Introduction to Competitive Programming

(Fall 2019)

The list of Kattis problems are selected from those listed on the Methods to Solve webpage, which is associated with the Competitive Programming 3 book.

Selection of USACO problems are limited to those before 2016.

	Key Ideas	Example Problems	Additional problems
Week 1 (Aug 19 -- Aug 23)	Sum and prefix sums: For many problems where data is stored in an 1D-array, computing the sum or prefix (or postfix) sums can reduce the complexity from O(n^2) to O(n). For some problems, it is necessary to store these sums in another array, requiring O(n) extra memory. For other problems, maintaining a running sum suffices. Some problems requires storing information other than sum of prefix. Map or Set: To store data for quick check of existence, one can use HashMap, HashSet, TreeMap, TreeSet.	Slides Introduction Slides Slides for Topic 1 Example Problems LeetCode: Find pivot index LeetCode: Subarray Sums Divisible by K LeetCode: Subarray Sum Equals K Kattis: Baloni LeetCode: Find the Duplicate Number	LeetCode: Two sum LeetCode: Number of Subarrays with Bounded Maximum (A bit harder. Needs to use information other than the sum for prefixes.) Kattis: CD Kattis: Jolly Jumpers USACO 2014 December Bronze 1: Marathon USACO 2015 December Silver 3: Breed Counting USACO 2013 March Bronze 2: Breed Proximity USACO 2012 November Bronze 1: Find the Cow! USACO 2015 February Bronze 2: COW
Week 2 (Aug 26 -- Aug 30)	Two pointers: One maintains two pointers (indices) into either one array or two arrays, and move the pointers based on values at the pointers. Sliding window: A window slides through an array (both ends of the window move along one direction). One maintains a summary of what are in the window, and decides how to slide based on that summary. PriortyQueue: implements the functionality of a multiset where operations such as addition, removal, and finding smallest are all efficient (O(1) or O(log N)). Without duplicate, one can use TreeSet instead. With duplicate, one can use TreeMap instead.	Slides Slides for Topic 2 Example Problems LeetCode: Two Sum II - Input array is sorted LeetCode: Container With Most Water LeetCode: Sliding Window Maximum USACO 2011 November Silver 2: Cow Lineup LeetCode: Minimum Window Substring (Req, Window) LeetCode: Subarray Product Less Than K (Req, Window)	LeetCode: Minimum Size Subarray Sum (Req, Window) LeetCode: Subarrays with K Different Integers (Req, Window) LeetCode: Longest Substring Without Repeating Characters (Bas, Window) LeetCode: Longest Repeating Character Replacement LeetCode: Permutation in String USACO 2013 Open Bronze 3: Photo USACO 2014 March Bronze 2: The Laze Cow USACO 2014 Open Bronze 2: Fair Photography USACO 2015 December Silver 2: High Card Wins
Week 3 (Sep 2 -- Sep 6)	Difference array. With range updates (changing array A's elements in an range by a constant value), maintaining the array where each element represents difference of two adjacent elements in A makes each update constant time. Some discrete event simulation can be viewed as range updates along the time dimension. Difference array to prefix-sum array is differentiation to integration in calculus. Balanced parenthesis strings. Stacks. provides last-in-first-out access; used implicitly for implementing function calls, and can be explicitly used for many tasks.	Slides Slides for Topic 3 Example Problems USACO 2012 January Bronze #2: Haybale Stacking (Req, Diff) Kattis: Disastrous Downtime ) (Req, Diff) LeetCode: Evaluate Reverse Polish Notation (Req, Stack) LeetCode: Minimum Add to Make Parentheses Valid LeetCode: Score of Parentheses	LeetCode: Valid Parentheses (Req, Stack) LeetCode: Baseball Game (Req, Stack) LeetCode: Asteroid Collision (Req, Stack) LeetCode: Valid Parenthesis String Kattis: Even Up Solitaire (2013 ICPC North American Qualifier) Kattis: Pairing Socks USACO 2013 January Silver 1: Painting the Fence USACO 2013 November Bronze 2: Goldilocks and the N Cows USACO 2012 November Bronze 2: Typo USACO 2012 November Silver 1: Clumsy Cows
Week 4 (Sep 9 -- Sep 13)	First competition.
Week 5 (Sep 16 -- Sep 20)	Stack continued Depth first search Floodfill	Slides Slides for Topic 4 Example Problems Kattis: Working at the Restaurant LeetCode: Max Area of Island (Req, DFS) LeetCode: Making A Large Island (Req, DFS) Kattis: Islands (Req, DFS)	LeetCode: Number of Islands (Req, DFS) LeetCode: Surrounded Regions (Req, DFS) LeetCode: Keys and Rooms LeetCode: Number of Enclaves LeetCode: Minesweeper Kattis: Sheba's Amoebas (Bas, DFS) Kattis: Counting Stars (Bas, DFS) Kattis: Getting Gold Kattis: 10 Kinds of People USACO 2014 March Bronze 3: Cow Art
Week 6 (Sep 23 -- Sep 27)	Breadth first search	Slides Slides for Topic 5 Example Problems Kattis: Grid (Req, BFS) Kattis: Rings (Req, BFS) LeetCode: Shortest Bridge (Req, BFS) LeetCode: Open the Lock (Req, BFS) Kattis: Fire	Kattis: Gregory the Grasshopper (Req, BFS) LeetCode: Pacific Atlantic Water Flow LeetCode: Course Schedule LeetCode: Course Schedule II Kattis: Horror List Kattis: Coast Length USACO 2013 February Bronze 3: Perimeter USACO 2014 Open Bronze 3. Decorating the Pastures
Week 7 (Sep 30 -- Oct 4)	Strings	Slides Slides for Topic 6 LeetCode: Count Binary Substrings (String, Req) LeetCode: Longest Common Prefix (String, Req) LeetCode: Valid Palindrome (String, Req) LeetCode: Groups of Special-Equivalent Strings (String, Req) LeetCode: Greatest Common Divisor of Strings LeetCode: String Compression USACO 2015 February, Bronze 1. Censoring (Bronze) (String, Req)	LeetCode: Goat Latin (String, Req) LeetCode: Count and Say LeetCode: Buddy Strings LeetCode: Repeated Substring Pattern LeetCode: Valid Palindrome II
Week 8 (Oct 7 -- Oct 11)	Second competition.	Second competition will cover the following topics. Stack (See Week 3) String (See Week 7) DFS (See Week 5) BFS (See Week 6)
Week 9 (Oct 14 -- Oct 18)	Binary Search and Meet-in-the-Middle	Slides Slides for Topic 7 LeetCode: Find First and Last Position of Element in Sorted Array (Req) LeetCode: Find Peak Element LeetCode: 3Sum Closest (Req) LeetCode: 4Sum II (Req) USACO 2015 January, Bronze 2. Cow Routing II (Req) USACO 2015 January, Bronze 3. It's All About the Base (Req)	LeetCode: H-Index LeetCode: 3Sum USACO 2014 February, Silver 1. Auto-Complete (Binary Search) USACO 2012 December, Bronze 2. Scrambled Letters (Binary Search)
Week 10 (Oct 21 -- Oct 25)	Mathematics and geometry	Slides
Week 11 (Oct 28 -- Nov 1)	Third competition.	Problem Topics Binary search (see week 9) Meet-in-the-Middle (see week 9) Sliding window (see week 2) Using data structures such as Set, Map, and PriorityQueue (see weeks 1 and 2) Traversal on 2D grid (DFS and/or BFS) (see weeks 5 and 6)
Week 12 (Nov 4 -- Nov 8)	Review of competitions 2 and 3.