An Introduction to Programming Concepts and OI-programming

1
An Introduction to Programming Concepts and
OI-programming

• from abstract theory to dirty tricks

2
Objectives Today

• Introduction to the concept of Algorithms
• Introduction to common algorithms in OI
  competitions
• Introduction to graph theory
• Introduction to complexity
• Philosophy of OI competitions
• OI-style programming

3
What is an Algorithm?

• From Wikipedia An algorithm is a finite set of
  well-defined instructions for accomplishing some
  task which, given an initial state, will
  terminate in a corresponding recognizable
  end-state.
• (what does that mean?)
• Usually, an algorithm solves a problem.
• Examples
• Insertion sort
• Binary Search
• An algorithm does not have to be a computer
  program! Think about other possible algorithms in
  real life

4
Problems

• Usually a set of well defined inputs and
  corresponding outputs
• Example the sorting problem
• Input a list of numbers
• Output a sorted list of numbers
• We can use a number of different sorting
  algorithms to solve the sorting problem

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Data Structures

• Supplementary objects that help store data in an
  algorithm
• Different data structures have different
  properties, and can store different types of
  data, and access them in different ways
• Selecting the right data structure can be very
  important, as you will learn later
• Examples arrays, queues, stacks more will be
  introduced later

6
Examples of algorithms

• Sorting algorithms
• Graph algorithms Djikstra, Warshall-floyd,
  Bellman-Ford, Prims, Kruskal
• Tree-Search algorithms BFS, DFS
• Linear Searching Algorithms

7
Examples of Data Structures

• Array random access
• Queue First in First Out
• Stack First in Last Out
• Heap extract min/max number
• Binary Search Tree Efficient insert, search,
  delete, etc.
• Hash Table fast lookup
• Other graph data structures discussed below

8
Examples of Techniques in Designing Algorithms

• Recursion
• Dynamic programming
• Greedy
• Divide and conquer
• Branch and bound
• (the above may have overlaps)

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Using and Creating Algorithms

• It is science. You can derive them.It is
  art. We have no way to teach you! Alan Tam
• Why study algorithms?
• To solve problems that can be directly solved by
  existing algorithms
• To solve problems that can be solved by combining
  algorithms
• To get feelings and inspirations on how to design
  new algorithms

10
Related Issues

• Proving correctness of algorithms (why? why not?)
• Other methods finding counter examples, Unus
  Conjecture of Competition
• Questions?

11
Graphs

• What is a graph?
• Informally, a set of relationships between things
• A graph is defined as G(V,E), where
• V is the set of vertices (singular vertex)
• E is the set of edges that connect some of the
  vertices
• A path is a sequence of vertices which are
  connected by edge(s)

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Example

• Map of Australia

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Common Types of Graphs

• Directed/Undirected Graph
• Weighted/Unweighted Graph
• Connectivity

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Trees

• A few common definitions (equivalent)
• Connected graph with no cycles
• There is a unique path between any two vertices
• Connected graph with v 1 edges (v num of
  vertices)
• Rooted/Unrooted Trees
• Heap, Binary Search Trees

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Representing a graph

• Adjacency Matrix
• Adjacency List

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Complexity

• What is complexity?
• We are not (yet!) concerned with the exact
  runtime or memory used
• We want to know how well an algorithm scales up
  (i.e. when there is a large input). Why?

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Complexity (contd)

• Heres why

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Quasi-Formal Definition of Big-O

• (you need not remember these)
• We say
• f(x) is in O(g(x))
• if and only if
• there exist numbers x0 and M such that
• f(x) M g(x) for x gt x0

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Example 1 Bubble sort

• For i 1 to n do For j i downto 2 do if
  aj gt aj-1 then swap(aj, aj-1)
• Time Complexity? O(n2)
• Swap Complexity?
• How about memory?

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Example 2 Insertion Sort

• Quick introduction to insertion sort (you will
  learn more in the searching and sorting
  training)
• 4 3 1 5 2
• 4 3 1 5 2
• 3 4 1 5 2
• 1 3 4 5 2
• 1 3 4 5 2
• 1 2 3 4 5
• Time Complexity ?

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Applications

• Usually, the time complexity of the algorithm
  gives us a rough estimation of the actual run
  time.
• O(n) for very large N
• O(n2) for n 1000-3000
• O(n3) for n 100-200
• O(n4) for n 50
• O(kn) for O(n!) for very small n, usually lt 20
• Keep in mind
• The constant of the algorithms (including the
  implementation)
• Computers vary in speeds, so the time needed will
  be different
• Therefore remember to test the program/computer
  before making assumptions!

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Computational Theory Topics

• P (Polynomical)
• Can be solved in polynomical time
• NP (Non-deterministic Polynomical)
• Can be checked in polynomial time
• NP does NOT stand for not-polynomial!!
• NP-Complete
• The hardest NP problems

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Philosophy of OI Competitions

• Objective of Competition
• The winner is determined by
• Fastest Program?
• Amount of time used in coding?
• Number of Tasks Solved?
• Use of the most difficult algorithm?
• Highest Score
• Therefore, during a competition, aim to get
  highest score, at all costs All is fair in
  love and war.

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Scoring

• A black box judging system
• Test data is fed into the program
• Output is checked for correctness
• No source code is manually inspected
• How to take advantage (without cheating of
  course!) of the system?

