mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-12-18 01:00:15 +00:00
07e991d553
* ci(pre-commit): Add pep8-naming to `pre-commit` hooks (#7038) * refactor: Fix naming conventions (#7038) * Update arithmetic_analysis/lu_decomposition.py Co-authored-by: Christian Clauss <cclauss@me.com> * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * refactor(lu_decomposition): Replace `NDArray` with `ArrayLike` (#7038) * chore: Fix naming conventions in doctests (#7038) * fix: Temporarily disable project euler problem 104 (#7069) * chore: Fix naming conventions in doctests (#7038) Co-authored-by: Christian Clauss <cclauss@me.com> Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
94 lines
3.1 KiB
Python
94 lines
3.1 KiB
Python
"""
|
|
|
|
This is a Python implementation for questions involving task assignments between people.
|
|
Here Bitmasking and DP are used for solving this.
|
|
|
|
Question :-
|
|
We have N tasks and M people. Each person in M can do only certain of these tasks. Also
|
|
a person can do only one task and a task is performed only by one person.
|
|
Find the total no of ways in which the tasks can be distributed.
|
|
"""
|
|
from collections import defaultdict
|
|
|
|
|
|
class AssignmentUsingBitmask:
|
|
def __init__(self, task_performed, total):
|
|
|
|
self.total_tasks = total # total no of tasks (N)
|
|
|
|
# DP table will have a dimension of (2^M)*N
|
|
# initially all values are set to -1
|
|
self.dp = [
|
|
[-1 for i in range(total + 1)] for j in range(2 ** len(task_performed))
|
|
]
|
|
|
|
self.task = defaultdict(list) # stores the list of persons for each task
|
|
|
|
# final_mask is used to check if all persons are included by setting all bits
|
|
# to 1
|
|
self.final_mask = (1 << len(task_performed)) - 1
|
|
|
|
def count_ways_until(self, mask, task_no):
|
|
|
|
# if mask == self.finalmask all persons are distributed tasks, return 1
|
|
if mask == self.final_mask:
|
|
return 1
|
|
|
|
# if not everyone gets the task and no more tasks are available, return 0
|
|
if task_no > self.total_tasks:
|
|
return 0
|
|
|
|
# if case already considered
|
|
if self.dp[mask][task_no] != -1:
|
|
return self.dp[mask][task_no]
|
|
|
|
# Number of ways when we don't this task in the arrangement
|
|
total_ways_util = self.count_ways_until(mask, task_no + 1)
|
|
|
|
# now assign the tasks one by one to all possible persons and recursively
|
|
# assign for the remaining tasks.
|
|
if task_no in self.task:
|
|
for p in self.task[task_no]:
|
|
|
|
# if p is already given a task
|
|
if mask & (1 << p):
|
|
continue
|
|
|
|
# assign this task to p and change the mask value. And recursively
|
|
# assign tasks with the new mask value.
|
|
total_ways_util += self.count_ways_until(mask | (1 << p), task_no + 1)
|
|
|
|
# save the value.
|
|
self.dp[mask][task_no] = total_ways_util
|
|
|
|
return self.dp[mask][task_no]
|
|
|
|
def count_no_of_ways(self, task_performed):
|
|
|
|
# Store the list of persons for each task
|
|
for i in range(len(task_performed)):
|
|
for j in task_performed[i]:
|
|
self.task[j].append(i)
|
|
|
|
# call the function to fill the DP table, final answer is stored in dp[0][1]
|
|
return self.count_ways_until(0, 1)
|
|
|
|
|
|
if __name__ == "__main__":
|
|
|
|
total_tasks = 5 # total no of tasks (the value of N)
|
|
|
|
# the list of tasks that can be done by M persons.
|
|
task_performed = [[1, 3, 4], [1, 2, 5], [3, 4]]
|
|
print(
|
|
AssignmentUsingBitmask(task_performed, total_tasks).count_no_of_ways(
|
|
task_performed
|
|
)
|
|
)
|
|
"""
|
|
For the particular example the tasks can be distributed as
|
|
(1,2,3), (1,2,4), (1,5,3), (1,5,4), (3,1,4),
|
|
(3,2,4), (3,5,4), (4,1,3), (4,2,3), (4,5,3)
|
|
total 10
|
|
"""
|