Algoritma
Dari Wikipedia bahasa Indonesia
Diagram Alur sering digunakan untuk menggambarkan sebuah algoritma.
Dalam matematika dan komputasi, algoritma merupakan kumpulan perintah untuk
menyelesaikan suatu masalah. Perintah-perintah ini dapat diterjemahkan secara bertahap
dari awal hingga akhir. Masalah tersebut dapat berupa apa saja, dengan catatan untuk
setiap masalah, ada kriteria kondisi awal yang harus dipenuhi sebelum menjalankan
algoritma. Algoritma akan dapat selalu berakhir untuk semua kondisi awal yang
memenuhi kriteria, dalam hal ini berbeda dengan heuristik. Algoritma sering mempunyai
langkah pengulangan (iterasi) atau memerlukan keputusan (logika Boolean dan
perbandingan) sampai tugasnya selesai.
Desain dan analisis algoritma adalah suatu cabang khusus dalam ilmu komputer yang
mempelajari karakteristik dan performa dari suatu algoritma dalam menyelesaikan
masalah, terlepas dari implementasi algoritma tersebut. Dalam cabang disiplin ini
algoritma dipelajari secara abstrak, terlepas dari sistem komputer atau bahasa
pemrograman yang digunakan. Algoritma yang berbeda dapat diterapkan pada suatu
masalah dengan kriteria yang sama.
Kompleksitas dari suatu algoritma merupakan ukuran seberapa banyak komputasi yang
dibutuhkan algoritma tersebut untuk menyelesaikan masalah. Secara informal, algoritma
yang dapat menyelesaikan suatu permasalahan dalam waktu yang singkat memiliki
kompleksitas yang rendah, sementara algoritma yang membutuhkan waktu lama untuk
menyelesaikan masalahnya mempunyai kompleksitas yang tinggi.
Sejarah istilah "algoritma"
Kata algoritma berasal dari latinisasi nama seorang ahli matematika dari Uzbekistan Al
Khawārizmi (hidup sekitar abad ke-9), sebagaimana tercantum pada terjemahan karyanya
dalam bahasa latin dari abad ke-12 "Algorithmi de numero Indorum" atau "Khwarizmi
concerning the Hindu art of reckoning
Nama lengkap Khwarizmi adalah Muhammad ibn Musa al-Khwarizmi.
algorisma adalah istilah yang merujuk kepada aturan-aturan aritmetis untuk
menyelesaikan persoalan dengan menggunakan bilangan numerik arab (sebenarnya dari
India, seperti tertulis pada judul di atas). Pada abad ke-18, istilah ini berkembang menjadi
algoritma, yang mencakup semua prosedur atau urutan langkah yang jelas dan
diperlukan untuk menyelesaikan suatu permasalahan.
Jenis-jenis Algoritma
Terdapat beragam klasifikasi algoritma dan setiap klasifikasi mempunyai alasan
tersendiri. Salah satu cara untuk melakukan klasifikasi jenis-jenis algoritma adalah
dengan memperhatikan paradigma dan metode yang digunakan untuk mendesain
algoritma tersebut. Beberapa paradigma yang digunakan dalam menyusun suatu
algoritma akan dipaparkan dibagian ini. Masing-masing paradigma dapat digunakan
dalam banyak algoritma yang berbeda.
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Divide and Conquer, paradigma untuk membagi suatu permasalahan besar
menjadi permasalahan-permasalahan yang lebih kecil. Pembagian masalah ini
dilakukan terus menerus sampai ditemukan bagian masalah kecil yang mudah
untuk dipecahkan. Singkatnya menyelesaikan keseluruhan masalah dengan
membagi masalah besar dan kemudian memecahkan permasalahan-permasalahan
kecil yang terbentuk.
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Dynamic programming, paradigma pemrograman dinamik akan sesuai jika
digunakan pada suatu masalah yang mengandung sub-struktur yang optimal (, dan
mengandung beberapa bagian permasalahan yang tumpang tindih . Paradigma ini
sekilas terlihat mirip dengan paradigma Divide and Conquer, sama-sama mencoba
untuk membagi permasalahan menjadi sub permasalahan yang lebih kecil, tapi
secara intrinsik ada perbedaan dari karakter permasalahan yang dihadapi.
