Methodology of Methodology of Problem SolvingProblem Solving

Efficiently Solving Computer Efficiently Solving Computer Programming Problems Programming Problems

Svetlin NakovSvetlin NakovTelerik Telerik

CorporationCorporationwww.telerik.com

Problems SolvingProblems SolvingFrom Chaotic to Methodological From Chaotic to Methodological

ApproachApproach

How to Solve Problems?How to Solve Problems?

1.1. Read and Analyze the ProblemsRead and Analyze the Problems

2.2. Use a sheet of paper and a pen for Use a sheet of paper and a pen for sketchingsketching

3.3. Think up, invent and try ideasThink up, invent and try ideas

4.4. Break the problem into subproblemsBreak the problem into subproblems

5.5. Check up your ideasCheck up your ideas

6.6. Choose appropriate data structuresChoose appropriate data structures

7.7. Think about the efficiencyThink about the efficiency

8.8. Implement your algorithm step-by-stepImplement your algorithm step-by-step

9.9. Thoroughly test your solutionThoroughly test your solution3

Understanding the Understanding the RequirementsRequirements

Read and Analyze the Read and Analyze the ProblemsProblems

Consider you are at traditional computer Consider you are at traditional computer programming exam or contestprogramming exam or contest

You have 3-4 problems to solve in 4-5 You have 3-4 problems to solve in 4-5 hourshours

First First read carefully all problemsread carefully all problems and try and try to estimate how complex each of them isto estimate how complex each of them is

Read the requirements, don't invent them!Read the requirements, don't invent them! Start solving the most easy problem firstStart solving the most easy problem first

Leave the most complex problem lastLeave the most complex problem last Approach the next problem when the Approach the next problem when the

previous is completely solved and well previous is completely solved and well testedtested 5

Analyzing the ProblemsAnalyzing the Problems Example: we are given 3 problems:Example: we are given 3 problems:

1.1. Shuffle-cardsShuffle-cards

Shuffle a deck of cards in random orderShuffle a deck of cards in random order

2.2. StudentsStudents

Read a set of students and their marks Read a set of students and their marks and print top and print top 1010 students with the best students with the best results (by averaging their marks)results (by averaging their marks)

3.3. Sorting numbersSorting numbers

Sort a set of numbers in increasing orderSort a set of numbers in increasing order

6

Analyzing the Problems Analyzing the Problems (2)(2)

Read carefully the problems and think a Read carefully the problems and think a bit about their possible solutionsbit about their possible solutions

Order the problems from the easiest to Order the problems from the easiest to the most complex:the most complex:

1.1. Sorting numbersSorting numbers Trivial – we can use the built-in sorting Trivial – we can use the built-in sorting

in .NETin .NET

2.2. Shuffle-cardsShuffle-cards Need to randomize the elements of arrayNeed to randomize the elements of array

3.3. StudentsStudents Needs summing, sorting and text file Needs summing, sorting and text file

processingprocessing 7

Using a Using a Paper and Paper and

a Pena PenVisualizing and Visualizing and Sketching your Sketching your

IdeasIdeas

Use a Sheet of Paper Use a Sheet of Paper and a Penand a Pen

Never start solving a problem Never start solving a problem without a sheet of paper and a penwithout a sheet of paper and a pen You need to sketch your ideasYou need to sketch your ideas

Paper and pen is the best Paper and pen is the best visualization toolvisualization tool

Allows your brain to think efficientlyAllows your brain to think efficiently

Paper works fasterPaper works faster than keyboard / screen than keyboard / screen

Other visualization toolOther visualization tool could also work well could also work well

9

Paper and PenPaper and Pen Consider the "cards shuffle" problemConsider the "cards shuffle" problem

We can sketch it to start thinkingWe can sketch it to start thinking

Some ideas immediately come, e.g.Some ideas immediately come, e.g. Split the deck into two parts and swap Split the deck into two parts and swap

them a multiple timesthem a multiple times Swap 2 random cards a random number Swap 2 random cards a random number

of timesof times Swap each card with a random cardSwap each card with a random card 10

Invent IdeasInvent IdeasThink-up, Invent Ideas and Check ThemThink-up, Invent Ideas and Check Them

Think up, Invent and Think up, Invent and Try IdeasTry Ideas

First take an example of the problemFirst take an example of the problem Sketch it on the sheet of paperSketch it on the sheet of paper

Next try to invent some idea that works Next try to invent some idea that works for your examplefor your example

Check if your idea will work for other Check if your idea will work for other examplesexamples Try to find a case that breaks your ideaTry to find a case that breaks your idea

Try challenging examples and unusual Try challenging examples and unusual casescases

If you find your idea incorrect, try to fix If you find your idea incorrect, try to fix it or just invent a new ideait or just invent a new idea

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Invent and Try Ideas – Invent and Try Ideas – ExampleExample

Consider the "cards shuffle" problemConsider the "cards shuffle" problem Idea #1: random number of times split Idea #1: random number of times split

the deck into left and right part and the deck into left and right part and swap themswap them How to represent the cards?How to represent the cards?

How to chose a random split point?How to chose a random split point?

How to perform the exchange?How to perform the exchange? Idea #2: swap each card with a random Idea #2: swap each card with a random

cardcard How many times to repeat this?How many times to repeat this?

