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Mastering Algorithms for Problem Solving in Python

What is an Algorithm?

Learn to define an algorithm as a precise sequence of steps designed to solve specific problems. Understand its historical origins from al-Khwarizmi's work to modern computation, and see practical examples that clarify algorithm implementation and design principles.

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Introduction to algorithm

An algorithm is an explicit, precise, unambiguous, mechanically executable sequence of elementary instructions, usually intended to accomplish a specific purpose. For example, here is an algorithm for singing that annoying song “99 Bottles of Beer on the Wall” for arbitrary values of the starting number of beer bottles:

Algorithm

BottlesofBeer(n)‾    For i←n down to 1Sing “i bottles of beer on the wall, i bottles of beer,”Sing “Take one down, pass it around, i−1 bottles of beer on the wall.”Sing “No bottles of beer on the wall, no bottles of beer,”Sing “Go to the store, buy some more, n bottles of beer on the wall.”\underline{Bottles of Beer(n)} \\ \space\space\space\space For\space i ←n\space down\space to\space 1\\ \hspace{1cm} Sing\space “i\space bottles\space of\space beer\space on\space the\space wall,\space i\space bottles\space of\space beer,” \\ \hspace{1cm} Sing\space “Take\space one\space down,\space pass\space it\space around,\space i − 1\space bottles\space of\space beer\space on\space the\space wall.” \\ \hspace{0.35cm} Sing\space ...