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Metode serakah. Sebuah algoritma serakah mirip dengan sebuah Pemrograman
dinamik, bedanya jawaban dari submasalah tidak perlu diketahui dalam setiap
tahap; dan menggunakan pilihan "serakah" apa yang dilihat terbaik pada saat itu.
Daftar algoritma
Berikut adalah daftar algoritma.
Lihat juga daftar struktur data, daftar topik umum algoritma, dan daftar istilah yang
berhubungan dengan algoritma dan struktur data
1. Algoritma kombinatorial
Algoritma kombinatorial umum
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Algoritma pencari-siklus Floyd: iterasi untuk mencari siklus dalam
barisan/sekuens
(uniformly distributed) Pseudorandom number generators:
o Blum Blum Shub
o Mersenne twister
Robinson-Schensted algorithm: generates permutations from pairs of Young
tableaux
Algoritma graph
Artikel utama untuk bagian ini adalah: Teori graph
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Algoritma Bellman-Ford: menghitung jarak terpendek pada graf berbobot, di
mana sisi bisa memiliki bobot negatif
Algoritma Dijkstra: menghitung jarak terpendek pada graf berbobot, tanpa sisi
berbobot negatif.
Algoritma Floyd-Warshall: menghitung solusi jarak terpendek untuk semua
pasang titik pada sebuah graf berarah dan berbobot
Algoritma Kruskal: mencari pohon rentang minimum pada sebuah graf
Algoritma Prim: mencari pohon rentang minimum pada sebuah graf
Algoritma Boruvka: mencari pohon rentang minimum pada sebuah graf
Algoritma Ford-Fulkerson: computes the maximum flow in a graph
Algoritma Edmonds-Karp: implementation of Ford-Fulkerson
Nonblocking Minimal Spanning Switch say, for a telephone exchange
Spring based algorithm: algorithm for graph drawing
Topological sort
Algoritma Hungaria: algorithm for finding a perfect matching
Algoritma pencarian
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Pencarian linear: mencari sebuah item pada sebuah list tak berurut
Algoritma seleksi: mencari item ke-k pada sebuah list
Pencarian biner: menemukan sebuah item pada sebuah list terurut
Pohon Pencarian Biner
Pencarian Breadth-first: menelusuri sebuah graf tingkatan demi tingkatan
Pencarian Depth-first: menelusuri sebuah graf cabang demi cabang
Pencarian Best-first: menelusuri sebuah graf dengan urutan sesuai kepentingan
dengan menggunakan antrian prioritas
Pencarian pohon A*: kasus khusus dari pencarian best-first
Pencarian Prediktif: pencarian mirip biner dengan faktor pada magnitudo dari
syarat pencarian terhadap nilai atas dan bawah dalam pencarian. Kadang-kadang
disebut pencarian kamus atau pencarian interpolasi.
Tabel Hash: mencari sebuah item dalam sebuah kumpulan tak berurut dalam
waktu O(1).
Algoritma string
Pencarian
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Algoritma brute force
Algoritma Aho-Corasick
Algoritma Bitap
Algoritma Boyer-Moore
Algoritma Knuth-Morris-Pratt
Algoritma Karp-Rabin
Approximate matching
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Levenshtein edit distance
Algoritma penyusunan
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Binary tree sort
Bogosort
Bubble sort: for each pair of indices, swap the items if out of order
Bucket sort
Comb sort
Cocktail sort
Counting sort
Gnome sort
Heapsort: convert the list into a heap, keep removing the largest element from the
heap and adding it to the end of the list
Insertion sort: determine where the current item belongs in the list of sorted ones,
and insert it there
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Merge sort: sort the first and second half of the list separately, then merge the
sorted lists
Pancake sorting
Pigeonhole sort
Quicksort: divide list into two, with all items on the first list coming before all
items on the second list.; then sort the two lists. Often the method of choice
Radix sort: sorts strings letter by letter
Selection sort: pick the smallest of the remaining elements, add it to the end of the
sorted list
Shell sort: an attempt to improve insertion sort
Smoothsort
Stupid sort
Topological sort
2. Compression algorithms
Lossless compression algorithms
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Burrows-Wheeler transform: preprocessing useful for improving lossless
compression
DEFLATE: lossless data compression
Delta encoding: aid to compression of data in which sequential data occurs
frequently
Incremental encoding: delta encoding applied to sequences of strings
LZW: lossless data compression (Lempel-Ziv-Welch)
