CSC 421: Algorithm Design & Analysis
- To appreciate the role of algorithms in problem solving and software design, recognizing that a given problem might be solved with a variety of algorithms.
- To be capable of selecting among competing algorithms and justifying their selection based on efficiency.
- To be capable of selecting and utilizing appropriate data structures in implementing algorithms as computer programs.
- To develop programs using different problem-solving approaches (divide-and-conquer, backtracking, dynamic programming), and be able to recognize when one approach is a better fit for a given problem.
- To design and implement programs to model real-world systems, and subsequently analyze their behavior.
Object-oriented programming review
design goals: highly cohesive, loosely coupled
OO concepts: class vs. object, interfaces, inheritance, polymorphism
data structures: List, Set, Map, Stack, Queue, Graph, ...
algorithm analysis: big-Oh, rate-of-growth, analyzing algorithms, recursion
brute force algorithms
straightforward, one-time approach
examples: league standings, circle of friends (HW1)
exhaustive search: string matching
generate-and-test: N-queens, Traveling Salesman, Knapsack
reduce problem to single, smaller instance
by-constant: sequential search, insertion sort, topological sort
by-constant-factor: binary search, fake coin problem
by-variable-amount: BST search, selection problem, dishonest hangman (HW2)
reduce problem to multiple smaller instances
examples: merge sort, quick sort, closest points, multiplication
trees: size, contains, toString, ... (HW3)
transform problem into a different, more easily solved problem
examples: presorting, balanced BST algorithms, Horner's Rule
problem reduction: lcm --> gcd
solve by making a sequence of choices/actions, select locally optimal
examples: minimal change, job scheduling
minimal spanning tree: Prim's algorithm
shortest path: modified BFS, Dijkstra's algorithm
data compression: Huffman codes
solve by making a sequence of choices/actions, back up and retry if fail
examples: N-queens, blob count, Boggle, KenKen (HW4)
branch-and-bound: job assignment
game search: game trees, minimax search, alpha-beta pruning
bottom-up alternative to divide-and-conquer, avoids redundancy
examples: binomial coefficient, World Series puzzle, game probabilities (HW5)
all-pairs shortest path: Floyd's algorithm
top-down with caching: change maker
analysis via recurrence relation, Master Theorem
space vs. time tradeoffs
examples: heap sort, hash tables, BinaryTree
string matching: Horspool's algorithm, Boyer-Moore algorithm
lower bounds on problems
brute force, info-theoretic, adversary argument, reduction
decision trees: searching, sorting
tractable vs. intractable vs. undecidable (Halting Problem)
P vs. NP, Turing machine vs. non-deterministic Turing machine
NP-complete problems (e.g., SAT), reductions (e.g., SAT --> CLIQUE)