23. Methodology of Problem Solving

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How to Solve Problems
Problem Solving
Software University
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#fund-common
Questions?
2

Table of Content
1. What Is a Problem?
2. Stages of Problem Solving
3. Complexity of a Problem
4. Example Problems
5. From...

What Is a Problem?
Current and Desired State Diff

 Definition - a doubtful or difficult matter,
requiring a solution
 Goals - anything you wish to achieve,
anywhere you w...

Stages
Stages of Solving a Problem

 Define the problem
 Analyse the problem
 Identify potential solutions
 Evaluate and choose the best solution
 Plan a...

 What are the steps to cross the street successfully ?
Problem Street Crossing
8

 Recognizing that there is a problem, identifying the nature
of the problem, defining the problem
Problem Identification
...

 Observation
 Inspection
 Fact-finding
 Developing a clear picture
of the problem
Structure of the Problem
10

 Generating a range of possible courses of action and trying to
evaluate them
 Analyzing the different possible solution...

 Connect all the nine dots,
using only 4 lines
Nine Dots Problem
12

 Let's think outside the box!
 What has changed?
 Our point of view
Nine Dots Problem
13

Examples
Solving Problems

The Missing Piece
15

 You are mixing cement and the recipe calls for five gallons of water
 You have a garden hose giving you all the water y...

 You have 10 stacks of 10 gold coins
 All the coins in one of these stacks are counterfeit,
all the other coins are not
...

Solutions

The Missing Piece
19

The Missing Piece
20
 The gradient of the teal hypotenuse is different than the
gradient of the red hypotenuse

 Fill the 4-gallon bucket
 Empty the 4-gallon bucket into the 7-gallon bucket
 Fill the 4-gallon bucket
 Pour the 3 ga...

 We take one coin from pile #1, two coins from pile #2, three coins
from pile #3 and so on until we have 10 coins from pi...

10 Piles of 10 Coins One of Which Is Fake (2)
23
 However, some of them will be fake
 Let's say we place them all on the...

Solving
From Chaotic to Methodological Approach

Read and Analyze the Problems
25
 Consider you are at a computer programming exam or contest
 You have 5 problems to sol...

Use a Sheet of Paper and a Pen
26
 Never start solving a problem without a sheet of paper + a pen
 You need to sketch yo...

Prefer Squared Paper
27
 Squared paper works best for
algorithmic problems
 Easy to draw a table
 Easy to draw a coordi...

Paper and Pen
28
 Consider a "Cards Shuffle" problem
 We can sketch it to start thinking
 Some ideas immediately come, ...

Invent Ideas
Think-up, Invent Ideas and Check Them

Think Up, Invent and Try Ideas
30
 First take an example of the problem
 Sketch it on the sheet of paper
 Next try to i...

Think Up, Invent and Try Ideas
31
 Idea #1: random number of times split the deck into left and
right part and swap them
...

Think Up, Invent and Try Ideas
32
 Idea #3: swap 2 random cards a random number of times
 How to choose two random cards...

Divide and Conquer
Decompose Problems into Manageable Pieces

Decompose the Problem
34
 Work decomposition is natural in engineering
 It happens every day in the industry
 Projects ...

Divide and Conquer – Example
35
 Let's try idea #1:
 Split the deck into left and right part and swap them
(many times)
...

Sub-Problem #1 (Single Exchange)
36
 Split the deck into two parts at random split point
 And exchange these 2 parts
 W...

Sub-Problem #2 (Single Exchange)
37
 Choosing a random split point
 Need to understand the concept of pseudo-random numb...

Sub-Problem #3 (Single Exchange)
38
 Combining a sequence of single exchanges to solve
the initial problem
 How many tim...

Check-Up Your Ideas
Don't Go Ahead Before Checking Your Ideas

Check-Up Your Ideas
40
 Check-up your ideas with examples
 It is better to find a problem before the idea is implemented...

Check-Up Your Ideas – Example
41
 Let's check the idea:
 After 3 random splits and swaps we obtain the start position
 ...

Invent New Idea If Needed
42
 What to do when you find your idea is not working in all cases?
 Try to fix your idea
 So...

Invent New Ideas – Example
43
 Invent a few new ideas:
 New idea #1 – multiple times select 2 random cards and
exchange ...

Check-Up the New Idea – Example
44

Implementation
Coding and Testing Step-By-Step

Start Coding: Checklist
46
 Never start coding before you find a correct idea that will meet
the requirements
 What shal...

Implement Your Algorithm Step-By-Step
47
 "Step-by-step" approach is always better than
"build all, then test"
 Implemen...

Testing the Code
Thoroughly Test Your Solution

Thoroughly Test Your Solution
49
 Always test thoroughly your solution
 Invest in testing!
 One 90-100% solved problem ...

How to Test?
50
 Testing could not certify absence of defects
 It just reduces the defects’ rates
 Well tested solution...

Read the Problem Statement
51
 Read carefully the problem statement
 Does your solution print exactly what is expected?
...

 …
 …
 …
Summary
52
 Problem solving needs methodology:
 Understanding and analyzing problems
 Using a sheet of pape...

 https://softuni.bg/courses/programming-fundamentals

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SoftUni Organizational Partners

 Software University – High-Quality Education and
Employment Opportunities
 softuni.bg
 Software University Foundation
...

 This course (slides, examples, demos, videos, homework, etc.)
is licensed under the "Creative Commons Attribution-NonCom...

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