LZ77 (algorithm): LZ77 and LZ78 are the names for the two lossless data
compression algorithms
LZMA: short for Lempel-Ziv-Markov chain-Algorithm
LZO: data compression algorithm that is focused on speed
PPM compression algorithm
Shannon-Fano coding
Truncated binary encoding
Run-length encoding: lossless data compression taking advantage of strings of
repeated characters
SEQUITUR algorithm: lossless compression by incremental grammar inference
on a string
EZW (Embedded Zerotree Wavelet)
Entropy encoding: coding scheme that assigns codes to symbols so as to match
code lengths with the probabilities of the symbols
o Huffman coding: simple lossless compression taking advantage of relative
character frequencies
 Adaptive Huffman coding: adaptive coding technique based on
Huffman coding
o Arithmetic coding: advanced entropy coding
o Range encoding: data compression method that is believed to approach the
compression ratio of arithmetic coding
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Entropy coding with known entropy characteristics
o Unary coding: code that represents a number n with n ones followed by a
zero
o Elias delta|gamma|omega coding: universal code encoding the positive
integers
o Fibonacci coding: universal code which encodes positive integers into
binary code words
o Golomb coding: form of entropy coding that is optimal for alphabets
following geometric distributions
o Rice coding: form of entropy coding that is optimal for alphabets
following geometric distributions
Lossy compression algorithms
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Linear predictive coding: lossy compression by representing the spectral envelope
of a digital signal of speech in compressed form
A-law algorithm: standard companding algorithm
Mu-law algorithm: standard analog signal compression or companding algorithm
Fractal compression: method used to compress images using fractals
Transform coding: type of data compression for "natural" data like audio signals
or photographic images
Vector quantization: technique often used in lossy data compression
Wavelet compression: form of data compression well suited for image
compression (sometimes also video compression and audio compression)
3. Computational geometry
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Gift wrapping algorithm: determining the convex hull of a set of points
Graham scan determining the convex hull of a set of points in the plane
Point in polygon: tests whether a given point lies within a given polygon
4. Grafik komputer
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Bresenham's line algorithm: plots points of a 2-dimensional array to form a
straight line between 2 specified points (uses decision variables)
DDA line algorithm: plots points of a 2-dimensional array to form a straight line
between 2 specified points (uses floating-point math)
Flood fill: fills a connected region of a multi-dimensional array with a specified
symbol
Painter's algorithm: detects visible parts of a 3-dimensional scenery
Ray tracing: realistic image rendering
5. Algoritma Kriptografi
Lihat juga Topik dalam kriptografi
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Symmetric (secret key) encryption:
o Advanced Encryption Standard (AES), winner of NIST competition
o Blowfish
o Data Encryption Standard (DES), sometimes DE Algorithm, winner of
NBS selection competition, replaced by AES for most purposes
o IDEA
o RC4 (cipher)
Asymmetric (public key) encryption or digital signature:
o DSA
o ElGamal
o RSA
o Diffie-Hellman key exchange
o NTRUEncrypt
Cryptographic Message digest functions:
o MD5 – Note that there is now a method of generating collisions for MD5
o RIPEMD-160
o SHA-1
o HMAC: keyed-hash message authentication
Cryptographically secure pseudo-random number generators
o Blum Blum Shub - based on the hardness of factorization
o Yarrow algorithm
o Fortuna, allegedly an improvement on Yarrow
Other
o Diffie-Hellman: key exchange
6. Algoritma Distributed systems
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Lamport ordering: a partial ordering of events based on the happened-before
relation
Snapshot algorithm: a snapshot is the process of recording the global state of a
system
Vector ordering: a total ordering of events
7. Algoritma Numerical
See also main article numerical analysis and list of numerical analysis topics
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Algoritma De Boor: computes splines.
