ICS 491: Competitve Programming – Lecture 1: Introduction

ICS 491: Competitive ProgrammingProf. Nodari Sitchinava

www.algoparc.ics.hawaii.edu

AlgoPARC

Lecture 2: Data Structures and StandardLibraries

ICS 491: Competitve Programming – Lecture 1: Introduction

A word of advice for (mini-) contests

Test your program before submitting. At the very least:Compile it!Run on sample test cases

ICS 491: Competitve Programming – Lecture 1: Introduction

A word of advice for (mini-) contests

Test your program before submitting. At the very least:Compile it!Run on sample test cases

./my_program < sample.in > myoutput.out

java MyProgram < sample.in > myoutput.out

diff myoutput.out sample.out

ICS 491: Competitve Programming – Lecture 1: Introduction

A word of advice for (mini-) contests

Test your program before submitting. At the very least:Compile it!Run on sample test cases

Test boundary conditionsSmallest inputLargest input

Progressively increase input sizeGenerate large inputs automatically

For multiple input variables (e.g., N, K ):Test if N > K and K > N (unless specified)Test smallest and largest for both

./my_program < sample.in > myoutput.out

java MyProgram < sample.in > myoutput.out

diff myoutput.out sample.out

ICS 491: Competitve Programming – Lecture 1: Introduction

DomJudge Responses

Accepted (AC)

Presentation Error (PE)Wrong Answer (WA)Time Limit Exceeded (TLE)Memory Limit Exceeded (MLE)Runtime Error (RTE)

e.g. Array out of boundsTest boundary conditions & large inputs

Good:

Bad:

ICS 491: Competitve Programming – Lecture 1: Introduction

Weekly Mini-Contest – 75 min

Compiling:

C:gcc -g -O2 -std=gnu11 -static 〈file.c〉 -lm

C++:g++ -g -O2 -std=gnu++14 -static 〈file.cpp〉Java:javac -encoding UTF-8 -sourcepath . -d . 〈file.java〉

Running Java:java -Dfile.encoding=UTF-8 -XX:+UseSerialGC -Xss64m

-Xms1920m -Xmx1920m 〈file〉

ICS 491: Competitve Programming – Lecture 1: Introduction

Solutions

ICS 491: Competitve Programming – Lecture 1: Introduction

Ad Hoc Problems

GamesCardChessOther (Tic Tac Toe, Rock-Paper-Scissors, Bingo, etc)

ICS 491: Competitve Programming – Lecture 1: Introduction

Ad Hoc Problems

GamesCardChessOther (Tic Tac Toe, Rock-Paper-Scissors, Bingo, etc)

Palindromes - does a word read the same forward andbackward?

ICS 491: Competitve Programming – Lecture 1: Introduction

Ad Hoc Problems

GamesCardChessOther (Tic Tac Toe, Rock-Paper-Scissors, Bingo, etc)

Palindromes - does a word read the same forward andbackward?Anagrams - do words contain the same set of characters?

Sort characters of both words and compare

ICS 491: Competitve Programming – Lecture 1: Introduction

Ad Hoc Problems

GamesCardChessOther (Tic Tac Toe, Rock-Paper-Scissors, Bingo, etc)

Palindromes - does a word read the same forward andbackward?Anagrams - do words contain the same set of characters?

Sort characters of both words and compare

TimeDates, Times, CalendarJava GregorianCalendar is very helpful

ICS 491: Competitve Programming – Lecture 1: Introduction

Ad Hoc Problems

GamesCardChessOther (Tic Tac Toe, Rock-Paper-Scissors, Bingo, etc)

Palindromes - does a word read the same forward andbackward?Anagrams - do words contain the same set of characters?

Sort characters of both words and compare

TimeDates, Times, CalendarJava GregorianCalendar is very helpful

Time wastersSpecifically designed to be long and tedious

ICS 491: Competitve Programming – Lecture 1: Introduction

Other Ad Hoc Problems

Basic data structuresarrays, stacks, heap/PQ, deque, set, multiset, map, BST)

ICS 491: Competitve Programming – Lecture 1: Introduction

Other Ad Hoc Problems

Basic data structuresarrays, stacks, heap/PQ, deque, set, multiset, map, BST)

Mathbasic: arithmetic series, basic combinatorics, baseconversion, modulo operationsadvanced: number theory, advanced combinatorics,probability, game theory

ICS 491: Competitve Programming – Lecture 1: Introduction

Other Ad Hoc Problems

Basic data structuresarrays, stacks, heap/PQ, deque, set, multiset, map, BST)

Mathbasic: arithmetic series, basic combinatorics, baseconversion, modulo operationsadvanced: number theory, advanced combinatorics,probability, game theory

Strings

ICS 491: Competitve Programming – Lecture 1: Introduction

Other Ad Hoc Problems

Basic data structuresarrays, stacks, heap/PQ, deque, set, multiset, map, BST)