Is this fast enough?Is this fast enough? 13

Invent and Try Invent and Try Ideas – Example Ideas – Example

(2)(2) Idea #3: swap 2 random cards a Idea #3: swap 2 random cards a

random number of timesrandom number of times How to choose two random cards?How to choose two random cards?

How many times repeat this?How many times repeat this? Idea #4: choose a random card and Idea #4: choose a random card and

insert it in front of the deckinsert it in front of the deck How to choose random card?How to choose random card?

How many times repeat this?How many times repeat this?

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Divide and ConquerDivide and ConquerDecompose Problems into Manageable Decompose Problems into Manageable

PiecesPieces

Decompose the Decompose the ProblemProblem

into Subproblemsinto Subproblems Work decomposition is natural in Work decomposition is natural in

engineeringengineering It happens every day in the industryIt happens every day in the industry

Projects are decomposed into subprojectsProjects are decomposed into subprojects Complex problems could be decomposed Complex problems could be decomposed

into several smaller subproblemsinto several smaller subproblems Technique known as "Divide and Technique known as "Divide and

Conquer"Conquer"

Small problems could easily be solvedSmall problems could easily be solved

Smaller subproblems could be further Smaller subproblems could be further decomposed as welldecomposed as well 16

Divide and Conquer – Divide and Conquer – ExampleExample

Let's try idea #1:Let's try idea #1: Multiple time split the deck into left and right Multiple time split the deck into left and right

part and swap thempart and swap them Divide and conquerDivide and conquer

Subproblem #1 (single exchange) – split the Subproblem #1 (single exchange) – split the deck into two random parts and exchange deck into two random parts and exchange themthem

Subproblem #2 – choosing a random split Subproblem #2 – choosing a random split pointpoint

Subproblem #3 – combining single exchangesSubproblem #3 – combining single exchanges

How many times to perform "single exchange"?How many times to perform "single exchange"?

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Subproblem #1 (Single Subproblem #1 (Single Exchange)Exchange)

Split the deck into 2 parts at Split the deck into 2 parts at random split point and exchange random split point and exchange these 2 partsthese 2 parts We visualize this by paper and pen:We visualize this by paper and pen:

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Subproblem #2 (Random Split

Point) Choosing a random split pointChoosing a random split point

Needs to understand the concept of Needs to understand the concept of pseudo-random numbers and how to pseudo-random numbers and how to use ituse it

In Internet lots of examples are In Internet lots of examples are available, some of them incorrectavailable, some of them incorrect

The class The class System.RandomSystem.Random can do the job can do the job Important detail is that the Important detail is that the RandomRandom

class should be instantiated only onceclass should be instantiated only once Not at each random number generationNot at each random number generation

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Subproblem #3 (Combining Single

Exchanges) Combining a sequence of single Combining a sequence of single

exchanges to solve the initial problemexchanges to solve the initial problem

How many times to perform single How many times to perform single exchanges to reliably randomize the exchanges to reliably randomize the deck?deck?

N times (where N is the number of the N times (where N is the number of the cards) seems enoughcards) seems enough

We have an algorithm:We have an algorithm: N times split at random position and N times split at random position and

exchange the left and right parts of exchange the left and right parts of the deckthe deck 20

Check-up Your IdeasCheck-up Your IdeasDon't go Ahead before Checking Your Don't go Ahead before Checking Your

IdeasIdeas

Check-up Your IdeasCheck-up Your Ideas Check-up your ideas with examplesCheck-up your ideas with examples

It is better to find a problem before the It is better to find a problem before the idea is implementedidea is implemented

When the code is written, changing When the code is written, changing radically your ideas costs a lot of time radically your ideas costs a lot of time and effortand effort

Carefully select examples for check-upCarefully select examples for check-up Examples should be simple enough to be Examples should be simple enough to be

checked by hand in a minutechecked by hand in a minute

Examples should be complex enough to Examples should be complex enough to cover the most general case, not just an cover the most general case, not just an isolated caseisolated case 22

Check-up Your Ideas – Check-up Your Ideas – ExampleExample

Let's check the idea:Let's check the idea:

After 3 random splits and swaps we After 3 random splits and swaps we obtain the start position obtain the start position seems seems like a bug!like a bug! 23

Invent New Idea If Invent New Idea If NeededNeeded

What to do when you find your idea is not What to do when you find your idea is not working in all cases?working in all cases? Try to fix your ideaTry to fix your idea

Sometime a small change could fix the Sometime a small change could fix the problemproblem

Invent new idea and carefully check itInvent new idea and carefully check it IterateIterate

It is usual that your first idea is not the It is usual that your first idea is not the bestbest

Invent ideas, check them, try various Invent ideas, check them, try various cases, find problems, fix them, invent cases, find problems, fix them, invent better idea, etc.better idea, etc. 24

Invent New Ideas – Invent New Ideas – ExampleExample

Invent few new ideas:Invent few new ideas: New idea #1 – multiple times select 2 New idea #1 – multiple times select 2

random cards and exchange themrandom cards and exchange them

New idea #2 – multiple times select a New idea #2 – multiple times select a random card and exchange it with the random card and exchange it with the first cardfirst card

New idea #3 – multiple times select a New idea #3 – multiple times select a random card and move it to an random card and move it to an external listexternal list

Let's check the new idea #2Let's check the new idea #2 Is it correct?Is it correct? 25

