Lecture_Notes/imperfect_notes/Intro_to_Problem_Solving.md

Basic things for Motivation/ First Essential talk

Importance of Small Difference

• Example 1 :
  • Ask about Breaking Bad
  • discuss the importance of extra 3% clear crystals that walter white made
• Example 2 :
  • show Pictures of fastest man in India , Asia , World
  • discuss the impact of small millisec difference in timings
• Depict it with the equation - (1.01)^365 = 37.78

Qualities Essential to be the Best

• Ask about some essential qualities needed
• Discuss the importance of few -
  • Consistency
  • Persistance
  • Hardwork in right direction
  • The will power

Performace Equation

• Discuss about the Performace Equation - Performance = Potential - interference
• why the potential should be increased and interference should be decreased
• How can the performance be enhanced
  • Attend All Classes
  • Be Mindful
  • Learning is important

Many technologies, Where to start from?

• discuss about multiple technologies available , maybe ask students about some names

  • frontend - js,react , angular , vue etc
  • backend - java , python , ruby etc
  • Machine Learning

• introduce Data structures and Algorithms

  • define and differentiate
    • Data Structure - Something we need to organise data / keep data / Store data = Algorithms - the process / the steps
    • give an example of toothbrush being placed in kitchen
  • discuss about the importance of Data structures and Algorithms
  • Eventually reach to the conclusion that Data structure and Algorithms are important

Building a site more important than learning about Data Structures and Algorithms ?**

• Ask the question and then discuss the result with examples

• Example 1 : E-Commerce

  • Dicuss the flow from searching a product to buying it
  • Discuss why we need Data structures and Algorithms in following functionalities
    • Searching a Product - need to be fast
    • Sorting - basis of price , category , reviews etc
    • Search typeahead - throw the name of trie just to introduce a wow-factor
    • Concurrency problem - 1 product , 2 buyers
  • Eventually convince that DSA is more important than just building a site

• Example 2 : Food Delivery

  • Finding nearest restaurant
  • Sorting the list of restaurant - basis of name , reviews , location
  • Utilisation of resources (Explain with the help of diagram)
    • Shortest path of delivery
    • Shortest time is another factor to consider
    • more factors which finally helps in better utilisation of resources

• Ask if it's now clear that DSA is the basic building block

How Problem Solving works?

• Dicuss about the computer and decision making

• How the computer doesn't have mind of its own

• How every step needed to be told to computer based on several decisions

• Example 1 : ATM Machine

  • Discuss the process outline
  • Discuss the process in detail using decision tree (Don't introduce the name yet)
  • after drawing a basic decision tree - introduce with the name "Decision Tree"
  • Keep on focusing on the importance of decisions in problem solving

• Example 2 : Super Mario

  • Engage students by asking about the game
  • Discuss what decision making happend when you press -> arrow

• Example 3 : Pubg Game

  • Engage students by asking about the game
  • Discuss what decision making happens while a person shoots in pubg
  • How does energy/health reduction happens , what are different variables involved to make one decision
    • Aim
    • Distance
    • Type of Gun
    • Body Armor

"Observation" - The key to solve Problems

• Discuss about Guass

  • Ask students if they know about him, what they know
  • state the problem - tell them his teacher gave him the problem
  • Problem : Find the sum of numbers from 1 -> 100
  • discuss that He didn't jump on problem directly, made observation (focus on observation)

• Prime Numbers

  • What are prime Numbers

  • why 1 and 0 are not prime

  • Given a number check if it's prime or not - ask students for the solution

    • Approach 1 : Iterate from 1 -> N and check if it is divisble or not

    • Approach 2 : Sqaure root approach - traverse only till square root

      • Intution - factors always occurs in pairs - focus on presenting it as an observation

      • give proof by examples

      • Time analysis between O(N) and O(squareRoot(N))

        • Considering one % (mod operation - ask if they know) takes 1 msec

          N	Approach 1 - N steps	Approach 2 - sqaureRoot(N) steps
          11	11 msec	3 msec
          101	101 msec	10 msec
          100000	16.6 min	1 sec
          10^18	116 days	1.66 min

      • Ask them if they appreciate the improvement in timings - put more focus

• Find sqaure root of a given Number

  • Explain the problem - have to find the integer part

  • Approach - 1 :

    • iterate i from 1 to N and check if square of i is <= N
    • if square <= N - it is current ans
    • else stop the process - WHY? - Explain

  • Ask if the Approach 1 is fast enough to increase the curiosity

  • Approach - 2 :

    • start by stating an observation
    • pick some random element and check if it's square is <= or > than N
    • based on previous checks decide to ignore one part - properly explain this with example
    • now rather than picking random , pick middle element
    • reason for picking middle element - it always removes atleast half of the prospect solution

  • Discuss the time Analysis

How Data Structures helps in Problem Solving?

• Discuss how just the way of organising the data can optimise the solution

• Give example of toothBrush , how toothbrush stored in kitchen would result in ineffeciency

• Dictionary Word Search

  • Discuss the process of searching a word in dictionary
  • Relation with the sqaure root problem
  • Name of the Algorithm - Binary Search

• How are we able to apply the Binary Search

  • Order matters (Main situation)
  • Arrangement of Data Matters / Organisation of Data Matters

• HC Verma Example - searching a word in HC verma

  • Why Binary search won't work

  • No particular organisation of data

  • Can sort all the words - But is it effecient ? NO!

  • Discuss Index / Appendix

  • How data is stored in a different way which improves efficency

  word	page nos.
  velocity	100 101 167

  • Data Structure used - Inverted Index
  • All search engines use this to optumise the search

Conclusion

- Importance of Observation
- Importance of Data structures and Algorithms
- Importance of 3 essential qualities
- Further work