Given the following: a.) What is the worst-case time complexity of this algorith

Question

Given the following:

a.) What is the worst-case time complexity of this algorithm? Support your answer.

b.) What is the best-case time complexity of this algorithm? Support your answer.

There is a deck of cards with 4 different suits (spades, clubs, hearts, and diamonds). You want to use the following algorithm to sort this deck of cards such that all cards with the same suit are grouped together in ascending order. i Step 1: Assign 4 boxes one for each suit, one for hearts, one for clubs, one for diamonds, and one for spades. ii) Step 2: Distribute the cards in the corresponding boxes one at a time such that each card is placed in the box with the correct corresponding suit. iii) Step 3: Independently, sort the cards that are in each box using Insertion sort. iv) Step 4: Go over the boxes in order and put all the sorted cards back together (order of the groups does not matter With only 4 suits, given a deck of size n (there could be n cards in the deck: there may be more than 52 standard cards in a deck.)

Explanation / Answer

Let n be the number of cards. then

Step 1 takes constant time, so it's time complexity is O(1)

Step 2 takes O(n) time to distribute in both best case and worst case

Step 3 insertion sort in each case sorts n/4 cards. This will take O(n) time in best case and O(n2) time in worst case.

Step 4 takes constant time again, so it's time complexity is O(1)

a. To sum up, in the best case, the time complexity is O(n)

b. In worst case, the time complexity is O(n2)

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