Why Algorithms Matter

Exercise #1

There’s an age old puzzle that goes as follows: You’re at a river with two buckets. One holds exactly 3 liters, and one holds exactly 5 liters. Figure out how to measure out exactly 4 liters using those two buckets.

1. Develop two different algorithms for measuring out 4 liters.
2. Which of your algorithms is more efficient? That is, how many steps does each algorithm take?

Exercise #2

How many steps would it take to insert the number 7 into the ordered array of [2, 4, 6, 8, 10, 12]?

Exercise #3

How many steps would it take to search for the number 8 in the ordered array: [2, 4, 6, 8, 10, 12]?

Exercise #4

How many steps does it take to perform binary search on array of size 200?

Exercise #5

How many steps does it take to perform binary search on array of size 400?

Exercise #6

Use your favorite object-oriented programming language to create a class that represents an ordered array. It should include functions/methods that serve as the key operations: Read, search, insert, and delete. Ensure that the insert operation inserts the value in the correct place within the ordered array.