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The OI Programming Process

• Reading the problems
• Choosing a problem
• Reading the problem
• Thinking
• Coding
• Testing
• Finalizing the program

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Reading the Problem

• Usually, a task consists of
• Title
• Problem Description
• Constraints
• Input/Output Specification
• Sample Input/Output
• Scoring

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Reading the Problem

• Constraints
• Range of variables
• Execution Time
• NEVER make assumptions yourself
• Ask whenever you are not sure
• (Do not be afraid to ask questions!)
• Read every word carefully
• Make sure you understand before going on

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Thinking

• Classify the problem
• Graph? Mathematics? Data Processing? Dynamic
  Programming? etc.
• Some complicated problems may be a combination of
  the above
• Draw diagrams, use rough work, scribble
• Consider special cases (smallest, largest, etc)
• Is the problem too simple?
• Usually the problem setters have something they
  want to test the contestants, maybe an algorithm,
  some specific observations, carefulness etc.
• Still no idea? Give up. Time is precious.

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Designing the Solution

• Remember, before coding, you MUST have an idea
  what you are doing. If you dont know what you
  are doing, do not begin coding.
• Some points to consider
• Execution time (Time complexity)
• Memory usage (Space complexity)
• Difficulty in coding
• Remember, during competition, use the algorithm
  that gains you most score, not the
  fastest/hardest algorithm!

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Coding

• Optimized for ease of coding, not for reading
• Ignore all the coding practices outside, unless
  you find them particularly useful in OI
  competitions
• No Comments needed
• Short variable names
• Use less functions
• NEVER use 16 bit integers (unless memory is
  limited)
• 16 bit integer may be slower! (PCs are usually
  32-bit, even 64 bit architectures should be
  somewhat-optimized for 32 bit)

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Coding (2)

• Use goto, break, etc in the appropriate
  situations
• Never mind what Djikstra has to say ?
• Avoid using floating point variables if possible
  (eg. real, double, etc)
• Do not do small (aka useless) optimizations to
  your code
• Save and compile frequently
• See example program code

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Testing

• Sample Input/OutputA problem has sample output
  for two reasons
• To make you understand what the correct output
  format is
• To make you believe that your incorrect solution
  has solved the problem correctly ?
• Manual Test Data
• Generated Test Data (if time allows)
• Boundary Cases (0, 1, other smallest cases)
• Large Cases (to check for TLE, overflows, etc)
• Tricky Cases

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Debugging

• Debugging find out the bug, and remove it
• Easiest method writeln/printf/cout
• Use of debuggers
• FreePascal IDE debugger
• gdb debugger

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Finalizing

• Check output format
• Any trailing spaces? Missing end-of-lines? (for
  printf users, this is quite common)
• better test once more with sample output
• Check I/O filename? stdio?
• Check exe/source file name
• Is the executable updated?
• Method of submission?
• Try to allocate 5 mins at the end of competition
  for finalizing

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Interactive Tasks

• Traditional Tasks
• Give input in one go
• Give output in one go
• Interactive Tasks
• Your program is given some input
• Your program gives some output
• Your program is given some more input
• Your program gives more output
• etc

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Example

• Guess the number
• Sample Run
• Judge I have a number between 1 and 5, can you
  guess?
• Program is it 1?
• J Too small
• P 2?
• J Too small
• P 3?
• J Too small
• P 4?
• J Correct
• P 5?
• J Too big
• P Your number is 4!

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Open Test Data

• Test data is known
• Usually quite difficult to solve
• Some need time consuming algorithms, therefore
  you are given a few hours (i.e. competition time)
  to run the program
• Tricks
• ALWAYS look at all the test data first
• Solve by hand, manually
• Solve partially by program, partially by hand
• Some with different programs
• Solve all with one program (sometimes
  impossible!)
• Make good use of existing tools you do not have
  to write all the programs if some are already
  available! (eg. sort, other languages, etc)

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Tricks

• No solution
• Solve for simple cases
• 50
• Special cases (smallest, largest, etc)
• Incorrect greedy algorithms
• Hard Code
• Stupid Hardcode begin writeln(random(100)) end.
• Naïve hardcode if input is x, output hc(x)
• More intelligent hardcode (sometimes not
  possible) pre-compute the values, and only save
  some of them
• Brute force
• Other Weird Tricks (not always useful)
• Do nothing (e.g.. Toggle, IODM)

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Pitfalls / Common Mistakes

• Misunderstanding the problem
• Not familiar with competition environment
• Output format
• Using complex algorithms unnecessarily
• Choosing the hardest problem first

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Advertisement (targeted ad)

• NOI/IOI will use Linux as competition environment
  exclusively
• We are thinking of providing Linux only
  environments for upcoming team formation test(s)
• Linux, when used properly, can be more powerful
  than Microsoft Windows TM for contests, because
  it has more powerful tools
• Eg. Command Line tools, Powerful Editors (vim,
  emacs), etc.

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The End

• Note most of the contents are introductions
  only. You may want to find more in-depth
  materials
• Books Introduction to Algorithms
• Online Google, Wikipedia
• HKOI Newsgroup, training websites of previous
  years, discuss with trainers/trainees.
• Training Many topics are further covered in
  later trainings
• Experience!
• Any Questions?