Homework #2

Due Monday, 7/27

Each problem below lists an estimate of its relative difficulty and how much time it requires as a percentage of the whole set. The total time estimate for this homework set is around 10-15 hours.

Please also read the learning objectives for this week.

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1) (Easy, 10% of total time)

Revisit your solution to homework #1, problem 5, which expresses an improper fraction as a proper one, and turn your solution into a function.

a) Write a function fractionString(n,d) which takes 2 parameters (n,d) and returns a string. For example, fractionString(7,4) should return "1 3/4", and fractionString(3,3) should (for now) return "1 0/3". As before, assume that n and d are both positive integers.

Note that returning a string is not the same as printing a string. You may use console.log() for debugging, but your function should have the correct string as its return value. You can also print your return value with an expression like console.log(fractionString(7,4)).

b) Write a second version of your function which improves the output in two special cases:

• A output string like "0 1/2" should be simplified to just "1/2";
• A output string like "1 0/3" should be simplified to just "1".

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2) (Moderate, 10%)

Rewrite each block below as the simplest equivalent you can discover. Your equivalent should produce the same final conditions as the original code given the same initial conditions. In each case, if there is an undeclared variable, assume it has been declared earlier and set to an unknown value.

a)

var i;
if ((n - Math.floor(n)) >= .5) {
  i = Math.ceil(n);
} else {
  i = Math.floor(n);
}

b)

var y, xIsFalse = (x? false : true);
if (xIsFalse)
  y = false;
else
  y = x;

c)

for (var count = 15 - i ; count < 15 ; count=count+1) {
  i = i-1;
  console.log(i+1)
}

d)

var x;
if (a) {
  if (b) {
    x = 0;
  } else {
    x = 1;
  }
} else {
  if (b) {
    x = 1;
  } else {
    x = 2;
  }
}

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3) (Moderate, 25%)

a) Write a function letterTriangle(n) which returns a single string as follows:

• the function receives a parameter n, an integer from 1 to 26;
• the output string will have n lines, each ending in a newline ('\n') character;
• the first line of the string is always 'A';
• each line will be a sequence of letters, going backward from some starting letter to 'A';
• each line starts one letter after the previous line's start.

As an example, the result of letterTriangle(4) will look like this when printed:

A
BA
CBA
DCBA

b) Adapting your solution to part a), write a function which returns a string containing the entire lyrics for the song "The Twelve Days of Christmas". Make sure that your result is grammatically and typographically correct (include line breaks, commas, etc. where needed), but keep redundancy within your program to a minimum. Don't just console.log() each line; as before, return them together as a single string which includes a '\n' at each line break. You may want to use helper functions, loops, and/or arrays to store repeated elements.

If you prefer a non-Christmas option, you may choose a different song with similarly repeating structure, such as "There was an Old Woman Who Swallowed a Fly". If you prefer a vegan option, you may write your own cruelty-free song.

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4) (Difficult, 20%)

Suppose the '&' key on your keyboard is missing, and you want to be able to continue programming without it. You decide to simulate the && operator with a function!

a) Write a function and2(a,b) which tries to simulate the && operator: it should always return the same result as (a && b) for any values of a and b. (For example, and2((0>1),true) should return false.) But you can't use && itself within your function!

b) Write another function and3(a,b,c) which tries to simulate a double-&& operator: it should always return the same result as (a && b && c) for any values of a,b,c. (For example, and3((1>0),(0>1),true) should return false.) As before, you're not allowed to use && itself. Remember that you can call functions from functions!

c) Now generalize your function to handle any number of values. You will learn better ways eventually, but for now use an array to store all the values. Your new function andN(values) should accept one parameter values, which is an array holding all the values to && together. If the argument you provide when calling the function holds values [a,b,c...z], as in andN([a,b,c...z]), the function should return the same result as the expression (a && b && c && ... z). Make sure to handle two special cases: length 0 (then return true) and length 1 (then return that single value). Again, don't use &&.

d) You've just realized that your effort was doomed: neither of your functions can replace the && operator in certain circumstances. Explain why, and find an example which demonstrates failure.

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5) (Moderate, 35%)

Imagine that a deck of playing cards is sorted by rank and suit: first all the Aces, then the Twos, etc, with the Kings last. Within each rank, the suits are in the order Hearts, Diamonds, Spades, Clubs. Number each card in order from 0 to 51 (i.e. 0=Ace of Hearts; 1=Ace of Diamonds; 51=King of Clubs), and let that ID number represent the corresponding card. Use this encoding scheme for each part below.

a) Write five related functions to compute different aspects of a card:

• rank(id) returns 1-13, representing the card's rank (for an id between 0-51).

• suit(id) returns 1-4, representing the card's suit (1 is Hearts, 4 is Clubs).

• color(id) returns "red" or "black".

• name(id) returns the full name of the card (e.g. "Four of Diamonds").

• cardID(rank,suit) returns 0-51, identifying the card id of a given rank and suit.

Assume each function is given valid arguments (i.e. the args are integers in the appropriate range). Your functions may call each other-- for example: color could be derived from suit. Try to reuse functions to avoid duplicating code.

Hint #1: Notice the patterns as the card id ranges from 0 to 51:

• rank(id) increases slowly, like a quotient;
• suit(id) cycles quickly through 1-4, (almost) like a remainder;
• color(id) alternates R,R,B,B,R,R,B,B...

Where have you seen that kind of pattern before?

Hint #2: Generate your card names by combining a rank word from one array and suit word from another.

Write your code into the template file. The template also includes a suite of assertions for testing your code. When you evaluate the entire template file, the assertions at the end will write messages to the console if your functions fail any test. Make sure you pass all the tests!

b) Now abandon the assumption of valid arguments and program defensively! Rewrite your five functions so that each returns the correct answer when all arguments are valid, but returns NaN if any argument is not an integer in the appropriate range.

You may use the provided template file, which has extra tests checking the results of invalid arguments.

Hint #3: you can test whether an number n is an integer with (n%1 === 0).

c) In the file with your solution to part b, extend the existing test suite: write 3 new assertions to test success cases and 3 more assertions to test failure cases.

(Please note: Problem 5 is the most important one in this homework, because variations of it will recur in several later homeworks. The cleaner your code is now, the easier it will be to modify later.)