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The Bellman-Ford algorithm is a way to compute the shortest path between a source node and all other nodes in the graph. Unlike Dijkstra's Algorithm, Bellman-Ford also works on graphs with negative...
Big O notation, or Big Oh notation, is often used to describe how the size of the input data affects an algorithm's usage of computational resources (usually running time or memory). Time and...
A binary heap is the most common implementation of a priority queue. It is stored as a binary tree which satisfies the heap property. The heap property ensures that the node with the highest...
Binary search is a basic algorithm used to locate a desired spot in logarithmic time. It works when you can query whether the answer is higher or lower than your current guess.
For example, say you...
Breadth First Search (BFS) is a non-informed search for trees. It involves visiting the nodes closest to the root before spreading out.
Implementation
Unlike DFS which has a very small memory...
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There are many different ways to store information in RAM. The different schemes are described by abstract data structures which all have various advantages and disadvantages. The following list is...
Explanation, Uses, Any other relevant information
Operation
Complexity
Description
sample
samples something?
Java
C++
How to use or build the structure in Java
How to use or build...
Depth First Search (otherwise known as DFS) is a search algorithm for trees. It is an uninformed search, meaning that it does not take in any information about the cost of going to and from nodes....
Dijkstra's algorithm is a method to compute the shortest path between two nodes in a graph. One possible use could be for calculating the best driving route in a road network (vertices are...
A dynamic array is simply an array with variable length. The array begins with a certain size and when that size is exceeded more memory is allocated and the size is increased accordingly. This...
Dynamic programming, often abbreviated “DP”, is a technique to efficiently solve recursion problems – problems whose solutions depend on solutions of smaller subproblems – by storing...
An Eulerian tour is any path in a graph that uses every edge exactly once. An Eulerian tour that starts and ends on the same vertex is called an Eulerian circuit. If and only if a graph is...
The Fibonacci Problem is a very well known computer science problem in which the program must calculate the nth term in the Fibonacci Sequence. The Fibonacci Sequence is as follows:
(1)
Note that...
Floyd-Warshall is an all-pairs shortest path algorithm which runs in time. It is a very simple algorithm, requiring only four or five lines in most implementations. It requires a matrix for the...
Graph theory is of central importance in computer science. Many important problems reduce to solving a well known problem on general graphs. It is thus incredibly important to be able to store...
Graph Theory deals with trees, and more generally, graphs. In general graphs are more interesting than trees as the can model real situations easily.
Algorithms
With graphs, choosing which...
A heap is a special type of tree with the property that every node is larger than its children. If every node is smaller than its children the heap is referred to as a min-heap. The most common...
If you are allowed to edit pages in this Site, simply click on edit button at the bottom of the page. This will open an editor with a toolbar pallette with options.
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When you are aware the solution will be at or near a particular level and you would like the advantages of the small memory requirement of DFS, you just do a normal DFS, but limit it to a certain...
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Problem 2: We have a bunch of cows and a bunch of types of grass. You want to get a unique grass for each cow. You have a cost c for grass g. You want to find the minimum...
This is the repository for audio, video, or transcriptions of 8th period lectures.
12/14/07
A linked list is, quite simply, a list in which each element is linked to the next, much like a chain. A linked list commonly keeps pointers to the first and last element, with elements pointing to...
**Memoization **is a dynamic programming technique in which solutions to subproblems are stored so they can be used in solutions to later problems. As an example, consider the Fibonacci Problem. In...
Introduction
A spanning tree is any subgraph of a graph that is a connected tree (in other words, the tree has to include every node in the graph, though not necessarily all edges). The...
Prim's Algorithm is a method to construct a minimal spanning tree. For example, this can be used when one wants to determine the minimal cost of connecting a number of cities to a water source (the...
A priority queue is a generalization of both the stack and queue. The difference is in the method of selecting which item to next pop off the data structure. A priority queue usually assigns a...
Pseudocode is a technique used to lay out the idea behind a program. Generally it comes out similar to the actual code, but easier for a human to read. For this reason, it provides a good...
