An Example of an Algorithm
Suppose you are given an unsorted list of numbers and want to find the largest number in this list.
- How do you do it?
- Do you have to look at every number in the list?
- Might you have to look at each number more than once?
- Is there a best or optimal way to do it?
- How do we measure how much work a computer must do when using an algorithm?
Here's an informally described algorithm:
And here is a more formal coding of the algorithm in a pseudocode
that is similar to most programming languages
- When you begin, the first number is the largest number in the list you've seen so far.
- Look at the next number, and compare it with the largest number you've seen so far.
- If this next number is larger, then make that the new largest number you've seen so far.
- Repeat steps 2 and 3 until you have gone through the whole list.
Given: a list of numbers "list"
largest = list
counter = 2
while counter <= length(list)
if list[counter] > largest
largest = list[counter]
counter = counter + 1
Are their other algorithms for solving this general problem?
- Sure: Sort the list of numbers and then pick the one at the end of the list.
- This is obviously not as good as the first algorithm.
It's easy to prove that:
- Any algorithm has to look at every number.
- You only have to look at each number once
- If we measure the work in terms of a basic operation of <i> comparing
one number with another</i> then finding the largest of N numbers takes
- So we can prove that our algorithm is optimal, in general
last modified on Tuesday, 22-Aug-2006 07:14:15 EDT