allocation number Algorithm
The allocation number algorithm is a computational method used to optimize the distribution of resources, tasks, or assets among different entities, such as individuals, departments, or servers, in a balanced and efficient manner. It is an essential tool in various fields, including operations research, computer science, and economics, where effective allocation plays a crucial role in maximizing overall performance or minimizing costs. The algorithm works by analyzing the relationships between the entities and the resources, taking into consideration factors like preferences, capacities, and constraints, and then iteratively adjusting the allocations to find the optimal solution.
One of the most well-known allocation number algorithms is the Hungarian method, which is used for solving the assignment problem, where the goal is to assign tasks or resources to agents in a way that minimizes the total cost or maximizes the total profit. The algorithm starts by constructing a cost matrix representing the costs associated with each possible assignment, then successively manipulates the matrix to find the optimal allocation. Another example is the Gale-Shapley algorithm, which addresses the stable matching problem by allocating resources based on preferences in a way that guarantees a stable outcome where no pair of entities would prefer to be matched with each other over their current allocation. In practice, allocation number algorithms are widely used in various applications, such as load balancing in computer networks, scheduling in manufacturing systems, and matching in market design.
from typing import List
def allocation_num(number_of_bytes: int, partitions: int) -> List[str]:
"""
Divide a number of bytes into x partitions.
In a multi-threaded download, this algorithm could be used to provide
each worker thread with a block of non-overlapping bytes to download.
For example:
for i in allocation_list:
requests.get(url,headers={'Range':f'bytes={i}'})
parameter
------------
: param number_of_bytes
: param partitions
return
------------
: return: list of bytes to be assigned to each worker thread
Examples:
------------
>>> allocation_num(16647, 4)
['0-4161', '4162-8322', '8323-12483', '12484-16647']
>>> allocation_num(888, 888)
Traceback (most recent call last):
...
ValueError: partitions can not >= number_of_bytes!
>>> allocation_num(888, 999)
Traceback (most recent call last):
...
ValueError: partitions can not >= number_of_bytes!
>>> allocation_num(888, -4)
Traceback (most recent call last):
...
ValueError: partitions must be a positive number!
"""
if partitions <= 0:
raise ValueError("partitions must be a positive number!")
if partitions >= number_of_bytes:
raise ValueError("partitions can not >= number_of_bytes!")
bytes_per_partition = number_of_bytes // partitions
allocation_list = [f"0-{bytes_per_partition}"]
for i in range(1, partitions - 1):
length = f"{bytes_per_partition * i + 1}-{bytes_per_partition * (i + 1)}"
allocation_list.append(length)
allocation_list.append(
f"{(bytes_per_partition * (partitions - 1)) + 1}-" f"{number_of_bytes}"
)
return allocation_list
if __name__ == "__main__":
import doctest
doctest.testmod()
