1. Compsci 201 Recursion+Percolation
Owen Astrachan
Jeff Forbes
October 11, 2017
10/11/17
Compsci 201, Fall 2017, Recursion+Percolation

2. Compsci 201, Fall 2017, Recursion+Percolation
L is for …
Loops
Iteration is a wonderful thing
Library
Where we find APIs rather than books
Lexicographic Order
AKA Alphabetical
Linked Lists
Next week’s topic
10/11/17
Compsci 201, Fall 2017, Recursion+Percolation

3. Compsci 201, Fall 2017, Recursion+Percolation
Plan for the Day
Recursion: motivation, what, why, where, how
Part of Percolation and other Problems
Foundational for Computer Science ?
What is the Percolation Assignment about?
Review from last week
Review of logistics for APT Quiz
10/11/17
Compsci 201, Fall 2017, Recursion+Percolation

4. Compsci 201, Fall 2017, Recursion+Percolation
Analyze trade-offs of different implementations of data structure supporting Monte Carlo Percolation simulation
We simulate by opening sites at random until there’s percolation
Princeton, Berkeley, Cornell, Duke, …
How to tell when top connects to bottom
More when we roll out the project
10/11/17
Compsci 201, Fall 2017, Recursion+Percolation

5. Interactive Visualization
Helpful in debugging and understanding
Better live!
10/11/17
Compsci 201, Fall 2017, Recursion+Percolation

6. Compsci 201, Fall 2017, Recursion+Percolation
Compare and Contrast
Two recursive “flood-fill” algorithms
Improve on what you’re given. Huge tradeoff
Several Union-Find aka Disjoint Set implementations: initialize N and then …
QuickFind: each operation is O(N)
Weighted QuickUnion: each is O(log N)
WQU + Path Compression: O(1)
Note technically not O(1), but less than 5 for any value of N that can be represented in our universe
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Compsci 201, Fall 2017, Recursion+Percolation

7. Compsci 201, Fall 2017, Recursion+Percolation
Adapt via APIs
Understand terminology of Percolation
Open, Full, Blocked, Percolates
Given Union-Find implementations, adapt them for this problem: fit to our interfaces
Analyze runtime and analyze storage
10/11/17
Compsci 201, Fall 2017, Recursion+Percolation

8. Google (DYM): Recursion
What is the Internet?
A network of networks ….
What is PageRank?
What’s a good website link?
What is Recursive DNS?
IP address of fxyztl.com
public int calc(int n){
return n*calc(n-1); }
10/11/17
Compsci 201, Fall 2017, Recursion+Percolation

9. Compsci 201, Fall 2017, Recursion+Percolation
Running Down a Dream
What if you’re running out of storage?
Buy more disk space
Move to cloud
Delete large files/move them
Finding large files programmatically
Look in this folder … what you will find?
Repeat until …
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Compsci 201, Fall 2017, Recursion+Percolation

10. Compsci 201, Fall 2017, Recursion+Percolation
Finding Large Files?
Open a folder and look in it
If there’s a file, check to see if it’s big
If there’s a directory, look in it for big files
Watch out for the infinite folders problem!
Coursework>201fall17>classwork>BigFiles.java
10/11/17
Compsci 201, Fall 2017, Recursion+Percolation

11. Compsci 201, Fall 2017, Recursion+Percolation
Recursive Examples
Structure of the problem leads to recursion
Big Files: folders contain folders which …
Finding Blobs: one cell + neighboring “blob”
Linked Lists (next week)
Algorithmic examples as well, structure sometimes not so apparent
Efficient sorting algorithms often recursive
Factorial is NOT necessarily recursive, but …
10/11/17
Compsci 201, Fall 2017, Recursion+Percolation

12. Compsci 201, Fall 2017, Recursion+Percolation
How do you calculate N!
Multiply 1 x 2 x 3 x … x N
public int fact(int n){
int prod = 1;
for(int k=2; k <= n; k++){
prod *= k; }
return prod;
10/11/17
Compsci 201, Fall 2017, Recursion+Percolation

