Bin packing问题指在给定的若干个物品中选出一定数量进行装箱,并使得所选的物品的体积和不超过每个箱子的容积,并且所选的箱子数量最少。这是一个NP-hard问题,暴力解法时间复杂度为指数级别,因此一般使用近似算法进行求解。
以下是一个基于深度优先搜索(DFS)的暴力解法示例:
class Bin:
def __init__(self, capacity):
self.capacity = capacity
self.remaining_capacity = capacity
def pack(self, item_size):
if item_size > self.remaining_capacity:
return False
self.remaining_capacity -= item_size
return True
class BinPacking:
def __init__(self, bin_capacity, item_sizes):
self.bin_capacity = bin_capacity
self.item_sizes = item_sizes
self.best_solution = None
def brute_force(self):
current_solution = []
self._dfs(current_solution)
def _dfs(self, current_solution):
if self.best_solution is not None and len(current_solution) >= len(self.best_solution):
return
if len(self.item_sizes) == 0:
self.best_solution = current_solution[:]
return
item_size = self.item_sizes.pop(0)
# try adding the item to existing bins
for i, bin in enumerate(current_solution):
if bin.pack(item_size):
self._dfs(current_solution)
bin.remaining_capacity += item_size
if bin.remaining_capacity == self.bin_capacity:
current_solution.pop(i)
else:
bin.remaining_capacity -= item_size
# try adding the item to a new bin
new_bin = Bin(self.bin_capacity)
if new_bin.pack(item_size):
current_solution.append(new_bin)
self._dfs(current_solution)
current_solution.pop()
self.item_sizes.insert(0, item_size)
详细说明:首先定义Bin类来表示一个箱子,包含容积和剩余容积的属性以及pack方法,用于将物