Algorithm design

Accurately modeling a problem is an art, and the key to applying algorithm design techniques to real-world problems. Most algorithms are designed to work on rigorously defined abstract structures. Algorithms and data structures are inseparable, however, by data structures, we do not mean data structure implementation for any specific OS or language.

Two basic paradigms used for modeling problems are divide and conquer and dynamic programming.

• Divide and conquer usually splits the problem in half and solves for each half, then combines the result to get the full solution.
• Dynamic programming is typically applied to optimization problems. The development of a dynamic-programming algorithm can be divided into a series of four steps:
  1. Characterize the structure of an optimal solution.
  2. Recursively define value of an optimal solution.
  3. Compute the value of an optimal solution in bottom-up fashion.
  4. construct an optimal solution from computed information.