The Algorithms | Python:
All Algorithms implemented in Python (github.com)
https://github.com/TheAlgorithms/Python
例如，在操作系统中使用Python实现银行家的算法
进程和资源
{
"作者。"Biney Kingsley (bluedistro@github.io), bineykingsley36@gmail.com",
"日期": 28-10-2018
}
Banker 银行家算法是一种资源分配和避免死锁的算法
由Edsger Dijkstra开发，它通过模拟所有资源的预定最大可能数量的分配来测试安全性。
该算法通过模拟分配预定的所有资源的最大可能数量来测试安全性，然后进行 "s-state"
检查，以测试所有其他未决活动可能出现的死锁情况。
然后再决定是否允许继续分配。
[来源]维基百科
[来源]Rosetta Code C的实现帮助很大。
https://rosettacode.org/wiki/Banker%27s_algorithm
from __future__ import annotations
import time
import numpy as np
test_claim_vector = [8, 5, 9, 7]
test_allocated_res_table = [
[2, 0, 1, 1],
[0, 1, 2, 1],
[4, 0, 0, 3],
[0, 2, 1, 0],
[1, 0, 3, 0],
]
test_maximum_claim_table = [
[3, 2, 1, 4],
[0, 2, 5, 2],
[5, 1, 0, 5],
[1, 5, 3, 0],
[3, 0, 3, 3],
]
class BankersAlgorithm:
def __init__(
self,
claim_vector: list[int],
allocated_resources_table: list[list[int]],
maximum_claim_table: list[list[int]],
) -> None:
"""
:param claim_vector: A nxn/nxm list depicting the amount of each resources
(eg. memory, interface, semaphores, etc.) available.
:param allocated_resources_table: A nxn/nxm list depicting the amount of each
resource each process is currently holding
:param maximum_claim_table: A nxn/nxm list depicting how much of each resource
the system currently has available
"""
self.__claim_vector = claim_vector
self.__allocated_resources_table = allocated_resources_table
self.__maximum_claim_table = maximum_claim_table
def __processes_resource_summation(self) -> list[int]:
"""
Check for allocated resources in line with each resource in the claim vector
"""
return [
sum(p_item[i] for p_item in self.__allocated_resources_table)
for i in range(len(self.__allocated_resources_table[0]))
]
def __available_resources(self) -> list[int]:
"""
Check for available resources in line with each resource in the claim vector
"""
return np.array(self.__claim_vector) - np.array(
self.__processes_resource_summation()
)
def __need(self) -> list[list[int]]:
"""
Implement safety checker that calculates the needs by ensuring that
max_claim[i][j] - alloc_table[i][j] <= avail[j]
"""
return [
list(np.array(self.__maximum_claim_table[i]) - np.array(allocated_resource))
for i, allocated_resource in enumerate(self.__allocated_resources_table)
]
def __need_index_manager(self) -> dict[int, list[int]]:
"""
This function builds an index control dictionary to track original ids/indices
of processes when altered during execution of method "main"
Return: {0: [a: int, b: int], 1: [c: int, d: int]}
>>> (BankersAlgorithm(test_claim_vector, test_allocated_res_table,
... test_maximum_claim_table)._BankersAlgorithm__need_index_manager()
... ) # doctest: +NORMALIZE_WHITESPACE
{0: [1, 2, 0, 3], 1: [0, 1, 3, 1], 2: [1, 1, 0, 2], 3: [1, 3, 2, 0],
4: [2, 0, 0, 3]}
"""
return {self.__need().index(i): i for i in self.__need()}
def main(self, **kwargs) -> None:
"""
Utilize various methods in this class to simulate the Banker's algorithm
Return: None
>>> BankersAlgorithm(test_claim_vector, test_allocated_res_table,
... test_maximum_claim_table).main(describe=True)
Allocated Resource Table
P1 2 0 1 1
<BLANKLINE>
P2 0 1 2 1
<BLANKLINE>
P3 4 0 0 3
<BLANKLINE>
P4 0 2 1 0
<BLANKLINE>
P5 1 0 3 0
<BLANKLINE>
System Resource Table
P1 3 2 1 4
<BLANKLINE>
P2 0 2 5 2
<BLANKLINE>
P3 5 1 0 5
<BLANKLINE>
P4 1 5 3 0
<BLANKLINE>
P5 3 0 3 3
<BLANKLINE>
Current Usage by Active Processes: 8 5 9 7
Initial Available Resources: 1 2 2 2
__________________________________________________
<BLANKLINE>
Process 3 is executing.
