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89 lines
2.9 KiB
Python
89 lines
2.9 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 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 = [[-1 for i in range(total+1)] for j in range(2**len(task_performed))]
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self.task = defaultdict(list) #stores the list of persons for each task
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#finalmask is used to check if all persons are included by setting all bits to 1
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self.finalmask = (1<<len(task_performed)) - 1
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def CountWaysUtil(self,mask,taskno):
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# if mask == self.finalmask all persons are distributed tasks, return 1
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if mask == self.finalmask:
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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 taskno > 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][taskno]!=-1:
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return self.dp[mask][taskno]
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# Number of ways when we dont this task in the arrangement
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total_ways_util = self.CountWaysUtil(mask,taskno+1)
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# now assign the tasks one by one to all possible persons and recursively assign for the remaining tasks.
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if taskno in self.task:
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for p in self.task[taskno]:
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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 assign tasks with the new mask value.
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total_ways_util+=self.CountWaysUtil(mask|(1<<p),taskno+1)
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# save the value.
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self.dp[mask][taskno] = total_ways_util
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return self.dp[mask][taskno]
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def countNoOfWays(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.CountWaysUtil(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 = [
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[ 1 , 3 , 4 ],
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[ 1 , 2 , 5 ],
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[ 3 , 4 ]
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]
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print(AssignmentUsingBitmask(task_performed,total_tasks).countNoOfWays(task_performed))
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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), (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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""" |