1+ """
2+
3+ This is a Python implementation for questions involving task assignments between people.
4+ Here Bitmasking and DP are used for solving this.
5+
6+ Question :-
7+ We have N tasks and M people. Each person in M can do only certain of these tasks. Also
8+ a person can do only one task and a task is performed only by one person.
9+ Find the total no of ways in which the tasks can be distributed.
10+ """
11+ 12+ from collections import defaultdict
13+ 14+ 15+ class AssignmentUsingBitmask :
16+ def __init__ (self , task_performed , total ):
17+ self .total_tasks = total # total no of tasks (N)
18+ 19+ # DP table will have a dimension of (2^M)*N
20+ # initially all values are set to -1
21+ self .dp = [
22+ [- 1 for i in range (total + 1 )] for j in range (2 ** len (task_performed ))
23+ ]
24+ 25+ self .task = defaultdict (list ) # stores the list of persons for each task
26+ 27+ # final_mask is used to check if all persons are included by setting all bits
28+ # to 1
29+ self .final_mask = (1 << len (task_performed )) - 1
30+ 31+ def count_ways_until (self , mask , task_no ):
32+ # if mask == self.finalmask all persons are distributed tasks, return 1
33+ if mask == self .final_mask :
34+ return 1
35+ 36+ # if not everyone gets the task and no more tasks are available, return 0
37+ if task_no > self .total_tasks :
38+ return 0
39+ 40+ # if case already considered
41+ if self .dp [mask ][task_no ] != - 1 :
42+ return self .dp [mask ][task_no ]
43+ 44+ # Number of ways when we don't this task in the arrangement
45+ total_ways_util = self .count_ways_until (mask , task_no + 1 )
46+ 47+ # now assign the tasks one by one to all possible persons and recursively
48+ # assign for the remaining tasks.
49+ if task_no in self .task :
50+ for p in self .task [task_no ]:
51+ # if p is already given a task
52+ if mask & (1 << p ):
53+ continue
54+ 55+ # assign this task to p and change the mask value. And recursively
56+ # assign tasks with the new mask value.
57+ total_ways_util += self .count_ways_until (mask | (1 << p ), task_no + 1 )
58+ 59+ # save the value.
60+ self .dp [mask ][task_no ] = total_ways_util
61+ 62+ return self .dp [mask ][task_no ]
63+ 64+ def count_no_of_ways (self , task_performed ):
65+ # Store the list of persons for each task
66+ for i in range (len (task_performed )):
67+ for j in task_performed [i ]:
68+ self .task [j ].append (i )
69+ 70+ # call the function to fill the DP table, final answer is stored in dp[0][1]
71+ return self .count_ways_until (0 , 1 )
72+ 73+ 74+ if __name__ == "__main__" :
75+ total_tasks = 5 # total no of tasks (the value of N)
76+ 77+ # Example 1
78+ task_performed = [[1 , 3 , 4 ], [1 , 2 , 5 ], [3 , 4 ]]
79+ print (
80+ AssignmentUsingBitmask (task_performed , total_tasks ).count_no_of_ways (
81+ task_performed
82+ )
83+ )
84+ 85+ # Example 2
86+ task_performed = [[1 , 2 ], [2 , 3 ], [1 , 3 ]]
87+ print (
88+ AssignmentUsingBitmask (task_performed , total_tasks ).count_no_of_ways (
89+ task_performed
90+ )
91+ )
92+ 93+ # Example 3
94+ task_performed = [[1 , 2 , 3 ], [2 , 3 , 4 ], [1 , 4 , 5 ]]
95+ print (
96+ AssignmentUsingBitmask (task_performed , total_tasks ).count_no_of_ways (
97+ task_performed
98+ )
99+ )
100+ 101+ # Example 4
102+ task_performed = [[1 ], [2 ], [3 ], [4 ], [5 ]]
103+ print (
104+ AssignmentUsingBitmask (task_performed , total_tasks ).count_no_of_ways (
105+ task_performed
106+ )
107+ )
108+ 109+ # Example 5
110+ task_performed = [[1 , 2 , 3 , 4 , 5 ], [1 , 2 , 3 , 4 , 5 ], [1 , 2 , 3 , 4 , 5 ]]
111+ print (
112+ AssignmentUsingBitmask (task_performed , total_tasks ).count_no_of_ways (
113+ task_performed
114+ )
115+ )
116+ 117+ # the list of tasks that can be done by M persons.
118+ task_performed = [[1 , 3 , 4 ], [1 , 2 , 5 ], [3 , 4 ]]
119+ print (
120+ AssignmentUsingBitmask (task_performed , total_tasks ).count_no_of_ways (
121+ task_performed
122+ )
123+ )
0 commit comments