Updated available resource stack for processes: 5 2 2 5
The process is in a safe state.
<BLANKLINE>
Process 1 is executing.
Updated available resource stack for processes: 7 2 3 6
The process is in a safe state.
<BLANKLINE>
Process 2 is executing.
Updated available resource stack for processes: 7 3 5 7
The process is in a safe state.
<BLANKLINE>
Process 4 is executing.
Updated available resource stack for processes: 7 5 6 7
The process is in a safe state.
<BLANKLINE>
Process 5 is executing.
Updated available resource stack for processes: 8 5 9 7
The process is in a safe state.
<BLANKLINE>
"""
need_list = self.__need()
alloc_resources_table = self.__allocated_resources_table
available_resources = self.__available_resources()
need_index_manager = self.__need_index_manager()
for kw, val in kwargs.items():
if kw and val is True:
self.__pretty_data()
print("_" * 50 + "\n")
while need_list:
safe = False
for each_need in need_list:
execution = True
for index, need in enumerate(each_need):
if need > available_resources[index]:
execution = False
break
if execution:
safe = True
# get the original index of the process from ind_ctrl db
for original_need_index, need_clone in need_index_manager.items():
if each_need == need_clone:
process_number = original_need_index
print(f"Process {process_number + 1} is executing.")
# remove the process run from stack
need_list.remove(each_need)
# update available/freed resources stack
available_resources = np.array(available_resources) + np.array(
alloc_resources_table[process_number]
)
print(
"Updated available resource stack for processes: "
+ " ".join([str(x) for x in available_resources])
)
break
if safe:
print("The process is in a safe state.\n")
else:
print("System in unsafe state. Aborting...\n")
break
def __pretty_data(self):
"""
Properly align display of the algorithm's solution
"""
print(" " * 9 + "Allocated Resource Table")
for item in self.__allocated_resources_table:
print(
f"P{self.__allocated_resources_table.index(item) + 1}"
+ " ".join(f"{it:>8}" for it in item)
+ "\n"
)
print(" " * 9 + "System Resource Table")
for item in self.__maximum_claim_table:
print(
f"P{self.__maximum_claim_table.index(item) + 1}"
+ " ".join(f"{it:>8}" for it in item)
+ "\n"
)
print(
"Current Usage by Active Processes: "
+ " ".join(str(x) for x in self.__claim_vector)
)
print(
"Initial Available Resources: "
+ " ".join(str(x) for x in self.__available_resources())
)
time.sleep(1)
if __name__ == "__main__":
import doctest
doctest.testmod()
p = BankersAlgorithm
print(p)
# snippet
from __future__ import annotations
import time
import numpy as np
test_claim_vector = [8, 5, 9, 7］
test_allocated_res_table = [
[2, 0, 1, 1],
[0, 1, 2, 1],
[4, 0, 0, 3],
[0, 2, 1, 0],
[1, 0, 3, 0],
]
test_maximum_claim_table = [
[3, 2, 1, 4],
[0, 2, 5, 2],
[5, 1, 0, 5],
[1, 5, 3, 0],
[3, 0, 3, 3],
]
class BankersAlgorithm:
def __init__(
自己。
claim_vector: list[int],
allocated_resources_table: list[list[int]]。
maximum_claim_table: list[list[int]],
) -> 无。
"""
:param claim_vector: 一个nxn/nxm的列表，描述了每个资源的数量
(例如，内存、接口、信号灯等)。
:param allocated_resources_table: 一个nxn/nxm的列表，描述了每个进程目前持有的每个
