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90 lines
3.0 KiB
Python
90 lines
3.0 KiB
Python
"""
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This is a Python implementation for questions involving task assignments between people.
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Here Bitmasking and DP are used for solving this.
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Question :-
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We have N tasks and M people. Each person in M can do only certain of these tasks. Also
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a person can do only one task and a task is performed only by one person.
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Find the total no of ways in which the tasks can be distributed.
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"""
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from collections import defaultdict
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class AssignmentUsingBitmask:
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def __init__(self, task_performed, total):
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self.total_tasks = total # total no of tasks (N)
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# DP table will have a dimension of (2^M)*N
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# initially all values are set to -1
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self.dp = [
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[-1 for i in range(total + 1)] for j in range(2 ** len(task_performed))
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]
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self.task = defaultdict(list) # stores the list of persons for each task
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# final_mask is used to check if all persons are included by setting all bits
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# to 1
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self.final_mask = (1 << len(task_performed)) - 1
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def count_ways_until(self, mask, task_no):
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# if mask == self.finalmask all persons are distributed tasks, return 1
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if mask == self.final_mask:
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return 1
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# if not everyone gets the task and no more tasks are available, return 0
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if task_no > self.total_tasks:
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return 0
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# if case already considered
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if self.dp[mask][task_no] != -1:
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return self.dp[mask][task_no]
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# Number of ways when we don't this task in the arrangement
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total_ways_util = self.count_ways_until(mask, task_no + 1)
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# now assign the tasks one by one to all possible persons and recursively
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# assign for the remaining tasks.
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if task_no in self.task:
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for p in self.task[task_no]:
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# if p is already given a task
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if mask & (1 << p):
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continue
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# assign this task to p and change the mask value. And recursively
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# assign tasks with the new mask value.
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total_ways_util += self.count_ways_until(mask | (1 << p), task_no + 1)
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# save the value.
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self.dp[mask][task_no] = total_ways_util
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return self.dp[mask][task_no]
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def count_no_of_ways(self, task_performed):
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# Store the list of persons for each task
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for i in range(len(task_performed)):
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for j in task_performed[i]:
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self.task[j].append(i)
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# call the function to fill the DP table, final answer is stored in dp[0][1]
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return self.count_ways_until(0, 1)
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if __name__ == "__main__":
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total_tasks = 5 # total no of tasks (the value of N)
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# the list of tasks that can be done by M persons.
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task_performed = [[1, 3, 4], [1, 2, 5], [3, 4]]
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print(
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AssignmentUsingBitmask(task_performed, total_tasks).count_no_of_ways(
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task_performed
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)
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)
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"""
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For the particular example the tasks can be distributed as
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(1,2,3), (1,2,4), (1,5,3), (1,5,4), (3,1,4),
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(3,2,4), (3,5,4), (4,1,3), (4,2,3), (4,5,3)
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total 10
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"""
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