Mathbasic: arithmetic series, basic combinatorics, baseconversion, modulo operationsadvanced: number theory, advanced combinatorics,probability, game theory

Strings

(Computational) Geometry

ICS 491: Competitve Programming – Lecture 1: Introduction

Other Ad Hoc Problems

Mathbasic: arithmetic series, basic combinatorics, baseconversion, modulo operationsadvanced: number theory, advanced combinatorics,probability, game theory

Strings

(Computational) Geometry

Basic data structuresarrays, stacks, heap/PQ, deque, set, multiset, map, BST)

ICS 491: Competitve Programming – Lecture 1: Introduction

Standard Libraries: Linear Data Structures

Static Array1D, 2D, and 3D arraysOK to waste a bit extra space (for contests)

saves ‘off by one’ RTEs

Dynamic arraysC: mallocC++: STL vector

Java: ArrayListJava: Vector

Initialize size with reserve() or resize()

ICS 491: Competitve Programming – Lecture 1: Introduction

Algorithms for arrays

SortingC++ STL: sort, partial sort, stable sort

Java: Collections.sortO(n) sorting (Counting/Radix/Bucket Sort)

Must implement yourselfTypically just use O(n log n) library implementations

ICS 491: Competitve Programming – Lecture 1: Introduction

Algorithms for arrays

SortingC++ STL: sort, partial sort, stable sort

Java: Collections.sortO(n) sorting (Counting/Radix/Bucket Sort)

Must implement yourselfTypically just use O(n log n) library implementations

SearchingO(n) linear searchO(log n) binary search

C++ STL <algorithm>: lower bound, upper bound,binary search

Java: Collections.binarySearch

ICS 491: Competitve Programming – Lecture 1: Introduction

Working with Bits

C++ STL: bitset, vector<bool>Java: BitSet

ICS 491: Competitve Programming – Lecture 1: Introduction

Working with Bits

C++ STL: bitset, vector<bool>Java: BitSet

Faster to use bitmasks (bits within integers) instead:Use 32/64-bit integers for up to 30/62 bits

ICS 491: Competitve Programming – Lecture 1: Introduction

Working with Bits

C++ STL: bitset, vector<bool>Java: BitSet

Faster to use bitmasks (bits within integers) instead:Use 32/64-bit integers for up to 30/62 bitsRepresent the set {1, 5}

int S = 34 3410 = 1000102

ICS 491: Competitve Programming – Lecture 1: Introduction

Working with Bits

C++ STL: bitset, vector<bool>Java: BitSet

Faster to use bitmasks (bits within integers) instead:

Is j-th item present? Is j-th bit of S set?S & (1 << j) & is bitwise AND

Use 32/64-bit integers for up to 30/62 bitsRepresent the set {1, 5}

int S = 34 3410 = 1000102

ICS 491: Competitve Programming – Lecture 1: Introduction

Working with Bits

C++ STL: bitset, vector<bool>Java: BitSet

Faster to use bitmasks (bits within integers) instead:

Is j-th item present? Is j-th bit of S set?S & (1 << j) & is bitwise AND

Use 32/64-bit integers for up to 30/62 bitsRepresent the set {1, 5}

int S = 34 3410 = 1000102

Set j-th bit of SS | (1 << j) | is bitwise OR

ICS 491: Competitve Programming – Lecture 1: Introduction

Working with Bits

C++ STL: bitset, vector<bool>Java: BitSet

Faster to use bitmasks (bits within integers) instead:

Is j-th item present? Is j-th bit of S set?S & (1 << j) & is bitwise AND

Use 32/64-bit integers for up to 30/62 bitsRepresent the set {1, 5}

int S = 34 3410 = 1000102

Set j-th bit of SS | (1 << j) | is bitwise OR

Clear j-th bit of SS & ~(1 << j) ˜ is bitwise NOT

ICS 491: Competitve Programming – Lecture 1: Introduction

Working with Bits

Toggle j-th bitS ^ (1 << j) ˆ is bitwise XOR

ICS 491: Competitve Programming – Lecture 1: Introduction

Working with Bits

Toggle j-th bitS ^ (1 << j) ˆ is bitwise XOR

return the value with only LSB setS & (-S) 40 & (−40) = 8

0...001010002 & 1..110110002 = 0...000010002

ICS 491: Competitve Programming – Lecture 1: Introduction

Working with Bits

Toggle j-th bitS ^ (1 << j) ˆ is bitwise XOR

return the value with only LSB setS & (-S) 40 & (−40) = 8

0...001010002 & 1..110110002 = 0...000010002

Set k LSBs to 1 (k < 30 or k < 62 for 32/64-bit integers)S = (1 << k) - 1

ICS 491: Competitve Programming – Lecture 1: Introduction

Linked Lists

C++ STL: listJava: LinkedList

ICS 491: Competitve Programming – Lecture 1: Introduction

Linked Lists

C++ STL: listJava: LinkedList

Slower than vectors/deques.Use only if need to insert items in the middle

ICS 491: Competitve Programming – Lecture 1: Introduction

Stack

C++ STL: stackJava: Stack

ICS 491: Competitve Programming – Lecture 1: Introduction

Stack

C++ STL: stackJava: Stack

Supports O(1) time operations:push() – insert to toppop() – delete from toptop() – return the top (without deleting)empty() – check if empty