Check-up the New Idea – Check-up the New Idea – ExampleExample

26

The The result result seems seems correctcorrect

Think about Data Think about Data StructuresStructuresSelect Data Structures that Will Work Select Data Structures that Will Work

WellWell

Choosing AppropriateChoosing AppropriateData StructuresData Structures

Choose appropriate data structures Choose appropriate data structures before the start of codingbefore the start of coding Think how to represent input dataThink how to represent input data Think how to represent intermediate Think how to represent intermediate

program stateprogram state Think how to represent the requested Think how to represent the requested

outputoutput You could find that your idea cannot You could find that your idea cannot

be implemented efficientlybe implemented efficiently Or implementation will be very Or implementation will be very

complex or inefficientcomplex or inefficient28

Choose Choose Appropriate Data Appropriate Data

Structures – Structures – ExampleExample How to represent a single card?How to represent a single card?

The best idea is to create a structure The best idea is to create a structure CardCard

FaceFace – could be – could be stringstring, , intint or or enumerationenumeration

SuitSuit – enumeration – enumeration

How to represent a deck of cards?How to represent a deck of cards? Array – Array – Card[]Card[]

Indexed list – Indexed list – List<Card>List<Card>

SetSet / / DictionaryDictionary / / QueueQueue / / StackStack – not a fit – not a fit 29

Efficiency and Efficiency and PerformancePerformance

Is Your Algorithm Fast Enough?Is Your Algorithm Fast Enough?

Think About the Think About the EfficiencyEfficiency

Think about efficiency before Think about efficiency before writing the first line of codewriting the first line of code Estimate the running time Estimate the running time

(asymptotic complexity)(asymptotic complexity) Check the requirementsCheck the requirements

Will your algorithm be fast enough to Will your algorithm be fast enough to conform with themconform with them

You don't want to implement your You don't want to implement your algorithm and find that it is slow algorithm and find that it is slow when testingwhen testing You will lose your timeYou will lose your time 31

Efficiency is not Always Efficiency is not Always RequiredRequired

Best solution is sometimes just not Best solution is sometimes just not neededneeded

Read carefully your problem statementRead carefully your problem statement

Sometimes ugly solution could work for Sometimes ugly solution could work for your requirements and it will cost you your requirements and it will cost you less timeless time

Example: if you need to sort Example: if you need to sort nn numbers, numbers, any algorithm will work when any algorithm will work when nn ∈∈ [0..500][0..500]

Implement complex algorithms only Implement complex algorithms only when the problem really needs themwhen the problem really needs them 32

Efficiency – ExampleEfficiency – Example How much cards we have?How much cards we have?

In a typical deck we have 52 cardsIn a typical deck we have 52 cards

No matter how fast the algorithm is – it No matter how fast the algorithm is – it will work fast enoughwill work fast enough

If we have N cards, we perform N If we have N cards, we perform N swaps swaps the expected running time is the expected running time is O(N)O(N)

O(N) will work fast for millions of O(N) will work fast for millions of cardscards

Conclusion: the efficiency is not an Conclusion: the efficiency is not an issue in this problemissue in this problem 33

ImplementationImplementationCoding and Testing Step-by-StepCoding and Testing Step-by-Step

Start Coding: Check Start Coding: Check ListList

Never start coding before you find correct Never start coding before you find correct idea that will meet the requirementsidea that will meet the requirements What you will write before you invent a What you will write before you invent a

correct idea to solve the problem?correct idea to solve the problem? Checklist to follow before start of coding:Checklist to follow before start of coding:

Ensure you understand well the requirementsEnsure you understand well the requirements Ensure you have invented a good ideaEnsure you have invented a good idea Ensure your idea is correctEnsure your idea is correct Ensure you know what data structures to useEnsure you know what data structures to use Ensure the performance will be sufficientEnsure the performance will be sufficient

35

Coding Check List – Coding Check List – ExampleExample

Checklist before start of coding:Checklist before start of coding: Ensure you understand well the Ensure you understand well the

requirementsrequirements Yes, shuffle given deck of cardsYes, shuffle given deck of cards

Ensure you have invented a correct ideaEnsure you have invented a correct idea Yes, the idea seems correct and is testedYes, the idea seems correct and is tested

Ensure you know what data structures to Ensure you know what data structures to useuse Class Class CardCard, enumeration , enumeration SuitSuit and and List<Card>List<Card>

Ensure the performance will be sufficientEnsure the performance will be sufficient Linear running time Linear running time good performance good performance 36

Implement yourImplement yourAlgorithm Step-by-StepAlgorithm Step-by-Step

"Step-by-step" approach is always "Step-by-step" approach is always better than "build all, then test"better than "build all, then test" Implement a piece of your program and Implement a piece of your program and

test ittest it

Than implement another piece of the Than implement another piece of the program and test itprogram and test it

Finally put together all pieces and test Finally put together all pieces and test itit

Small increments (steps) reveal errors Small increments (steps) reveal errors earlyearly "Big-boom" integration takes more time"Big-boom" integration takes more time 37

Step #1 – Class CardStep #1 – Class Card

38

class Card class Card

{{

public string Face { get; set; }public string Face { get; set; }

public Suit Suit { get; set; }public Suit Suit { get; set; }

public override string ToString() public override string ToString()

{{

String card = "(" + this.Face + " " + this.Suit String card = "(" + this.Face + " " + this.Suit

+")";+")";

return card;return card;

