1. Spring 2018
EECS 110: Homework IV

2. Homework IV Problems: Extra Credits: Mandelbrot set
Time Travel Securities, Inc.
Pi from pie
Extra Credits:
Sequence Sums

3. Problem 2: TT Securities The Menu
Function tts() prints a menu (0) Input a new list (1) Print the current list (2) Find the average price (3) Find the standard deviation (4) Find the min and its day (5) Find the max and its day (6) Your TT investment plan (9) Quit Enter your choice:

4. Problem 2: TT Securities The Input and Options
Take user’s choice
Can be integer or a string
Print warning if choice is not valid
9: Quit
0: Take input as a list
Ex: [20,10,30]
Start with an empty list
New list will be appended to the current
Change the type of input()if necessary!

5. Problem 2: TT Securities The Options
1: Print out the current list
For each entry, print out the index and the value
Ex: Day | Price | | | 30.00
2, 4, 5: Straight-forward

6. Problem 2: TT Securities The Options
3: Find Standard Deviation
List L has average Lav
Standard deviation is sqrt((sum(L[i]-Lav)**2)/len(L))
6: Find the best buy day and sell day
To maximize profit (note: buy day < sell day)
Comments:
Add new options for extra credit (up to 10 pts)
Should have a helper function for each option

7. Problem 2: TT Securities Example Flow
def tts(): quit = False while ... # quit is not True # print menu ... # get user input # if input is 9, quit = True # else print out the answer

8. Problem 3: Calculating π Overview
Idea: π = Area of the circle inscribed a 2 by 2 square
Estimating π using random dart-throwing
A square from (-1,-1) to (1,1) -1 1
Area of Circle =
Number of darts hit the circle
Area of Square
Total number of darts

9. Problem 3: Calculating π forPi(n)
Take input n as a positive integer
Sequentially throw n darts into the square:
Each throw = randomly choose a point
A point has coordinate (x,y) between -1 and 1
Determine if (x,y) is in the circle
After each throw:
Print out number of darts thrown so far
Number of darts hit the circle
The current estimate of π

10. Problem 3: Calculating π Example Flow
def forPi(n): # initiate variables ... for i in ... # pick (x,y) randomly # if (x,y) is in the circle # update the number of hits # print out things

11. Problem 3: Calculating π whilePi(error)
Take input error as a positive floating point
Throw darts until the estimate error < error
Estimate error = |estimate π – actual π|
After each throw print as in forPi(n)

12. Problem 3: Calculating π Example Flow
def whilePi(error): # initiate variables ... while # estimate error > error # pick (x,y) randomly # if (x,y) is in the circle # update the number of hits # update the estimation # print out things

13. Problem 3: Calculating π Hints
Choosing random number random.uniform(-1.0,1.0)
Distance between (x,y) and (0,0): sqrt(x**2+y**2)

14. Extra Credit: Sequence Sums Overview
Look and Say
Harmonic series
Harmonic series without d (Kempner series)

15. Extra Credit: Sequence Sums Look and Say
Look and Say sequence: 1, 11, 21, 1211, , , ,…
readOne(s) returns the reading of string s:
Examples: readOne('11') returns '21' readOne('312211') returns ' '
Should use both recursion and loop
Base case: len(s) == 1 '

16. Extra Credit: Sequence Sums Look and Say
Weep(n) generates the first n terms:
Example: Weep(8) prints '

17. Extra Credit: Sequence Sums Harmonic Series
Harmonic series is 1 + 1/2 + 1/3 + 1/4 + 1/5 + …
Divergence (very slow)
harmonicN(numToReach) returns the smallest number of terms required to exceed numToReach '

18. Extra Credit: Sequence Sums Harmonic Series without d
Harmonic series without digit d: remove all term that has digit d in the denominator
Example, d = 2: remove the following terms: 1/2, 1/12, 1/20, 1/21,…, 1/32, 1/42,…
Convergence (very slow)
Withoutd(d,Numterms) returns the Harmonic series without d, calculated using exactly Numterms terms '

19. Extra Credit: Sequence Sums Hints
Python may lose precision
Use package decimal:
Preamble: from decimal import * getcontext().prec = 20
Turn number to Decimal format Decimal(n)
Operations stay the same
Turn Decimal format to string: str(x) '

20. Have fun + Good luck :D