_used = stones_left
                    stones_left = 0
                else:
                    capacity_used += capacity
                    stones_left -= capacity
        elif strategy == 'longest_distance':
            # 优先运输距离较长的石头
            for vehicle, distance in vehicles_distances:
                if stones_left <= 0:
                    break
                capacity = capacities[vehicles.index(vehicle)]
                if capacity >= stones_left:
                    stones_left = 0
                else:
                    stones_left -= capacity
 
    return min_rounds
 
# 示例数据
vehicles = ["船", "马车", "外星飞船"]
capacities = [1000, 500, 2000]  # 对应每辆车的承载能力
distances = [50, 20, 80]  # 对应每块石头到达施工现场的距离
total_stones = 10000  # 假设需要运输的石头总数
 
# 计算最小运输次数（按每次尽可能多地运输石头策略）
min_rounds_max_capacity = calculate_min_transport_rounds_optimized(vehicles, capacities, distances, total_stones, strategy='max_capacity')
print(f"按每次尽可能多地运输石头策略，完成运输任务所需的最小运输次数为: {min_rounds_max_capacity}")
 
# 计算最小运输次数（按优先运输距离较长的石头策略）
min_rounds_longest_distance = calculate_min_transport_rounds_optimized(vehicles, capacities, distances, total_stones, strategy='longest_distance')
print(f"按优先运输距离较长的石头策略，完成运输任务所需的最小运输次数为: {min_rounds_longest_distance}")

问题一思路代码

问题1:建立数学模型，收集相关数据，以最大的赫夫金字塔为例 ，计算在给定的运输车辆数量和载重量下，完成石料运输任务所需的最小运输次数。