Introduction to algorithms, Schemes and Mind Maps of Advanced Algorithms

This a notes of related to algorithms. you will get to know about basic of Algorithms.

Typology: Schemes and Mind Maps

2024/2025

Available from 08/01/2025

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Introduction to Algorithms
What is an algorithm ?
The word Algorithm means ” A set of rules
to be followed in calculations or other
problem-solving operations ” Or ” A
procedure for solving a mathematical
problem in a finite number of steps
frequently by recursive operations “.
Therefore Algorithm refers to a sequence of
finite steps to solve a particular problem.
Algorithms can be simple and complex
depending on what you want to
achieve.
We need to pick the “BEST” algorithm
There can be multiple ways to solve a
problem, but we want to minimize some
criteria in the procedure :
1. Time required to solve the problem
(Time complexity)
2. Extra space required to solve the
problem (Space complexity)
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Introduction to Algorithms

What is an algorithm? The word Algorithm means ” A set of rules to be followed in calculations or other problem-solving operations ” Or ” A procedure for solving a mathematical problem in a finite number of steps frequently by recursive operations “. Therefore Algorithm refers to a sequence of finite steps to solve a particular problem. Algorithms can be simple and complex depending on what you want to achieve. We need to pick the “BEST” algorithm There can be multiple ways to solve a problem, but we want to minimize some criteria in the procedure :

  1. Time required to solve the problem (Time complexity)
  2. Extra space required to solve the problem (Space complexity)

How Time complexity is measured Consider a job : Given a square plot of land with side = ‘a’, we need to buy fencing material to block animals from coming in.Also, we need to buy fertilizers for the total land area. Amount of fencing required For a square plot of side = ‘a’, the perimeter is = 4a. Amount of fertilizer required

Quick Glimpse of ‘Decidability’ For any algorithm (procedure), ask this question :  Can you tell me when the result is produced? If the answer is ‘YES’, then the algorithm is decidable. If the answer is ‘NO’ then the algorithm is undecidable. To fence ‘a’ metre of the plot takes 1 minute. How long will it take to fence the plot with side = ‘na’? 4na minutes. To spread fertilizer over ‘a 2 ’ area takes 1 hour. How long will it take to fertilize the plot with side = ‘na’? n 2 a 2 hours. We have planted the seeds. How long will it take for them to fully grow? not decidable : undecidable.