Page 103 - Computer science 868 Class 12
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Similarly, for any problem solving be it our day-to-day work, or any mathematical or computational problem, we need
                 to follow a set of steps in a proper sequence, to achieve our desired goal. In mathematics and computer science, this
                 process of listing instructions step-wise is called an Algorithm.

                                                               Definition

                       An algorithm is a set of well-defined finite steps or rules to be followed to solve any given problem.



                 The word Algorithm derives from the name of the book “Algoritmi” written in Latin.
                 The book was a translation of the works of eminent Persian scientist, astronomer and
                 mathematician of the 9th century, Abdullah Muhammad bin Musa al-Khwarizmi, often
                 referred as “The father of Algebra”, But the idea of algorithms existed long before that.
                 Let us go back to history, and know about a few of them.
                 •  Vedic mathematicians used the “ūrdhva tiryagbhyāṃ” algorithm to perform integer
                   multiplication quickly.


                                                                                                   Muhammad Ibn Musa al
                                                                                                         Khwarizmi
                                                                                                        (1646–1716),
                                                                                                      a Mathematician
                                                                                                   Astronomer, Geographer
                                                                                                        and Historian




                 •  Vedic mathematicians Brahmagupta, Bhaskara and Jaydeva developed a cyclic algorithm called “Chakravala” to
                   solve quadratic equations.
                 •  The  Babylonian-Sumerian  method  of  extracting  roots  is  believed  to  be  the  first  documented  algorithm  of
                   mathematical computation.
                 •  The Sieve of Eratosthenes algorithm was designed by Greek mathematicians to find prime numbers.

                     3.3 PSEUDOCODES AND FLOWCHARTS
                 We now know that an algorithm is a step-by-step sequence of solving a problem. It is written in a natural language like
                 English. There is no standard form or syntax for writing an algorithm. It is a systematic and logical approach for solving
                 a specific problem and is used in planning during the software development process.

                 There can be several other approaches to do the same namely using pseudo codes and flowcharts. Let us discuss them
                 one by one.


                 3.3.1 Pseudocodes
                 A pseudocode is an informal way of writing a program, but not in any high-level language. It represents the algorithm
                 in simple English statements (or any other recognised language) and mathematical notations. Like algorithms, there is
                 no definite syntax to follow when writing pseudocodes and it is mainly used for documentation purposes. In pseudo
                 code, knowledge of programming language is not compulsory, rather the plan to derive an efficient solution to the
                 problem and expressing it in simple language is a must.

                                                               Definition

                       Pseudocode is a representation of an algorithm in any standard human readable language and mathematical notations.




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                                                                            Implementation of Algorithms to Solve Problems  101
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