}}

} } 

enum Suit enum Suit

{{

CLUB, DIAMOND, HEART, SPADECLUB, DIAMOND, HEART, SPADE

}}

Testing the class Testing the class CardCard to get to get feedback as early as possible:feedback as early as possible:

The result is as expected:The result is as expected:

Step #1 – TestStep #1 – Test

39

static void Main()static void Main()

{{

Card card = new Card() { Face="A", Suit=Suit.CLUB };Card card = new Card() { Face="A", Suit=Suit.CLUB };

Console.WriteLine(card);Console.WriteLine(card);

}}

(A CLUB)(A CLUB)

Step #2 – Create and Step #2 – Create and Print a Deck of CardsPrint a Deck of Cards

40

static void Main()static void Main(){{ List<Card> cards = new List<Card>();List<Card> cards = new List<Card>(); cards.Add(new Card() { Face = "7", Suit = cards.Add(new Card() { Face = "7", Suit = Suit.HEART });Suit.HEART }); cards.Add(new Card() { Face = "A", Suit = cards.Add(new Card() { Face = "A", Suit = Suit.SPADE });Suit.SPADE }); cards.Add(new Card() { Face = "10", Suit = cards.Add(new Card() { Face = "10", Suit = Suit.DIAMOND });Suit.DIAMOND }); cards.Add(new Card() { Face = "2", Suit = cards.Add(new Card() { Face = "2", Suit = Suit.CLUB });Suit.CLUB }); cards.Add(new Card() { Face = "6", Suit = cards.Add(new Card() { Face = "6", Suit = Suit.DIAMOND });Suit.DIAMOND }); cards.Add(new Card() { Face = "J", Suit = cards.Add(new Card() { Face = "J", Suit = Suit.CLUB });Suit.CLUB }); PrintCards(cards);PrintCards(cards);}}static void PrintCards(List<Card> cards) static void PrintCards(List<Card> cards) {{ foreach (Card card in cards) foreach (Card card in cards) Console.Write(card);Console.Write(card); Console.WriteLine();Console.WriteLine();}}

Testing the deck of cards seems to Testing the deck of cards seems to be working correctly:be working correctly:

Step #2 – TestStep #2 – Test

41

(7 HEART)(A SPADE)(10 DIAMOND)(2 CLUB)(6 DIAMOND)(J (7 HEART)(A SPADE)(10 DIAMOND)(2 CLUB)(6 DIAMOND)(J

CLUB)CLUB)

Step #3 – Single Step #3 – Single ExchangeExchange

42

static void PerformSingleExchange(List<Card> cards)static void PerformSingleExchange(List<Card> cards)

{{

Random rand = new Random();Random rand = new Random();

int randomIndex = rand.Next(1, cards.Count - 1);int randomIndex = rand.Next(1, cards.Count - 1);

Card firstCard = cards[1];Card firstCard = cards[1];

Card randomCard = cards[randomIndex];Card randomCard = cards[randomIndex];

cards[1] = randomCard;cards[1] = randomCard;

cards[randomIndex] = firstCard;cards[randomIndex] = firstCard;

}}

To test the single exchange we use To test the single exchange we use the following code:the following code:

The result is unexpected:The result is unexpected:

Step #3 – TestStep #3 – Test

43

static void Main()static void Main(){{ List<Card> cards = new List<Card>();List<Card> cards = new List<Card>(); cards.Add(new Card() { Face = "2", Suit = cards.Add(new Card() { Face = "2", Suit = Suit.CLUB });Suit.CLUB }); cards.Add(new Card() { Face = "3", Suit = Suit.HEART cards.Add(new Card() { Face = "3", Suit = Suit.HEART });}); cards.Add(new Card() { Face = "4", Suit = Suit.SPADE cards.Add(new Card() { Face = "4", Suit = Suit.SPADE });}); PerformSingleExchange(cards);PerformSingleExchange(cards); PrintCards(cards);PrintCards(cards);}}

(2 CLUB)(3 HEART)(4 SPADE)(2 CLUB)(3 HEART)(4 SPADE)

The first element of list is at index The first element of list is at index 0, not 1:0, not 1:

The result is again incorrect (3 The result is again incorrect (3 times the same):times the same):

Step #3 – Fix Bug and Step #3 – Fix Bug and TestTest

44

static void PerformSingleExchange(List<Card> cards)static void PerformSingleExchange(List<Card> cards){{ Random rand = new Random();Random rand = new Random(); int randomIndex = rand.Next(1, cards.Count - 1);int randomIndex = rand.Next(1, cards.Count - 1); Card firstCard = cards[0];Card firstCard = cards[0]; Card randomCard = cards[randomIndex];Card randomCard = cards[randomIndex]; cards[0] = randomCard;cards[0] = randomCard; cards[randomIndex] = firstCard;cards[randomIndex] = firstCard;}}

(3 HEART)(2 CLUB)(4 SPADE)(3 HEART)(2 CLUB)(4 SPADE)(3 HEART)(2 CLUB)(4 SPADE)(3 HEART)(2 CLUB)(4 SPADE)(3 HEART)(2 CLUB)(4 SPADE)(3 HEART)(2 CLUB)(4 SPADE)

Random.Next()Random.Next() has exclusive end has exclusive end range:range:

The result now seems correct:The result now seems correct:

