Chapter 4 Problem Set II

Key new concepts: patterns, guards, where, let, case.

Some of these problems are classical exercises with solutions online. Please do not search for them or read them before turning in your work.

Exercises

1. First Third. Return the sum of the first and third elements in the list. Example: firstThird [10,30,50,90] == 60.

2. Take a list of items that can be compared for equality (Eq a) and reduce repeats to a single element. Only reduce repeats that are next to each other in the list.

     noTwins [1,1,5,1,2,2,2] == [1,5,1,2]

3. (CodingBat sum67.) Return the sum of the integers in the array, except ignore sections of numbers starting with a 6 and extending to the next 7 (every 6 will be followed by at least one 7). Return 0 for no numbers.

sum67 [1, 2, 2] == 5
sum67 [1, 2, 2, 6, 99, 99, 7] == 5
sum67 [1, 1, 6, 7, 2] == 4

4. (Discuss!) Make a newFibonacci function that takes in the two starting values for the Fibonacci sequence (usually 1 and 1) and then the term in the sequence that you want, and computes that term in the sequence.

      newFibonacci 1 1 10 == 55
      newFibonacci 5 8 9 == 233

Hint: Get the standard Fibonacci fib function working, then move it completely inside a let binding so you can alter the starting values.

Block Game

Block Game. Do this bronze level USA Computing Olympiad problem. (You should start with a list of pairs of words, that is [(String,String)]; you do not have to read them from a file.)

Examples to check:

blockGame [("SOCKS","ROCKS")] -- make sure you get two 'S'
blockGame [("ALL","LAX"),("B","BBB")] -- 1A, 3B, 2L, 1X

The output should be a list of ordered pairs of a letter, then how many of that block you need, like [('S',2),('K',1), etc...].

Laser Tag

After a class discussion, you should be able to do these.

5. Laser Tag I. You are playing laser tag on the integer coordinate plane. You stand at (x0,y0) and fire your laser parallel to one of the axes. We will write the direction using unit coordinates, so (1,0) will be the positive x-direction. The coordinates of the other players are in a list. Assuming that you hit a player, report the coordinates of the player who is hit.

      laserTag (1,2) (0,1)
               [(5,2), (1,-4), (1,50), (1,25), (1,30)]
               == (1,25)

6. Laser Tag II. (Save for later if needed.) We continue to play the laser tag game, except now there are both people and double-sided mirrors oriented at 45 degrees to the coordinate axes. Represent the objects by triples (x,y,c) where c is a character * for a person, / or \ for a mirror (depending on the orientation). Assume that eventually the laser will hit someone (maybe you?!). Find the coordinates of the person who gets hit.

     laserTagMirrors (1,2) (0,1)
                     [(1,2,'*'), (5,2,'*'), (1,5,'/'), (4,5,'*'), (-3,5,'*')]
                     == (4,5)

Flipping the mirror at (1,5) should make the answer (-3,5). You should draw some test cases and make a tester function to verify your code is correct when there are more mirrors.

Dangers and Annoyances

The \ character is an “escape character”, so to include it in a string, you need to write '\\' (a Char) or "\\" (a String).