13. Recursive Terminology
Recursive methods must have a base case
Simple to do, don’t need “help”
Recursive calls make progress toward base case
Some measure gets smaller, toward base case
What’s n!
It’s n * (n-1)!
What’s the base case? 1! Is 1
10/11/17
Compsci 201, Fall 2017, Recursion+Percolation

14. Compsci 201, Fall 2017, Recursion+Percolation
Don’t do this!
public int fact(int n){
if (n == 1) return 1;
return n*fact(n-1); }
n=4
int x = fact(4);
return 4*fact(3)
The call of fact(3) calls a “clone” or “copy”
Doesn’t call “itself”, is re-entrant code
public int fact(int n){
if (n == 1) return 1;
return n*fact(n-1); }
10/11/17
Compsci 201, Fall 2017, Recursion+Percolation

15. Compsci 201, Fall 2017, Recursion+Percolation
Don’t do this 2
public int fact(int n){
if (n == 1) return 1;
return n*fact(n-1); }
n=4
int x = fact(4);
return 4*fact(3)
public int fact(int n){
if (n == 1) return 1;
return n*fact(n-1); }
n=3
public int fact(int n){
if (n == 1) return 1;
return n*fact(n-1); }
10/11/17
Compsci 201, Fall 2017, Recursion+Percolation

16. Compsci 201, Fall 2017, Recursion+Percolation
Don’t do this 3
public int fact(int n){
if (n == 1) return 1;
return n*fact(n-1); }
n=4
int x = fact(4);
return 4*fact(3)
return 3 * fact(2)
public int fact(int n){
if (n == 1) return 1;
return n*fact(n-1); }
n=3
public int fact(int n){
if (n == 1) return 1;
return n*fact(n-1); }
n=2
10/11/17
Compsci 201, Fall 2017, Recursion+Percolation

17. Compsci 201, Fall 2017, Recursion+Percolation
Don’t do this 3
public int fact(int n){
if (n == 1) return 1;
return n*fact(n-1); }
n=4
int x = fact(4);
return 4*fact(3)
return 3 * fact(2)
When n is 2 …?
return 2 * fact(1)
public int fact(int n){
if (n == 1) return 1;
return n*fact(n-1); }
n=3
public int fact(int n){
if (n == 1) return 1;
return n*fact(n-1); }
n=2
10/11/17
Compsci 201, Fall 2017, Recursion+Percolation

18. Compsci 201, Fall 2017, Recursion+Percolation
Base Case Reached
public int fact(int n){
if (n == 1) return 1;
return n*fact(n-1); }
n=4
return 2*fact(1)
Evaluates to 2*1
Return to call of fact(1)
public int fact(int n){
if (n == 1) return 1;
return n*fact(n-1); }
n=3
n=1
public int fact(int n){
if (n == 1) return 1;
return n*fact(n-1); }
public int fact(int n){
if (n == 1) return 1;
return n*fact(n-1); }
n=2
10/11/17
Compsci 201, Fall 2017, Recursion+Percolation

19. Compsci 201, Fall 2017, Recursion+Percolation
Base Case Reached
public int fact(int n){
if (n == 1) return 1;
return n*fact(n-1); }
n=4
int x = fact(4)
n = 1 returns 1
n = 2 returns 2
n = 3 returns 6
n = 4 returns 24
public int fact(int n){
if (n == 1) return 1;
return n*fact(n-1); }
n=3
public int fact(int n){
if (n == 1) return 1;
return n*fact(n-1); }
n=1
public int fact(int n){
if (n == 1) return 1;
return n*fact(n-1); }
n=2
10/11/17
Compsci 201, Fall 2017, Recursion+Percolation

20. Compsci 201, Fall 2017, Recursion+Percolation
WOTO … See Woto
10/11/17
Compsci 201, Fall 2017, Recursion+Percolation

21. Compsci 201, Fall 2017, Recursion+Percolation
John Tukey:
Cooley-Tukey FFT
Bit is a binary digit
Box or Box and Whiskers Plots
Far better an approximate answer to the right question, which is often vague, than an exact answer to the wrong question, which can always be made precise.
The combination of some data and an aching desire for an answer does not ensure that a reasonable answer can be extracted from a given body of data.
10/11/17
Compsci 201, Fall 2017, Recursion+Percolation