Step #3 – Fix Again Step #3 – Fix Again and Testand Test

45

static void PerformSingleExchange(List<Card> cards)static void PerformSingleExchange(List<Card> cards){{ Random rand = new Random();Random rand = new Random(); int randomIndex = rand.Next(1, cards.Count);int randomIndex = rand.Next(1, cards.Count); Card firstCard = cards[0];Card firstCard = cards[0]; Card randomCard = cards[randomIndex];Card randomCard = cards[randomIndex]; cards[0] = randomCard;cards[0] = randomCard; cards[randomIndex] = firstCard;cards[randomIndex] = firstCard;}}

(3 HEART)(2 CLUB)(4 SPADE)(3 HEART)(2 CLUB)(4 SPADE)(4 SPADE)(3 HEART)(2 CLUB)(4 SPADE)(3 HEART)(2 CLUB)(4 SPADE)(3 HEART)(2 CLUB)(4 SPADE)(3 HEART)(2 CLUB)

Shuffle the entire deck of cards:Shuffle the entire deck of cards:

The result is surprisingly incorrect:The result is surprisingly incorrect:

Step #4 – Shuffle the Step #4 – Shuffle the DeckDeck

46

static void ShuffleCards(List<Card> cards)static void ShuffleCards(List<Card> cards){{ for (int i = 1; i <= cards.Count; i++)for (int i = 1; i <= cards.Count; i++) {{ PerformSingleExchange(cards);PerformSingleExchange(cards); }}}}

Initial deck: (7 HEART)(A SPADE)(10 DIAMOND)(2 CLUB)Initial deck: (7 HEART)(A SPADE)(10 DIAMOND)(2 CLUB)(6 DIAMOND)(J CLUB)(6 DIAMOND)(J CLUB)After shuffle: (7 HEART)(A SPADE)(10 DIAMOND)(2 CLUB)After shuffle: (7 HEART)(A SPADE)(10 DIAMOND)(2 CLUB)(6 DIAMOND)(J CLUB)(6 DIAMOND)(J CLUB)

When we step through the code with When we step through the code with the debugger, the result seems correct:the debugger, the result seems correct:

Without the debugger the result is Without the debugger the result is wrong!wrong!

Step #4 – Strange BugStep #4 – Strange Bug

47

Initial deck: (7 HEART)(A SPADE)(10 DIAMOND)(2 CLUB)Initial deck: (7 HEART)(A SPADE)(10 DIAMOND)(2 CLUB)(6 DIAMOND)(J CLUB)(6 DIAMOND)(J CLUB)After shuffle: (10 DIAMOND)(7 HEART)(A SPADE)(J CLUB)After shuffle: (10 DIAMOND)(7 HEART)(A SPADE)(J CLUB)(2 CLUB)(6 DIAMOND)(2 CLUB)(6 DIAMOND)

RandomRandom should be instantiated only should be instantiated only once:once:

The result finally is correct with The result finally is correct with and without the debuggerand without the debugger

Step #4 – Fix Again Step #4 – Fix Again and Testand Test

48

private static Random rand = new Random();private static Random rand = new Random();static void PerformSingleExchange(List<Card> static void PerformSingleExchange(List<Card> cards)cards){{ int randomIndex = rand.Next(1, cards.Count);int randomIndex = rand.Next(1, cards.Count); Card firstCard = cards[0];Card firstCard = cards[0]; Card randomCard = cards[randomIndex];Card randomCard = cards[randomIndex]; cards[0] = randomCard;cards[0] = randomCard; cards[randomIndex] = firstCard;cards[randomIndex] = firstCard;}}

TestingTestingThoroughly Test Your SolutionThoroughly Test Your Solution

Thoroughly Test your Thoroughly Test your SolutionSolution

Wise software engineers say that:Wise software engineers say that: Inventing a good idea and implementing Inventing a good idea and implementing

it is half of the solutionit is half of the solution Testing is the second half of the Testing is the second half of the

solutionsolution Always test thoroughly your solutionAlways test thoroughly your solution

Invest in testingInvest in testing One 100% solved problem is better than One 100% solved problem is better than

2 or 3 partially solved2 or 3 partially solved Testing existing problem takes less Testing existing problem takes less

time than solving another problem from time than solving another problem from scratchscratch 50

How to Test?How to Test? Testing could not certify absence Testing could not certify absence

of defectsof defects It just reduces the defects rateIt just reduces the defects rate

Well tested solutions are more Well tested solutions are more likely to be correctlikely to be correct

Start testing with a good Start testing with a good representative of the general caserepresentative of the general case Not a small isolated caseNot a small isolated case

Large and complex test, butLarge and complex test, but

Small enough to be easily checkableSmall enough to be easily checkable 51

How to Test? (2)How to Test? (2) Test the border casesTest the border cases

E.g. if E.g. if nn ∈∈ [ [00....500500] ] try try nn==00 , , nn==11, , nn==22, , nn==499499, , nn==500500

If a bug is found, repeat all tests If a bug is found, repeat all tests after fixing it to avoid regressionsafter fixing it to avoid regressions

Run a load testRun a load test How to be sure that your algorithm is How to be sure that your algorithm is

fast enough to meet the fast enough to meet the requirements?requirements?

Use copy-pasting to generate large Use copy-pasting to generate large test datatest data 52

Read the Problem Read the Problem StatementStatement

Read carefully the problem statementRead carefully the problem statement Does your solution print exactly what is Does your solution print exactly what is

expected?expected? Does your output follow the requested Does your output follow the requested

format?format? Did you remove your debug printouts?Did you remove your debug printouts?