ICS 491: Competitve Programming – Lecture 1: Introduction

Queue

C++ STL: queueJava: Queue

ICS 491: Competitve Programming – Lecture 1: Introduction

Queue

C++ STL: queueJava: Queue

Supports O(1) time operations:push() – insert to backpop() – delete from frontfront() – return the front (without deleting)back() – return the back (without deleting)empty() – check if empty

ICS 491: Competitve Programming – Lecture 1: Introduction

Deque: double-ended queue

C++ STL: dequeJava: Deque

ICS 491: Competitve Programming – Lecture 1: Introduction

Deque: double-ended queue

C++ STL: dequeJava: Deque

Supports O(1) time operations:push back() – insert to backpop front() – delete from frontpush front() – insert to frontpop back() – delete from back

ICS 491: Competitve Programming – Lecture 1: Introduction

Balanced BST

C++ STL: map/setJava: TreeMap/TreeSet

Map: key-value pairSet: only keys

ICS 491: Competitve Programming – Lecture 1: Introduction

Balanced BST

C++ STL: map/setJava: TreeMap/TreeSet

Supports O(log n) time operations:search(key)

insert(key)

findMin()

findMax()

successor(key)

predecessor(key)

delete(key)

Map: key-value pairSet: only keys

ICS 491: Competitve Programming – Lecture 1: Introduction

Priority Queue

C++ STL: priority queue

Java: PriorityQueue

ICS 491: Competitve Programming – Lecture 1: Introduction

Priority Queue

C++ STL: priority queue

Java: PriorityQueue

Supports O(log n) time operations:ExtractMax()/pop() – remove and return largestelementInsert(v)/push()

top() – look up the largest element

ICS 491: Competitve Programming – Lecture 1: Introduction

Priority Queue

C++ STL: priority queue

Java: PriorityQueue

Supports O(log n) time operations:ExtractMax()/pop() – remove and return largestelementInsert(v)/push()

top() – look up the largest element

For MinHeap – insert negative elements

ICS 491: Competitve Programming – Lecture 1: Introduction

Questions about Standard Library Data Structures?

ICS 491: Competitve Programming – Lecture 1: Introduction

Other Ad Hoc problems

Basic data structuresarrays, stacks, heap/PQ, deque, set, multiset, map, BST)

Mathbasic: arithmetic series, basic combinatorics, baseconversion, modulo operationsadvanced: number theory, advanced combinatorics,probability, game theory

Strings

(Computational) Geometry

ICS 491: Competitve Programming – Lecture 1: Introduction

Example: Computational Geometry

Not covered in ICS 311At least one problem in ICPCOften hard to get right, especially without preparation

ICS 491: Competitve Programming – Lecture 1: Introduction

Example: Computational Geometry

Not covered in ICS 311At least one problem in ICPCOften hard to get right, especially without preparation

Problem 1. Given a set of N points randomly scattered on a 2Dplane, find the pair of points with the greatest separatingEuclidean distance.

Points are defined by (x , y ) coordinates.Euclidean distance between p1 = (x1, y1) and p2 = (x2, y2) isdefined as ||p1, p2|| =

√(x1 − x2)2 + (y1 − y2)2

ICS 491: Competitve Programming – Lecture 1: Introduction

Example: Computational Geometry

Simple solution:Check distance between every pairHint: sufficient to compare ||p1, p2||2

ICS 491: Competitve Programming – Lecture 1: Introduction

Example: Computational Geometry

Simple solution:Check distance between every pairHint: sufficient to compare ||p1, p2||2

Analysis:Number of pairs: O(n2)Fine if N ≤ 1, 000

ICS 491: Competitve Programming – Lecture 1: Introduction

Computational Geometry: Better Solution

What if N = 100, 000?

ICS 491: Competitve Programming – Lecture 1: Introduction

Computational Geometry: Better Solution

What if N = 100, 000?Consider only points on the convex hull

ICS 491: Competitve Programming – Lecture 1: Introduction

Computational Geometry: Better Solution

What if N = 100, 000?Consider only points on the convex hull

ICS 491: Competitve Programming – Lecture 1: Introduction

Computational Geometry: Better Solution

What if N = 100, 000?Consider only points on the convex hull

Analysis: Expected ≈ O(√

N) points on the convex hull

ICS 491: Competitve Programming – Lecture 1: Introduction

Questions?