Thursday, January 14, 2010

A Quick Tip: The Different Classes Of Algorithms

Algorithms are the heart of computer science. They are the thoughts, the ideas, and the most fun part of this industry. Scientists categorize the various known algorithms into 4 classes: Logarithmic, Linear, Quadratic and Exponential. Let's look at those briefly:
1- Logarithmic Algorithms:
   This type is the fastest of those 4 classes. It has a run curve that looks something like this:

Where the x here is the number of items to be processed by the algorithm, and y is the time takes by the algorithm. As you can see from the figure, the time taken increases slowly when the number of items to be processed increase. Binary Search is a perfect example for a logarithmic algorithm. If you recall, binary search, divides the array into two halves and excludes one half each time it does a search. Here's a code example of binary search implementation in C#:
bool BSearch(int[] list, int item, int first, int last)
 if(last - first < 2)
             return list[first] == item || list[last] == item;
        int mid = (first + last)/2;
        if(list[mid] == item)
             return true;
        if (list[mid] > item)
                return BSearch(list, item, first, mid - 1);
 return BSearch(list, item, mid + 1, last);

2- Linear Algorithms:
  Runs in time, linear to the input items. It's curve looks like the following:

A linear search is a typical example of that, where one would traverse the array or, whatever data structure, item by item. An implementation of linear search looks like this:

bool LinearSearch(int[] list, int item)
     for(int i = 0; i < list.Length; i++)
          if(list[i] == item)
              return true;
        return false;
3- Quadratic Algorithm:    This one runs time grows to to the power of 2, with each increase in the input sizes, which means while processing 2 items the algorithm will do 4 steps, 3 items will take 9 steps, 4 items will take 16 steps, etc. The next figure shows how a quadratic curve might look like:

A famous example of an algorithm with quadratic growth is Selection Sort:

void SelectionSrot(int[] list)
            int i, j;
            int min, temp;

            for (i = 0; i < list.Length - 1; i++)
                min = i;

                for (j = i + 1; j < list.Length; j++)
                    if (list[j] < list[min])
                        min = j;

                temp = list[i];
                list[i] = list[min];
                list[min] = temp;

4- Exponential Algorithm:
This is the super slow of this list of four. It grows exponentially (that is, for 2 items it takes 2 ^ 2, for 3 items it takes 2^3, for 4 items it takes 2 ^ 4, etc.
Again algorithms are the key to computer science, the most fun part of programmer's  job. Choose your algorithms carefully and always try to improve.

Hope this helps.


kink said...

A more fine-grained and comprehensive listing:

Galilyou said...

Nice table, good link. Thank you!