Be sure to solve the requested problem, Be sure to solve the requested problem, not the problem you think is requested!not the problem you think is requested! Example: "Write a program to print the Example: "Write a program to print the

number of permutations on n elements" number of permutations on n elements" means to print a single number, not a set means to print a single number, not a set of permutations!of permutations!

53

Testing – ExampleTesting – Example Test with full deck of 52 cardsTest with full deck of 52 cards

Serious error found Serious error found change the change the algorithmalgorithm

Change the algorithmChange the algorithm Exchange the first card with a random card Exchange the first card with a random card

exchange cards 0, 1, …, N-1 with a exchange cards 0, 1, …, N-1 with a random cardrandom card

Test whether the new algorithm worksTest whether the new algorithm works Test with 1 cardTest with 1 card Test with 2 cardsTest with 2 cards Test with 0 cardsTest with 0 cards Load test with 52 000 cardsLoad test with 52 000 cards 54

Test with 52 Cards – Test with 52 Cards – ExampleExample

55

static void TestShuffle52Cards()static void TestShuffle52Cards()

{{

List<Card> cards = new List<Card>();List<Card> cards = new List<Card>();

string[] allFaces = new string[] { "2", "3", "4", "5", string[] allFaces = new string[] { "2", "3", "4", "5",

"6","6",

"7", "8", "9", "10", "J", "Q", "K", "A" };"7", "8", "9", "10", "J", "Q", "K", "A" };

Suit[] allSuits = new Suit[] { Suit.CLUB, Suit[] allSuits = new Suit[] { Suit.CLUB,

Suit.DIAMOND, Suit.DIAMOND,

Suit.HEART, Suit.SPADE };Suit.HEART, Suit.SPADE };

foreach (string face in allFaces)foreach (string face in allFaces)

foreach (Suit suit in allSuits)foreach (Suit suit in allSuits)

{{

Card card = new Card() { Face = face, Suit = Card card = new Card() { Face = face, Suit =

suit };suit };

cards.Add(card);cards.Add(card);

}}

ShuffleCards(cards);ShuffleCards(cards);

PrintCards(cards);PrintCards(cards);

}}

The result is surprising:The result is surprising:

Half of the cards keep their initial Half of the cards keep their initial positionspositions We have serious problem – the We have serious problem – the

randomization algorithm is not reliablerandomization algorithm is not reliable

Test with 52 Cards – Test with 52 Cards – Example (2)Example (2)

56

(4 DIAMOND)(4 DIAMOND)(2 DIAMOND)(2 DIAMOND)(6 HEART)(6 HEART)(2 SPADE)(2 SPADE)(A SPADE)(7 (A SPADE)(7

SPADE)SPADE)(3 DIAMOND)(3 SPADE)(4 SPADE)(4 HEART)(3 DIAMOND)(3 SPADE)(4 SPADE)(4 HEART)(6 CLUB)(K (6 CLUB)(K

HEART)HEART)(5 CLUB)(5 DIAMOND)(5 HEART)(5 CLUB)(5 DIAMOND)(5 HEART)(A HEART)(9 CLUB)(10 (A HEART)(9 CLUB)(10

CLUB)(A CLUB)CLUB)(A CLUB)(6 SPADE)(7 CLUB)(7 DIAMOND)(6 SPADE)(7 CLUB)(7 DIAMOND)(3 CLUB)(9 (3 CLUB)(9

HEART)HEART)(8 CLUB)(8 CLUB)(3 HEART)(3 HEART)(9 SPADE)(9 SPADE)(4 CLUB)(8 HEART)(4 CLUB)(8 HEART)(9 (9

DIAMOND)DIAMOND)(5 SPADE)(8 DIAMOND)(J HEART)(5 SPADE)(8 DIAMOND)(J HEART)(10 DIAMOND)(10 (10 DIAMOND)(10

HEART)(10 SPADE)HEART)(10 SPADE)(Q HEART)(2 CLUB)(Q HEART)(2 CLUB)(J CLUB)(J SPADE)(Q (J CLUB)(J SPADE)(Q

CLUB)CLUB)(7 HEART)(2 HEART)(Q SPADE)(7 HEART)(2 HEART)(Q SPADE)(K CLUB)(K CLUB)(J DIAMOND)(6 (J DIAMOND)(6

DIAMOND)DIAMOND)(K SPADE)(K SPADE)(8 SPADE)(8 SPADE)(A DIAMOND)(A DIAMOND)(Q DIAMOND)(K (Q DIAMOND)(K

DIAMOND)DIAMOND)

Fixing the AlgorithmFixing the Algorithm New idea that slightly changes the algorithm:New idea that slightly changes the algorithm:

Exchange the first card with a random card Exchange the first card with a random card exchange cards 0, 1, …, N-1 with a random cardexchange cards 0, 1, …, N-1 with a random card

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static void PerformSingleExchange(List<Card> cards, int static void PerformSingleExchange(List<Card> cards, int index)index){{ int randomIndex = rand.Next(1, cards.Count);int randomIndex = rand.Next(1, cards.Count); Card firstCard = cards[index];Card firstCard = cards[index]; cards[index] = cards[randomIndex];cards[index] = cards[randomIndex]; cards[randomIndex] = firstCard;cards[randomIndex] = firstCard;}}static void ShuffleCards(List<Card> cards)static void ShuffleCards(List<Card> cards){{ for (int i = 0; i < cards.Count; i++)for (int i = 0; i < cards.Count; i++) PerformSingleExchange(cards, i);PerformSingleExchange(cards, i);}}

