# An Example from Computer Languages

Here is an example drawn from my own personal experience. Many years ago when I was a graduate student there was a fellow student who was pursuing a project in DNA research. His particular problem had a very trivial statement. A strand of DNA can be thought of as simply a very long sequence of four elements, which could be represented by the letters A, C, T and G. His task was to see if any sequence of M values was repeated. Here N, the number of elements in the DNA sequence, is hugely long but M, the size of the repeated sequence, was very small.

At the time FORTRAN was, and still is, considered the most ``efficient'' computer language. To find the repeated sequence the student therefore wrote a very short and direct FORTRAN program. If you don't read FORTRAN don't worry, this program is simply the obvious triply nested loop, where the two outer loops control the starting point for a comparison search, and the third inner loops compares the next M elements. If the inner loop completes without finding any differences, then a matching sequence has been found.

The student tried the program on some small data sets and measured the time. Extrapolating these measurements, the student then discovered that to run on the real data set would take several days. At this time the mean time between failure of computers was measured in hours, so the depressed student determined that the likelihood of being able to run the program to completion was very small.