Algoritma De Casteljau: computes Bezier curves
False position method: approximates roots of a function
Gauss-Jordan elimination: solves systems of linear equations
Algoritma Gauss-Legendre: computes the digits of pi
Gauss-Newton algorithm: find minimum of function of several variables
Kahan summation algorithm: a more accurate method of summing floating-point
numbers
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Levenberg-Marquardt algorithm: find minimum of function of several variables
MISER algorithm: Monte Carlo simulation, numerical integration
Newton's method: finds zeros of functions with calculus
Bracketing Methods:
Rounding functions: the classic ways to round numbers
Secant method: approximates roots of a function
Shifting nth-root algorithm: digit by digit root extraction
Square root: approximates the square root of a number
Strassen algorithm
Optimization algorithms
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Simplex algorithm: An algorithm for solving the linear programming problem
Branch and bound
Simulated annealing
Genetic algorithms
Particle swarm
Tabu search
Local search
Digital signal processing
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CORDIC: Fast trigonometric function computation technique.
Fast Fourier transform: determines the frequencies contained in a (segment of a)
signal
o Cooley-Tukey FFT algorithm
Rainflow-counting algorithm: Reduces a complex stress history to a count of
elementary stress-reversals for use in fatigue analysis
Osem: algorithm for processing of medical images
Goertzel algorithm Can be used for DTMF digit decoding.
Discrete Fourier transform
o Rader's FFT algorithm
o Bluestein's FFT algorithm
8. Number theoretic algorithms
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Discrete logarithm:
o Baby-step giant-step
o Pollard's rho algorithm for logarithms
o Pohlig-Hellman algorithm
o Index calculus algorithm
Euclidean algorithm: computes the greatest common divisor
Integer factorization: breaking an integer into its prime factors
o Trial division
o Lenstra elliptic curve factorization
o Pollard's rho algorithm
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Pollard's p-1 algorithm
Congruence of squares
Quadratic sieve
Special number field sieve
General number field sieve
Jones's period proxy algorithm
Multiplication algorithms: fast multiplication of two numbers
Primality tests: determining whether a given number is prime
o AKS primality test
o Miller-Rabin primality test
o Sieve of Eratosthenes
o Sieve of Atkin
9. Numerical algebra
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Buchberger's algorithm: finds a Gröbner basis
Eigenvalue algorithm
Exponentiating by squaring: quickly computes powers of numbers and matrices
Gram-Schmidt process: orthogonalizes a set of vectors
Knuth-Bendix completion algorithm: for rewriting rule systems
Multivariate division algorithm: for polynomials in several indeterminates
10. Parsing
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Recursive descent parser: A top-down parser suitable for LL(k) grammars
LL parser: A relatively simple linear time parsing algorithm for a limited class of
context-free grammars
LR parser: A more complex linear time parsing algorithm for a larger class of
context-free grammars. Variants:
o Operator-precedence parser
o SLR (Simple LR) parser
o LALR (Look-ahead LR) parser
o Canonical LR parser
Packrat parser: A linear time parsing algorithm supporting some context-free
grammars and parsing expression grammars
CYK algorithm: An O(n3) algorithm for parsing any context-free grammar
Earley's algorithm: Another O(n3) algorithm for parsing any context-free grammar
11. Teknik perangkat lunak
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Algorithms for Recovery and Isolation Exploiting Semantics: recovery
Unicode Collation Algorithm
CHS conversion: Converting between disk addressing systems
Cyclic redundancy check: calculation of a check word
Parity: Simple/fast error detection technique. Is a number even or odd?
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Diff: compare two sequences. An example of Dynamic programming (dynamic
refers to the property that the optimal solution can be constructed by combining
optimal solutions to sub-problems e.g. quicksort).
12. Algoritma kuantum
Application of quantum computation to various categories of problems and algorithms
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Grover's algorithm: provides quadratic speedup for many search problems
Shor's algorithm: provides exponential speedup for factorizing a number
Deutsch-Jozsa algorithm: criterion of balance for Boolean function
13. Algoritma medis
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Medical algorithm
Texas Medication Algorithm Project
14. Lainnya
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Astronomical algorithms
Banker's algorithm
Baum-Welch algorithm
Doomsday algorithm: day of the week
Levenberg-Marquardt nonlinear least squares fitting algorithm
Marzullo's algorithm: distributed clock synchronization
Page replacement algorithms
Risch algorithm
Schreier-Sims algorithm
Todd-Coxeter algorithm
Viterbi algorithm
Xor swap algorithm: menukar nilai 2 variabel tanpa menggunakan buffer
tambahan
How ancient Sinhala Brahmi numerals were invented
by Brigadier (Retd) B. Munasinghe
Man made an attempt to count on their fingers or the use of
pebbles and then invented words for numbers and later
devised a system of symbols to record them. The people of
this Island can be proud that some of these attempts of the
ancient Sinhala is preserved on various rock inscriptions.