The result now seems correct:The result now seems correct:

Cards are completely randomizedCards are completely randomized

Test with 52 Cards Test with 52 Cards (Again)(Again)

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(9 HEART)(5 CLUB)(3 CLUB)(7 SPADE)(6 CLUB)(5 SPADE)(6 (9 HEART)(5 CLUB)(3 CLUB)(7 SPADE)(6 CLUB)(5 SPADE)(6

HEART) (4 CLUB)(10 CLUB)(3 SPADE)(K DIAMOND)(10 HEART)HEART) (4 CLUB)(10 CLUB)(3 SPADE)(K DIAMOND)(10 HEART)

(8 CLUB)(A CLUB)(J DIAMOND)(K SPADE)(9 SPADE)(7 CLUB)(8 CLUB)(A CLUB)(J DIAMOND)(K SPADE)(9 SPADE)(7 CLUB)

(10 DIAMOND)(9 DIAMOND)(8 HEART)(6 DIAMOND)(8 SPADE)(5 (10 DIAMOND)(9 DIAMOND)(8 HEART)(6 DIAMOND)(8 SPADE)(5

DIAMOND)(4 HEART) (10 SPADE)(J CLUB)(Q SPADE)(9 CLUB)DIAMOND)(4 HEART) (10 SPADE)(J CLUB)(Q SPADE)(9 CLUB)

(J HEART)(K CLUB)(2 HEART) (7 HEART)(A HEART)(3 (J HEART)(K CLUB)(2 HEART) (7 HEART)(A HEART)(3

DIAMOND)(K HEART)(A SPADE)(8 DIAMOND)(4 SPADE)(3 HEART)DIAMOND)(K HEART)(A SPADE)(8 DIAMOND)(4 SPADE)(3 HEART)

(5 HEART)(Q HEART)(4 DIAMOND)(2 SPADE)(A DIAMOND)(2 (5 HEART)(Q HEART)(4 DIAMOND)(2 SPADE)(A DIAMOND)(2

DIAMOND)(J SPADE)(7 DIAMOND)(Q DIAMOND)(2 CLUB)DIAMOND)(J SPADE)(7 DIAMOND)(Q DIAMOND)(2 CLUB)

(6 SPADE)(Q CLUB)(6 SPADE)(Q CLUB)

Test with 1 CardTest with 1 Card

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static void TestShuffleOneCard()static void TestShuffleOneCard()

{{

List<Card> cards = new List<Card>();List<Card> cards = new List<Card>();

cards.Add(new Card() { Face = "A", Suit = cards.Add(new Card() { Face = "A", Suit =

Suit.CLUB });Suit.CLUB });

CardsShuffle.ShuffleCards(cards);CardsShuffle.ShuffleCards(cards);

CardsShuffle.PrintCards(cards);CardsShuffle.PrintCards(cards);

}}

Unhandled Exception: Unhandled Exception:

System.ArgumentOutOfRangeException: Index was out of System.ArgumentOutOfRangeException: Index was out of

range. Must be non-negative and less than the size of range. Must be non-negative and less than the size of

the collection. Parameter name: indexthe collection. Parameter name: index

……

Create a method to test with 1 card:Create a method to test with 1 card:

We found a bug:We found a bug:

Test with 1 Card – Bug Test with 1 Card – Bug FixingFixing

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static void ShuffleCards(List<Card> cards)static void ShuffleCards(List<Card> cards)

{{

if (cards.Count > 1)if (cards.Count > 1)

{{

for (int i = 0; i < cards.Count; i++)for (int i = 0; i < cards.Count; i++)

{{

PerformSingleExchange(cards, i);PerformSingleExchange(cards, i);

}}

}}

}}

We take 1 card are special case:We take 1 card are special case:

Test shows that the problem is fixedTest shows that the problem is fixed

Test with 2 CardsTest with 2 Cards

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static void TestShuffleTwoCards()static void TestShuffleTwoCards(){{ List<Card> cards = new List<Card>();List<Card> cards = new List<Card>(); cards.Add(new Card() { Face = "A", Suit = cards.Add(new Card() { Face = "A", Suit = Suit.CLUB });Suit.CLUB }); cards.Add(new Card() { Face = "3", Suit = cards.Add(new Card() { Face = "3", Suit = Suit.DIAMOND });Suit.DIAMOND }); CardsShuffle.ShuffleCards(cards);CardsShuffle.ShuffleCards(cards); CardsShuffle.PrintCards(cards);CardsShuffle.PrintCards(cards);}}

(3 DIAMOND)(A CLUB)(3 DIAMOND)(A CLUB)

Create a method to test with 2 cards:Create a method to test with 2 cards:

Bug: sequential executions get the Bug: sequential executions get the same result:same result:

The problem: the first and the second The problem: the first and the second cards always exchange each other cards always exchange each other exactly onceexactly once

Test with 2 Cards – Bug Test with 2 Cards – Bug FixingFixing

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static void PerformSingleExchange(List<Card> cards, int static void PerformSingleExchange(List<Card> cards, int

index)index)

