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Non-Linear Growth
Exponents are important to understand when it comes to the execution speed of an algorithm. If the number of operations grows quickly as the amount of input data increases, the algorithm will become slower and slower.
| Linear | Quadratic |
|---|---|
2 * 2 = 4 |
2 ** 2 = 4 |
3 * 2 = 6 |
3 ** 2 = 9 |
4 * 2 = 8 |
4 ** 2 = 16 |
5 * 2 = 10 |
5 ** 2 = 25 |
6 * 2 = 12 |
6 ** 2 = 36 |
7 * 2 = 14 |
7 ** 2 = 49 |
8 * 2 = 16 |
8 ** 2 = 64 |
9 * 2 = 18 |
9 ** 2 = 81 |
- The doubling formula,
2*x, results in linear or straight growth. - The quadratic formula,
x^2, keeps growing faster and faster.
What Does This Have to Do With Code?
Generally we try to avoid writing code that causes the usage of a resource to grow quadratically (with an exponent).
- Sometimes that's a lot of computations (CPU utilization / slowness).
- Sometimes that's a lot of memory usage (RAM utilization)
- Sometimes that's a large storage requirement (disk space)
A notable exception is in cryptography and security: we want to force attackers to waste resources trying to get at our information.