22. Compsci 201, Fall 2017, Recursion+Percolation
Flood Fill, Blob Count, …
10/11/17
Compsci 201, Fall 2017, Recursion+Percolation

23. Compsci 201, Fall 2017, Recursion+Percolation
Applications …
Flood-fill for painting/photo apps
Redeye removal?
Make region transparent
Finding “blobs” or “edges”
We’ll use recursion
Always possible to do without
10/11/17
Compsci 201, Fall 2017, Recursion+Percolation

24. Compsci 201, Fall 2017, Recursion+Percolation
Blob Counting Ideas
How do I count “my region” or “my blob”?
Ask my neighbors their size
I’m the +1 to their result
Avoid double-counting!
Colors indicate calls
White calls green
Pink calls red
10/11/17
Compsci 201, Fall 2017, Recursion+Percolation

25. Compsci 201, Fall 2017, Recursion+Percolation
Bookkeeping Details
Blobs marked with ‘*’ – aka asterisk
We will “fill” or “mark” cells when counting
Filling avoids counting cells twice
Filling allows for visualization as well
BlobModel.blobFill method: (row,col) for start
lookFor character, e.g., ‘*’
fillWith character, e.g., ‘1’ or ‘7’ or …
If blob not big enough? Repeat: lookFor = fillWith
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Compsci 201, Fall 2017, Recursion+Percolation

26. Looking for Blobs Everywhere
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Compsci 201, Fall 2017, Recursion+Percolation

27. Blobs starting at (row,col)
If this could be part of a blob? Ask neighbors to help find size of the blob
10/11/17
Compsci 201, Fall 2017, Recursion+Percolation

28. Recursive Terminology
Recursive methods must have a base case
Simple to do, don’t need “help”
Recursive calls make progress toward base case
Some measure gets smaller, toward base case
What’s n!
It’s n * (n-1)!
What’s the base case? 1! Is 1
10/11/17
Compsci 201, Fall 2017, Recursion+Percolation

29. Compsci 201, Fall 2017, Recursion+Percolation
When does process stop?
If (row,col) is not in bounds? Do nothing
If grid[row][col] != lookFor? Do nothing
Otherwise (what do we know here?)
In bounds AND looking for ‘*’ for example
Look at horizontal and vertical neighbors
Use results of recursive calls to create return
10/11/17
Compsci 201, Fall 2017, Recursion+Percolation

30. Compsci 201, Fall 2017, Recursion+Percolation
blobFill(row,col)
Returns a value, make sure value used
Both in original calls
And in recursive calls
How do we know this will terminate?
Each recursive call “marks” a cell
myGrid[row][col] = fillWith
Unless fillWith == lookFor, not infinite!
10/11/17
Compsci 201, Fall 2017, Recursion+Percolation

31. Compsci 201, Fall 2017, Recursion+Percolation
WOTO for Blobs
10/11/17
Compsci 201, Fall 2017, Recursion+Percolation

32. How to search 8 neighbors?
We need to make 8 recursive calls
W, NW, N, NE, E, SE, S, SW
See coding “trick” below
int[] rd = {0,-1,-1,-1,0,1,1,1};
int[] cd = {-1,-1,0,1,1,1,0,-1};
for(int d = 0; d < rd.length; d+= 1){
int nr = row + rd[d];
int nc = col + cd[d];
size += blobFill(nr,nc, …) }
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Compsci 201, Fall 2017, Recursion+Percolation

33. Compsci 201, Fall 2017, Recursion+Percolation
Krysta Svore
Manages Microsoft Quantum Architectures and Computation Group (QuArC)
“We think a quantum computer could possibly solve these [hard] types of problems in a time frame that’s more reasonable than the life of the universe, maybe a couple of years, or a couple of days, or a couple of seconds,” Svore said. “Exponentially faster.”
10/11/17
Compsci 201, Fall 2017, Recursion+Percolation