Exponential Complexity
As we have seen previously, algorithms that have an exponential runtime complexity scale really poorly. There are many examples of problems for which only an O(kn) solution is known. Improving these algorithms is a very dynamic area of study in computer science. Examples of these include the traveling salesman problem and cracking a password using a brute force approach. Now, let's see an example of such problem.
A prime number is only divisible by itself and one. The example problem we present here is called the prime factorization problem. It turns out that if you have the right set of prime numbers, you can create any other possible number by multiplying them all together. The problem is to find out these prime numbers. ...
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