资源的数量。
:param maximum_claim_table: 一个nxn/nxm的列表，描述了每个资源的数量
系统目前有多少资源可用
"""
self.__claim_vector = claim_vector
self.__allocated_resources_table = allocated_resources_table
self.__maximum_claim_table = maximum_claim_table
def __processes_resource_summation(self) -> list[int]:
"""
检查已分配的资源是否与索赔向量中的每个资源一致
"""
返回 [
sum(p_item[i] for p_item in self.__allocated_resources_table)
for i in range(len(self.__allocated_resources_table[0])
]
def __available_resources(self) -> list[int]:
"""
检查可用的资源，与索赔向量中的每个资源保持一致
"""
返回 np.array(self.__claim_vector) - np.array(
self.__processes_resource_summation()
)
def __need(self) -> list[list[int]]。
"""
实现安全检查器，通过确保以下几点来计算需求
max_claim[i][j] - alloc_table[i][j] <= avail[j]
"""
返回 [
list(np.array(self.__maximum_claim_table[i]) - np.array(alloted_resource))
for i, allocated_resource in enumerate(self.__allocated_resources_table)
]
def __need_index_manager(self) -> dict[int, list[int]]。
"""
这个函数建立了一个索引控制字典，以跟踪进程的原始id/indices
在执行方法 "main "时被改变的进程的原始id/indices。
返回。{0：[a：int，b：int]，1：[c：int，d：int]}。
>> (BankersAlgorithm(test_claim_vector, test_allocated_res_table,
... test_maximum_claim_table)._BankersAlgorithm__need_index_manager()
... ) # doctest: +normalize_whitespace
{0: [1, 2, 0, 3], 1: [0, 1, 3, 1], 2: [1, 1, 0, 2], 3: [1, 3, 2, 0],
4: [2, 0, 0, 3]}
"""
return {self.__need().index(i): i for i in self.__need()}.
def main(self, **kwargs) -> None:
"""
利用这个类中的各种方法来模拟班克的算法
返回。无
>>> BankersAlgorithm(test_claim_vector, test_allocated_res_table,
... test_maximum_claim_table）.main(describe=True)
已分配的资源表
P1 2 0 1 1
<空白行></p><p><p>
P2 0 1 2 1
<空白行> <BLANKLINE
P3 4 0 0 3
<空白线路>
P4 0 2 1 0
<空白线路>
P5 1 0 3 0
<空白行>
系统资源表
P1 3 2 1 4
<空白行> 系统资源表
P2 0 2 5 2
<空白线路>
P3 5 1 0 5
<空白线路>
P4 1 5 3 0
<空白线路>
P5 3 0 3 3
<空白线路>
当前活动进程的使用情况： 8 5 9 7
初始可用资源。 1 2 2 2
__________________________________________________
<空白线路>
进程3正在执行。
更新了进程的可用资源栈。5 2 2 5
该进程处于安全状态。
<BLANKLINE>
Process 1 is executing.
Updated available resource stack for processes: 7 2 3 6
The process is in a safe state.
<BLANKLINE>
Process 2 is executing.
Updated available resource stack for processes: 7 3 5 7
The process is in a safe state.
<BLANKLINE>
Process 4 is executing.
Updated available resource stack for processes: 7 5 6 7
The process is in a safe state.
<BLANKLINE>
Process 5 is executing.
Updated available resource stack for processes: 8 5 9 7
The process is in a safe state.
<BLANKLINE>
"""
need_list = self.__need()
alloc_resources_table = self.__allocated_resources_table
available_resources = self.__available_resources()
need_index_manager = self.__need_index_manager()
for kw, val in kwargs.items():
if kw and val is True:
self.__pretty_data()
print("_" * 50 + "\n")
while need_list:
safe = False
for each_need in need_list:
execution = True
for index, need in enumerate(each_need):
if need > available_resources[index]:
execution = False
break
if execution:
safe = True
# get the original index of the process from ind_ctrl db
for original_need_index, need_clone in need_index_manager.items():
if each_need == need_clone:
process_number = original_need_index
print(f"Process {process_number + 1} is executing.")
