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# Creative Reductions
## ...and Wrap Up
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CS 137 // 2021-12-08

## Administrivia
- Assignment 2 is returned on Gradescope
- 
 Assignment 3 due today

# Final Exam
- Tuesday, December 14th
- 2:00 PM to 3:50 PM
- Collier-Scripps 301

## Final Exam
- **Format of the exam**:
    + Written, in-class, 110-minute exam
    + Closed textbook/notes/internet
- 
 Exam will be cumulative and cover materials from the entire semester

## Final Exam "Cheatsheet"
- You may bring a one 8.5x11 sheet of paper with you to the final exam
- This sheet may have notes on both sides as long as:
    + All notes are **handwritten** by **YOU**
- 
 My hope is that thinking through what to include on the sheet and preparing it will be an effective study mechanism

# Questions
## ...about anything?

# Reductions

## Reductions
- A problem $A$ is reducible to a problem $B$ if:
    + An instance of $A$ can be converted to an equivalent instance of $B$
    + Thus, if $B$ is solvable, then so is $A$

## Reductions
- **Fact:** If $A$ is an $NP$-hard problem and $A$ is polynomially reducible to $B$, then $B$ is also $NP$-hard
- To prove a problem is $NP$-hard, we just need to reduce a well-known $NP$-hard problem to it

![NP reduction diagram](../../assets/images/np-reduction-diagram.png)

## Creative Reductions
- [Classic Nintendo Games are NP Hard](https://arxiv.org/pdf/1203.1895.pdf)
    + [Video Explanation](https://www.youtube.com/watch?v=oS8m9fSk-Wk)

# Reflections

## Overall Theme of the Course
- Identifying and solving problems **efficiently**
    + 
 Understand and apply various data structures and algorithm design techniques
    + 
 Be able to analyze the accuracy and efficiency of algorithms and compare approaches
- 
 Recognizing **hard** problems and where that hardness comes from

## Data Structures
- Sequential
    + Array list, linked list, array deque, etc.
- 
 Hierarchical
    + Trees, binary search trees, heaps, etc.
- 
 Dictionaries (maps)
    + Hashtables
- 
 Relational
    + Graphs

## Techniques
- Greedy
- 
 Divide and conquer
- 
 Dynamic programming
- 
 Reductions

## Algorithms
- Sorting
    + Heapsort, merge sort, quick sort
- 
 Graphs
    + DFS, BFS, topological sort, Prim's, Kruskal's, Dijkstra's
- 
 Dynamic programming
    + Fibonacci, word segmentation, edit distance, seam carving

# Evaluations
- [Click Here for Evaluation](http://drake.qualtrics.com/jfe/form/SV_brQ0Lfq6EixLEto)

# Practice Problems

## Practice Problems
- Asymptotic notation (Skiena 2-11, 2-23)
- Writing an algorithm (Skiena 3-18, 4-49, 5-5)
- Data structure design (Skiena 3-20)
- Data structure comparison (Skiena 4-19)
- Graphs (Skiena 7-1, 7-2)