Introduction to Algorithms

This book covers techniques for the design and analysis of algorithms. The algorithmic techniques covered include: divide and conquer, backtracking, dynamic programming, greedy algorithms, and hill-climbing.Any solvable problem generally has at least one algorithm of each of the following types:1.the obvious way;2.the methodical way;3.the clever way; and4.the miraculous way.On the first and most basic level, the "obvious" solution might try to exhaustively search for the answer. Intuitively, the obvious solution is the one that comes easily if you're familiar with a programming language and the basic problem solving techniques.The second level is the methodical level and is the heart of this book: after understanding the material presented here you should be able to methodically turn most obvious algorithms into better performing algorithms.The third level, the clever level, requires more understanding of the elements involved in the problem and their properties or even a reformulation of the algorithm (e.g., numerical algorithms exploit mathematical properties that are not obvious). A clever algorithm may be hard to understand by being non-obvious that it is correct, or it may be hard to understand that it actually runs faster than what it would seem to require.The fourth and final level of an algorithmic solution is the miraculous level: this is reserved for the rare cases where a breakthrough results in a highly non-intuitive solution.Naturally, all of these four levels are relative, and some clever algorithms are covered in this book as well, in addition to the methodical techniques. Let's begin.