# remove the process run from stack
need_list.remove(each_need)
# update available/freed resources stack
available_resources = np.array(available_resources) + np.array(
alloc_resources_table[process_number]
)
print(
"Updated available resource stack for processes: "
+ " ".join([str(x) for x in available_resources])
)
break
if safe:
print("The process is in a safe state.\n")
else:
print("System in unsafe state. Aborting...\n")
break
def __pretty_data(self):
"""
Properly align display of the algorithm's solution
"""
print(" " * 9 + "Allocated Resource Table")
for item in self.__allocated_resources_table:
print(
f"P{self.__allocated_resources_table.index(item) + 1}"
+ " ".join(f"{it:>8}" for it in item)
+ "\n"
)
print(" " * 9 + "System Resource Table")
for item in self.__maximum_claim_table:
print(
f"P{self.__maximum_claim_table.index(item) + 1}"
+ " ".join(f"{it:>8}" for it in item)
+ "\n"
)
print(
"Current Usage by Active Processes: "
+ " ".join(str(x) for x in self.__claim_vector)
)
print(
"Initial Available Resources: "
+ " ".join(str(x) for x in self.__available_resources())
)
time.sleep(1)
if __name__ == "__main__":
import doctest
doctest.testmod()
#代码块
全文分四部分：
什么是银行家算法？
银行家算法中的数据结构
银行家算法自然语言描述
银行家算法流程图表示
一、什么是银行家算法？
银行家算法是操作系统的经典算法之一，用于避免死锁情况的出现。
它最初是为银行设计的（因此得名），通过判断借贷是否安全，然后决定借不借。
在银行中，客户申请贷款的数量是有限的，每个客户在第一次申请贷款时要声明完成该项目所需的最大资金量，在满足所有贷款要求时，客户应及时归还。银行家在客户申请的贷款数量不超过自己拥有的最大值时，都应尽量满足客户的需要。
用在操作系统中，银行家、出借资金、客户，就分别对应操作系统、资源、申请资源的进程。
每一个新进程进入系统时，必须声明需要每种资源的最大数目，其数目不能超过系统所拥有的的资源总量。当进程请求一组资源时，系统必须首先确定是否有足够的资源分配给该进程，若有，再进一步计算在将这些资源分配给进程后，是否会使系统处于不安全状态如果不会才将资源分配给它，否则让进程等待。
二、银行家算法中的数据结构
为了实现银行家算法，在系统中必须设置这样四个数据结构：
1）Available向量：系统中可利用的资源数目
2）Max矩阵：每个进程对每种资源的最大需求
3）Allocation矩阵：每个进程已分配的各类资源的数目
4）Need矩阵：每个进程还需要的各类资源数
其中三个矩阵间存在下述关系：
Need[i,j] = Max[i,j] - allocation[i, j]
三、银行家算法自然语言描述
将银行家算法的逻辑转化为自然语言：
设Requesti是进程Pi的请求向量，如果Requesti［j］=K，表示进程Pi需要K个Rj类型的资源。当Pi发出资源请求后，系统按下述步骤进行检查：
(1) 若 Requesti[j] ≤ Need[i,j]，转向(2)，否则认为出错（因为它所需的资源数目已超过它所宣布的最大值）。
(2) 若 Requesti[j] ≤ Available[j]，转向(3)，否则须等待（表现为进程Pi受阻）。
(3) 系统尝试把资源分配给进程Pi，并修改下面数据结构中的数值：
Available[j] = Available[j] – Requesti[j]
Allocation[i,j] = Allocation[i,j] + Requesti[j]
Need[i,j] = Need[i,j] –Requesti[j]
(4) 试分配后，执行安全性算法，检查此次分配后系统是否处于安全状态。若安全，才正式分配；否则，此次试分配作废，进程Pi等待。
四、银行家算法流程图表示
最后，用流程图表示银行家算法。此前介绍过如何用流程图描述算法，这里不再赘述，有需要的可以
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