Algorithms

This book aims to be an accessible introduction to the design and analysis of efficient algorithms. Throughout the book we will introduce only the most basic techniques and describe the rigorous mathematical methods needed to analyze them. The topics covered include: - The **divide and conquer** tec

[Top]( Chapters: 1, [2]( [3]( [4]( [5]( [6]( [7]( [8]( [9]( [A]( 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 genera

[Top]( Chapters: [1]( 2, [3]( [4]( [5]( [6]( [7]( [8]( [9]( [A]( Before we begin learning algorithmic techniques, we take a detour to give ourselves some necessary mathematical tools. First, we cover mathematical definitions of terms that are used later on in the book. By expanding your mathematical

[Top]( Chapters: [1]( [2]( 3, [4]( [5]( [6]( [7]( [8]( [9]( [A]( The first major algorithmic technique we cover is **divide and conquer**. Part of the trick of making a good divide and conquer algorithm is determining how a given problem could be separated into two or more similar, but smaller, subp

[Top]( Chapters: [1]( [2]( [3]( 4, [5]( [6]( [7]( [8]( [9]( [A]( As deterministic algorithms are driven to their limits when one tries to solve hard problems with them, a useful technique to speed up the computation is **randomization**. In randomized algorithms, the algorithm has access to a random

[Top]( Chapters: [1]( [2]( [3]( [4]( 5, [6]( [7]( [8]( [9]( [A]( **Backtracking** is a general algorithmic technique that considers searching every possible combination in order to solve an optimization problem. Backtracking is also known as **depth-first search** or **branch and bound**. By inserti

[Top]( Chapters: [1]( [2]( [3]( [4]( [5]( 6, [7]( [8]( [9]( [A]( **Dynamic programming** can be thought of as an optimization technique for particular classes of backtracking algorithms where subproblems are repeatedly solved. Note that the term dynamic in dynamic programming should not be confused

[Top]( Chapters: [1]( [2]( [3]( [4]( [5]( [6]( 7, [8]( [9]( [A]( In the backtracking algorithms we looked at, we saw algorithms that found decision points and recursed over all options from that decision point. A **greedy algorithm** can be thought of as a backtracking algorithm where at each decisi

[Top]( Chapters: [1]( [2]( [3]( [4]( [5]( [6]( [7]( [8]( 9, [A]( Please edit and omit unweighted in title ## Representation of Graph ### Adjacency Matrix The rows/columns are the source/target vertex, the matrix is a square matrix with non-negative entries, 0 if there is no edge between the vertices

Calculating distances is common in spatial and other search algorithms, as well as in computer game physics engines. However, the common Euclidean distance requires calculating **square roots**, which is often a relatively heavy operation on a CPU. ## You don't need a square root to compare distance

[Top]( Chapters: [1]( [2]( [3]( [4]( [5]( [6]( [7]( [8]( [9]( A Welcome to the Ada implementations of the [Algorithms]( Wikibook. For those who are new to [Ada Programming]( a few notes: - All examples are fully functional with all the needed input and output operations. However, only the code neede