Bitmasking and DP added (#705)

Author: adMenon

dynamic_programming/bitmask.py

@@ -0,0 +1,90 @@
+"""
+
+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 __future__ import print_function
+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
+        
+        #finalmask is used to check if all persons are included by setting all bits to 1
+        self.finalmask = (1<<len(task_performed)) - 1
+    
+    
+    def CountWaysUtil(self,mask,taskno):
+        
+        # if mask == self.finalmask all persons are distributed tasks, return 1
+        if mask == self.finalmask:
+            return 1
+
+        #if not everyone gets the task and no more tasks are available, return 0
+        if taskno > self.total_tasks:
+            return 0
+
+        #if case already considered
+        if self.dp[mask][taskno]!=-1:
+            return self.dp[mask][taskno]
+
+        # Number of ways when we dont this task in the arrangement
+        total_ways_util = self.CountWaysUtil(mask,taskno+1)
+
+        # now assign the tasks one by one to all possible persons and recursively assign for the remaining tasks.
+        if taskno in self.task:
+            for p in self.task[taskno]:
+                
+                # 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.CountWaysUtil(mask|(1<<p),taskno+1)
+        
+        # save the value.
+        self.dp[mask][taskno] = total_ways_util
+        
+        return self.dp[mask][taskno] 
+
+    def countNoOfWays(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.CountWaysUtil(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).countNoOfWays(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
+    """