Album of Algorithms and Techniques
Contents

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Combinatorial Algorithms
Generation of all subsets with K elements
Generation of permutation sequences

Linear Algebraic Equations
LU decomposition
Solution of linear algebraic equations
Determinant of a matrix
Inverse of a matrix

Merging

Mode Problem

Number-Theory
Complex arithmetic
Diophantine linear equation
Euclid's GCD (and LCM) algorithm
Euler's number e
Euler's constant gamma
Extended Euclid's algorithm
Factorial
Fibonacci numbers
Modular linear equations
Number Pi
Number of combinations
Primes
Roman to decimal and the other way round
Rational arithmetic

Functions
Area of a triangle
Exponential function
FLOOR, CEILING and MOD
Natural logarithm
Logarithms with other bases than e
Sine and cosine function
Square root of positive real numbers
SQRT(P**2 + Q**2)
Power - integer exponent
Power - real exponent

Polynomials and Matrices
Evaluation
Evaluation of polynomial and its derivatives
Addition
Addition for sparse polynomials
Division
Matrix multiplication

Random Numbers and Permutations
Linear congruential generator
Random permutation
Random sampling

Interpolation and Extrapolation
Polynomial
Rational function
Cubic spline interpolation

Selecting
Smallest and largest simultaneously
Find
Modifind
Select

Searching
Binary search
Interpolation search
Sequential search
Sequential search without sentinel
Search in associative arrays
Search an array of abscissas
All pairs of numbers A.I, A.J with A.I+A.J=X

Sorting
Counting sort
Shellsort
 Heapsort
iterative Quicksort
recursive Quicksort
sophisticated Quicksort
Quicksort - sorting in descending order
Topological

String-Matching
Matcher for real strings
Naive string matcher
Knuth-Morris-Pratt matcher
Boyer-Moore algorithm

Subset-Sum Problem
Exponential-time exact algorithm
Dynamic programming
Greedy algorithm
Polynomial-time approximation algorithm

Techniques
Beforehand computed constants
Bit array encoded as decimal number
Bitwise operations
How to interchange the values of variables
Recursion elimination
Representation of stacks, queues, and deques
Sentinels
Test data sets
 Test environment
Universal unit