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Problems Problem 1 – Collision detection of balls Many games have complex physics engines, and one major function of these engines is to figure out if two objects are colliding. Weirdly-shaped objects are often approximated as balls. In this problem, we will figure out if two balls are colliding.

We will think in 2D to simplify things, though 3D isn’t different conceptually. For calculating collision, we only care about a ball’s position in space and its size. We can store position with its center x-y coordinates, and we can use its radius for size. So a ball is a tuple of (x, y, r).

To figure out if two balls are colliding, we need to compute the distance between their centers, then see if this distance is less than the sum of their radii. If so, they are colliding.

Write a function that takes two balls and computes if they are colliding. Then call the function with two sets of balls.

The first set is (0, 0, 1) and (3, 3, 1); these should not be colliding. The second set is (5, 5, 2) and (2, 8, 3); these should be colliding.

Problem 2 – Pig-Latin Converter Write a program that lets the user enter in some English text, then converts the text to Pig-Latin. To review, Pig-Latin takes the first letter of a word, puts it at the end, and appends “ay”. The only exception is if the first letter is a vowel, in which case we keep it as it is and append “hay” to the end.

E.g. “hello” → “ellohay”, and “image” → “imagehay” It will be useful to define a list or tuple at the top called VOWELS. This way, you can check if a letter x is a vowel with the expression x in VOWELS. programminghomeworkhelp.com It’s tricky for us to deal with punctuation and numbers with what we know so far, so instead, ask the user

“My name is John Smith”.split(“ ”) → [“My”, “name”, “is”, “John”, “Smith”] Using this list, you can go through each word and convert it to Pig-Latin. Also, to get a word except for the first letter, you can use word[1:].

Hints: It will make your life much easier – and your code much better – if you separate tasks into functions, e.g. have a function that converts one word to Pig-Latin rather than putting it into your main program code.

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Solutions # collision.py # Example solution for Lab 6, problem 1 # # Aseem Kishore # # 6.189 - Intro to Python # IAP 2008 - Class 4 # Imports should usually go at the top of a program instead of in the main code. from math import * # These helper functions let me "abstract away" the syntax of getting a ball's # x- and y- coordinates, or its radius. This makes my code more readable and # also helps prevent bugs where I use x instead of y, etc. def get_x(ball): return ball[0] def get_y(ball): return ball[1] def get_r(ball): return ball[2] programminghomeworkhelp.com

# I got this function from the second day of class. We've been trying to tell # you guys the importance of functions; here's one -- reuse. There are many # applications for finding the distance between two points; detecting collision # is one, so we can reuse the function. This is also why we don't ask for input # or print our result inside the function. def distance(x1, y1, x2, y2): return sqrt((x2-x1)**2 + (y2-y1)**2) # Here is my detect collision function. Note that I'm NOT taking six variables # like x1, y1, r1, x2, y2, r2 -- that's the purpose of combining x, y, r into a # tuple, as every ball has an x, y and r. def collision(ball1, ball2): d = distance(get_x(ball1), get_y(ball1), get_x(ball2), get_y(ball2)) sum_of_radii = get_r(ball1) + get_r(ball2) return d < sum_of_radii # My test cases print "First test case:", a = (0, 0, 1) b = (3, 3, 1) programminghomeworkhelp.com

if collision(a, b): print "Oops, we detected a collision!" else: print "Passed!" print "Second test case:", a = (5, 5, 2) b = (2, 8, 3) if collision(a, b): print "Passed!" else: print "Oops, we didn't detect a collision!" # piglatin.py # Example solution for Lab 6, problem 2 # # Aseem Kishore # # 6.189 - Intro to Python # IAP 2008 - Class 4 VOWELS = ('a', 'e', 'i', 'o', 'u') programminghomeworkhelp.com

# Helper function that converts one word into Pig-Latin. Remember, our word is # the function's argument, like 4 is the argument in sqrt(4). We don't need to # know anything about the sentence from which the word came. # # Also, remember that strings are index-able, just like lists and tuples.

But, # they are immutable, like tuples. So when we want to append "ay" or "hay" to # the end, we can't use append(). But, we can use the string concatenation (+) # operator to return a new string. # # e.g. we can't do "a".append("b"), but we can do "a" + "b". def convert_word(word): first_letter = word[0] if first_letter in VOWELS: # if word starts with a vowel... return word + "hay" # then keep it as it is and add hay to the end else: return word[1:] + word[0] + "ay" # like the lab mentions, word[1:] # returns the word except word[0] programminghomeworkhelp.com

# From this function, it's easy to take a sentence and convert it to Pig-Latin. def convert_sentence(sentence): list_of_words = sentence.split(' ') new_sentence = "" # we'll keep concatenating words to this... for word in list_of_words: new_sentence = new_sentence + convert_word(word) # ...like this new_sentence = new_sentence + " " # but don't forget the space! return new_sentence # Now, let's write the main program code, to ask the user and convert. print "Type in a sentence, and it'll get converted to Pig-Latin!" print "Please don't use punctuation or numbers." print "Also, we can't handle uppercase/lowercase yet, so lowers only please!" print text = raw_input() # nothing in the parentheses, because there's nothing else # extra to tell the user before he is allowed to type print print convert_sentence(text)

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