The inscriptions that record almost all our ancient Sinhala numerals is at the Dhakkina
Vihare rock inscription in Anuradhapura. The inscription is a record of donations of land
to this Tisa maha stupa during the period of King Sirinaga (195-214 AD).
These ancient numerals of the Sinhala, have a close resemblance to the numerals
preserved in most other ancient states in the Indian subcontinent. They all appear to have
evolved from a common source. The earliest known specimen is of King Asoka of the
third Cent BC, where the numerals 1, 2, 4, 6, 7 and 9, are preserved on at inscription near
Bombay in Nanaghat as:
The next important
trace of these numerals, are of the second Cent AD at Nasik, India. The numerals are
similar to those at Dakkhini Vihare and are of the same period.
The scan of best preserved of the numerals used by the Sinhala, the 3, 4, 5, 6, 8, 9, from
Dhakkina Vihare (2 Cent AD) and numeral 2 from Kasimotti (1 Cent AD) and numeral 7
from Baki-ala (1 Cent AD), to complete the list is shown below. A vivid description of
these symbols is found in samskrti cultural quarterly No. 17 No. 3 of 1984 by Dr. Abaya
Aryasinghe.
As per the book `The History of Mathematics by David M
Burton' which traces the origin of the present universally
accepted numerals, it was Al-Khowarizmi the famous
Arab mathematician who introduced these numerals in his
book Algorithmi de numero indorum in 830 AD. Here he
described the use of these nine numeral and zero as a place holder in the Indians
mathematics. This knowledge was taken to Spain by the moors and the oldest dated
European manuscript preserved is the Cordex Vigilanus (976 AD).
The Italian Leonardo of Pisa (Fabonacci) the greatest mathematician of the middle ages
in his book liber Abaci (Book of counting) was the first to suggest the advantages of
these numerals over the Roman numerals. The Portuguese or the Dutch re-exported these
numerals back to the island.
The symbols for ancient Sinhala
numerals for 3, 4, 5, 6, 7, 8, 9, 40, 50,
70, 100 and 1000 are all recorded at
the Dhakkina Vihare ( inscription of
Ceylon volume II part II No. 100)- Dr.
S. Paranavithana. These are on 17
slabs marked from I to XVII in the
same book. These numerals appear
with the symbol for the then Sinhala standard measure of land, the Kariha. For the
convenience of visitors to this site, a description where to look in the slabs at Dhakkina
Vihare is given below along with the scans of the slabs.
The scans of inscription shown above are those at Baki - Ala and Kariamottai. These are
described in inscriptions of Ceylon volume II part I -Dr. S. Paranavitana.
Dhakkina Vihare - 2 Cent AD
a. Slab No. V: line 1 ninth letter is the sign for the Karisa
(KA) followed numeral 100 and 6 then the KA symbol
followed by numeral 3. (Fig i)
b. Slab No. VII: line 2 ; tenth letter is KA followed by numeral 100 and 4, then KA
symbol followed by numeral 70 and 7.
c. Slab No. IX: line 7; numeral 100 and numeral 9, the KA symbol and
numeral 4. (Fig ii)
d. Slab XI: line 5; numeral 50 Ka symbol then numeral 5. (Fig iii)
e. Slab XII: line 4; first letter numeral 100 and 4 followed by KA symbol
and numeral 20. (Fig v)
f. Slab XIII: line 6: third symbol is KA followed by numerals 1000 then KA followed by
numeral 100. (Fig v)
g. Slab XIV: line 7 first symbol KA followed by numeral 50 (Fig vi) the letter eighteen
KA and 50.
Line 8; first symbol is KA followed by numeral 8. Second symbol first line from bottom
(Fig vi) Line 9; first symbol is KA symbol followed by numeral 40.
sumber dari :
1. id.wikipedia.org
2. members.tripod.com/~khorasan/TajikPersonalities/Khwarizmi.htm
3. http://www-groups.dcs.stand.ac.uk/~history/Miscellaneous/Pearce/Lectures/Ch8_3.html