{{

int randomIndex = rand.Next(0, cards.Count);int randomIndex = rand.Next(0, cards.Count);

Card firstCard = cards[index];Card firstCard = cards[index];

Card randomCard = cards[randomIndex];Card randomCard = cards[randomIndex];

cards[index] = randomCard;cards[index] = randomCard;

cards[randomIndex] = firstCard;cards[randomIndex] = firstCard;

}}

We allow each card to be exchanged with We allow each card to be exchanged with any other random card, including itselfany other random card, including itself

Test shows that the problem is fixedTest shows that the problem is fixed

Test with Test with 00 Cards; Cards; Regression TestsRegression Tests

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Testing with Testing with 00 cards (empty list) cards (empty list) generates an empty list generates an empty list correct correct resultresult

Seems like the cards shuffle algorithm Seems like the cards shuffle algorithm works correctly after the last few fixesworks correctly after the last few fixes

Needs a regression testNeeds a regression test Test again that new changes did not Test again that new changes did not

break all previously working casesbreak all previously working cases Test with full deck of 52 cards; with 1 Test with full deck of 52 cards; with 1

card; with 2 cards with card; with 2 cards with 00 cards cards everything workseverything works

Load Test – 52 000 Load Test – 52 000 CardsCards

Finally we need a load test with 52 Finally we need a load test with 52 000 cards:000 cards:

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static void TestShuffle52000Cards()static void TestShuffle52000Cards()

{{

List<Card> cards = new List<Card>();List<Card> cards = new List<Card>();

string[] allFaces = new string[] {"2", "3", "4", "5",string[] allFaces = new string[] {"2", "3", "4", "5",

"6", "7", "8", "9", "10", "J", "Q", "K", "A"};"6", "7", "8", "9", "10", "J", "Q", "K", "A"};

Suit[] allSuits = new Suit[] { Suit.CLUB, Suit[] allSuits = new Suit[] { Suit.CLUB,

Suit.DIAMOND, Suit.DIAMOND,

Suit.HEART, Suit.SPADE};Suit.HEART, Suit.SPADE};

for (int i = 0; i < 1000; i++)for (int i = 0; i < 1000; i++)

foreach (string face in allFaces)foreach (string face in allFaces)

foreach (Suit suit in allSuits)foreach (Suit suit in allSuits)

cards.Add(new Card() { Face = face, Suit = suit cards.Add(new Card() { Face = face, Suit = suit

});});

ShuffleCards(cards);ShuffleCards(cards);

PrintCards(cards);PrintCards(cards);

}}

SummarySummary1.1. Problems solving needs methodology:Problems solving needs methodology:

Understanding and analyzing problemsUnderstanding and analyzing problems Using a sheet of paper and a pen for Using a sheet of paper and a pen for

sketchingsketching Thinking up, inventing and trying ideasThinking up, inventing and trying ideas Decomposing problems into subproblemsDecomposing problems into subproblems Selecting appropriate data structuresSelecting appropriate data structures Thinking about the efficiency and Thinking about the efficiency and

performanceperformance Implementing step-by-stepImplementing step-by-step Testing the nominal case, border cases Testing the nominal case, border cases

and efficiencyand efficiency65

Methodology of Methodology of Problem Problem SolvingSolving

Questions?Questions?

http://academy.telerik.com

ExercisesExercises1.1. Following the problems Following the problems

solving methodology try solving methodology try to approach the following to approach the following problem: We are given N problem: We are given N points (N < points (N < 100100 000000) in the ) in the plane (represented as plane (represented as integer coordinates integer coordinates xxii and and yyii). Write a program to ). Write a program to find all possible horizontal find all possible horizontal or vertical straight lines or vertical straight lines that split the plane into that split the plane into two parts, each holding two parts, each holding equal number of points equal number of points (points at the line are not (points at the line are not counted).counted).

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Exercises (2)Exercises (2)

2.2. Following the problems solving methodology Following the problems solving methodology solve the following problem: we are given a set solve the following problem: we are given a set SS of of nn integer numbers and a positive integer integer numbers and a positive integer kk ((kk ≤ ≤ nn ≤ 10). Alternating sequence of numbers ≤ 10). Alternating sequence of numbers is a sequence that alternatively changes from is a sequence that alternatively changes from increasing to decreasing of vice versa after increasing to decreasing of vice versa after each of its elements. Write a program to each of its elements. Write a program to generate all alternating sequences generate all alternating sequences ss11, , ss22, …, , …, sskk

consisting of consisting of kk distinct elements from distinct elements from SS..

Example: S = { 2, 5, 3, 4 } Example: S = { 2, 5, 3, 4 } {2, 4, 3}, {2, 5, {2, 4, 3}, {2, 5, 3}, {2, 5, 4}, {3, 2, 4}, {3, 2, 5}, {3, 4, 2}, {3, 3}, {2, 5, 4}, {3, 2, 4}, {3, 2, 5}, {3, 4, 2}, {3, 5, 2}, {3, 5, 4}, {4, 2, 3}, {4, 2, 5}, {4, 3, 5}, 5, 2}, {3, 5, 4}, {4, 2, 3}, {4, 2, 5}, {4, 3, 5}, {5, 2, 3}, {5, 2, 4}, {5, 3, 4} {5, 2, 3}, {5, 2, 4}, {5, 3, 4}

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