The very first container class we implemented was the random bag, which supported two operations:

add, which adds an element to the random bag, and

removeRandom, which chooses a random element from the bag and returns it$.$

Below is our implemented code for RandomBag class. First, RandomBag.hppNext, RandomBag, cpp:Your task in this problem is to answer the following questions. Before that, recall the following important fact:Fact: The vector: : erase $()$ function, takes time proportional to the distance between the element being removed and the last element of the Vector. The reason for this is that whenever a gap opens up in the vector, it has to shift all the elements after the gap down one spot, As a result, removing from the very end of a vector is quite fast $-$ it runs in time O$(1)-$ but removing from the very front of a vector takes time O$($n$).$Q$1(5$ points$)$ Look at the implementation of our RandomBag: :removeRandom function. What is its worst$-$case time complexity? How about its best$-$case time complexity? How about its average$-$case time complexity?Q$2(5$ points$)$ Based on your answer to the previous part of this question, what is the worst$-$case time complexity of removing all the elements of an n$-$element RandomBag? What's the best$-$case time complexity? How about its average case?Q$3(10$ points$)$ In the preceding discussion, we mentioned that removing the very last element of a vector is much more efficient that removing an element closer to the middle. Write another member function RandomBag: :removeRandomFast so that it always runs in worst$-$case O$(1)$ time. In fact, there should only be two lines of code that are different from our current implementation.