A queue is a FIFO (First In First Out) data structure. It is extensively used in programming in algorithms such as Breadth-First Search and in scheduling where first-come-first-serve is desired.
A...
Rabin-Karp hashing is a method of using linear time precomputation to allow constant time hashing of arbitrary substrings with a polynomial hash.
Polynomial Hash
For a string , a polynomial hash of...
Recursion problems are those whose solutions depend on solutions to smaller subproblems. One famous example of a Recursion problem is the Fibonacci sequence, in which every term is the sum of the...
Repeated squaring is a technique used to evaluate the term of a sequence in O(log N) time. It relies on an efficient method to compute from and , for example, multiplying and .
The...
Introduction
Shortest path refers to a graph theory problem in which one wishes to find the shortest path between two vertices. Single source shortest path is where you are given a starting node...
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The Sliding Window Trick is a dynamic programming technique in which memory is recycled as it becomes useless. Take, for example, the Fibonacci problem. If you are using a Bottom-up Approach to...
A stack is a LIFO (Last In First Out) or equivalently a FILO (First In Last Out) data structure. It finds use in a number of situations including the Depth-First Search in graph theory and the...
The main topics in string manipulation are Rabin-Karp Hashing, Knuth-Morris-Pratt String Matching, Suffix Arrays, and Suffix Trees.
A suffix array is simply an array with the suffices of a string or array sorted. For example, the suffix array of the string "abracadabra" is...
A suffix trie is a trie which contains all the suffices of a string. The root node is special, not representing a letter. Then, each node is one letter and any simple path from root to leaf is a...
Introduction
This is the wiki of the Senior Computer Team at TJHSST (Thomas Jefferson High School for Science and Technology). The purpose of this site is to provide a pool of computer science...
Data Structures
Graph Theory
Dynamic Programming
String Manipulation
Contests
A Tree is a data structure built of connected nodes much like a linked list. The difference is that nodes can have more than one successor (child) in a Tree. Trees are the underlying structure...
The United States of America Computing Olympiad (USACO) is a computer programming competition aimed primarily at secondary school students in the United States. Participants of the USACO submit...
Special Chinese USACO Contest (1 Division) 2007
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GOLD...
The XXX contest for the 20yy-20zz competition year of USACO.
Gold Problems
Silver Problems
Bronze Problems
The December contest for the 2007-2008 competition year of USACO.
Gold Problems
Silver Problems
Bronze Problems
Part of USACO Dec07
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BRONZE PROBLEMS
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Three problems...
Part of USACO Dec07
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SILVER PROBLEMS
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Three problems...
The December contest for the 2008-2009 competition year of USACO.
Gold Problems
Silver Problems
Bronze Problems
Part of USACO Dec08
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BRONZE...
Part of USACO Dec08
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GOLD...
Part of USACO Dec08
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SILVER...
The December contest for the 2009-2010 competition year of USACO.
Gold Problems
Silver Problems
Bronze Problems
Part of USACO Dec09
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BRONZE...
Part of USACO Dec09
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GOLD...
Part of USACO Dec09
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SILVER...
The February contest for the 2007-2008 competition year of USACO.
Gold Problems
Silver Problems
Bronze Problems
Part of USACO Feb08
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BRONZE PROBLEMS
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Three problems...
Part of USACO Feb08
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GOLD PROBLEMS
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Three problems...
Part of USACO Feb08
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SILVER PROBLEMS
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Three problems...
The February contest for the 2008-2009 competition year of USACO.
Gold Problems
Silver Problems
Bronze Problems
Part of USACO Feb09
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BRONZE...
Part of USACO Feb09
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GOLD...
Part of USACO Feb09
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SILVER...
The February contest for the 2009-2010 competition year of USACO.
Gold Problems
Silver Problems
Bronze Problems
Part of USACO Feb10
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BRONZE...
Part of USACO Feb10
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GOLD...
Part of USACO Feb10
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SILVER...
The special holiday contest for the 2008-2009 competition year of USACO.
