# Problem 02

## Problem 02

An algorithm consists of two steps: a slow part which takes 99% of the computation time, and a fast part which takes 1% of the computation time. After someone improved the slow part (and didn't touch the fast part), the slow part takes only 98% of the total execution time. Before the improvement, the algorithm took 600 seconds to execute. How many seconds does it take after this improvement?

### Solution

The fast part is unchanged, so it takes 1% of 600 seconds, which is 6 seconds. After the improvement, these 6 seconds are now 2% of the total, which means the total is now 300 seconds.

### Remarks

Intuitively, students don't seem to think it's a big improvement. Their answer are all around 594 seconds. And this is a problematic misconception, especially for a computer science major. While not directly related to any theory of discrete mathematics, it is an important lesson in evaluating improvements to their work.