Design a data structure that supports all following operations in average O(1) time.
Note: Duplicate elements are allowed.
insert(val): Inserts an item val to the collection.
remove(val): Removes an item val from the collection if present.
getRandom: Returns a random element from current collection of elements. The probability of each element being returned is linearly related to the number of same value the collection contains.
Example:
// Init an empty collection.
RandomizedCollection collection = new RandomizedCollection();
// Inserts 1 to the collection. Returns true as the collection did not contain 1.
collection.insert(1);
// Inserts another 1 to the collection. Returns false as the collection contained 1. Collection now contains [1,1].
collection.insert(1);
// Inserts 2 to the collection, returns true. Collection now contains [1,1,2].
collection.insert(2);
// getRandom should return 1 with the probability 2/3, and returns 2 with the probability 1/3.
collection.getRandom();
// Removes 1 from the collection, returns true. Collection now contains [1,2].
collection.remove(1);
// getRandom should return 1 and 2 both equally likely.
collection.getRandom();
import random
 class RandomizedCollection(object):
     def __init__(self):
         self.l = []
         self.d = collections.defaultdict(set)
 
     def insert(self, val):
         b = val not in self.d
         self.d[val].add(len(self.l))
         self.l.append(val)
         return b
 
     def remove(self, val):
         if val not in self.d:
             return False
         i, newVal = self.d[val].pop(), self.l[-1]
         if len(self.d[val]) == 0:
             del self.d[val]
         self.l[i] = newVal
         if newVal in self.d:
             self.d[newVal].add(i)
             self.d[newVal].discard(len(self.l)-1)
         self.l.pop()
         return True
 
     def getRandom(self):
         return random.choice(self.l)
import random
 class RandomizedCollection(object):
     def __init__(self):
         self.l = []
         self.d = collections.defaultdict(set)
 
     def insert(self, val):
         b = val not in self.d
         self.d[val].add(len(self.l))
         self.l.append(val)
         return b
 
     def remove(self, val):
         if val not in self.d:
             return False
         i, newVal = self.d[val].pop(), self.l[-1]
         if len(self.d[val]) == 0:
             del self.d[val]
         self.l[i] = newVal
         if newVal in self.d:
             self.d[newVal].add(i)
             self.d[newVal].discard(len(self.l)-1)
         self.l.pop()
         return True
 
     def getRandom(self):
         return random.choice(self.l)