Gold Problems
Part of USACO Hol09
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GOLD...
The special holiday bonus contest for the 2009-2010 competition year of USACO.
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GOLD...
The January contest for the 2007-2008 competition year of USACO.
Gold Problems
Silver Problems
Bronze Problems
Part of USACO Jan08
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BRONZE PROBLEMS
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Three problems...
Part of USACO Jan08
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GOLD PROBLEMS
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Three problems...
Part of USACO Jan08
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SILVER PROBLEMS
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Three problems...
The January contest for the 2008-2009 competition year of USACO.
Gold Problems
Silver Problems
Bronze Problems
Part of USACO Jan09
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BRONZE...
Part of USACO Jan09
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GOLD...
Part of USACO Jan09
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SILVER...
The January contest for the 2009-2010 competition year of USACO.
Gold Problems
Silver Problems
Bronze Problems
Part of USACO Jan10
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BRONZE...
Part of USACO Jan10
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GOLD...
Part of USACO Jan10
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SILVER...
The March contest for the 2007-2008 competition year of USACO.
Gold Problems
Silver Problems
Bronze Problems
Part of USACO Mar08
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BRONZE PROBLEMS
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Three problems...
Part of USACO Mar08
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GOLD PROBLEMS
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Three problems...
Part of USACO Mar08
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SILVER PROBLEMS
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Three problems...
The March contest for the 2008-2009 competition year of USACO.
Gold Problems
Silver Problems
Bronze Problems
Part of USACO Mar09
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BRONZE...
Part of USACO Mar09
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GOLD...
Part of USACO Mar09
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SILVER...
The March contest for the 2009-2010 competition year of USACO.
Gold Problems
Silver Problems
Bronze Problems
Part of USACO Mar10
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BRONZE...
Part of USACO Mar10
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GOLD...
Part of USACO Mar10
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SILVER...
The November contest for the 2007-2008 competition year of USACO.
Gold Problems
Silver Problems
Bronze Problems
Part of USACO November 2007
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BRONZE PROBLEMS
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Three...
Part of USACO November 2007
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GOLD PROBLEMS
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Three...
Part of USACO November 2007
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SILVER PROBLEMS
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Three...
The November contest for the 2008-2009 competition year of USACO.
Gold Problems
Silver Problems
Bronze Problems
Part of USACO Nov08
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BRONZE...
Part of USACO Nov08
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GOLD...
Part of USACO Nov08
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SILVER...
The November contest for the 2009-2010 competition year of USACO.
Gold Problems
Silver Problems
Bronze Problems
Part of USACO Nov09
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BRONZE...
Part of USACO Nov09
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GOLD...
Part of USACO Nov09
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SILVER...
The qualifying round for the 2007-2008 competition year of USACO.
Gold Problems
Silver Problems
Bronze Problems
Part of USACO October 2007
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BRONZE PROBLEMS
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Two problems...
Part of USACO October 2007
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GOLD PROBLEMS
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Two problems...
Part of USACO October 2007
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SILVER PROBLEMS
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Two problems...
The October contest for the 2008-2009 competition year of USACO.
Problems
Part of USACO Oct08
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GOLD...
The October contest for the 2009-2010 competition year of USACO.
Problems
Part of USACO Oct09
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GOLD...
The US Open contest for the 2007-2008 competition year of USACO.
Gold Problems
Silver Problems
Bronze Problems
Part of USACO Open08
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BRONZE PROBLEMS
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Four problems...
Part of USACO Open08
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GOLD PROBLEMS
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Three problems...
Part of USACO Open08
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SILVER PROBLEMS
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Four problems...
The US Open contest for the 2008-2009 competition year of USACO.
Gold Problems
Silver Problems
Bronze Problems
Part of USACO Open09
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BRONZE...
Part of USACO Open09
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GOLD...
Part of USACO Open09
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SILVER...
The US Open contest for the 2009-2010 competition year of USACO.
Gold Problems
Silver Problems
Bronze Problems
Part of USACO Xxxyz
Insert problems here
