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Ch3 HW1

  1. Write a function CONSTRAIN that takes three inputs called X, MAX, and MIN. If X is less than MIN, it should return MIN; if X is greater than MAX, it should return MAX. Otherwise, since X is between MIN and MAX, it should return X. (CONSTRAIN 3 -50 50) should return 3. (CONSTRAIN 92 -50 50) should return 50.

  2. Write the function MEAN that finds the arithmetic mean of a nonempty list of numbers.

  3. Write the function STDDEV that finds the standard deviation of a nonempty list of numbers. You need not bother to divide by (n-1) instead of n.

  4. Write a function HOWCOMPUTE. HOWCOMPUTE takes three numbers as input and figures out what operation would produce the third from the first two. Possible answers: ‘ADD ‘SUBTRACT ‘MULTIPLY and ‘BEATS-ME.

  5. Write a function to act as referee in the Rock-Scissors-Paper game. In this game, each player picks one of Rock, Scissors, or Paper, and then both players tell what they picked. Rock “breaks” Scissors, so if the first player picks Rock and the second picks Scissors, the first player wins. Scissors ‘‘cuts’’ Paper, and Paper ‘‘covers’’ Rock. If both players pick the same thing, it’s a tie. The function PLAY should take two inputs, each of which is either ROCK, SCISSORS, or PAPER, and return one a number 1 = first player wins, 2 = second player wins, or 0 = tie. Examples: (PLAY ’ROCK ’SCISSORS) should return 1. (PLAY ’PAPER ’SCISSORS) should return 2.

  6. A palindrome is a sequence that reads the same forwards and backwards. The list (A B C D C B A) is a palindrome; (A B C A B C) is not. Write a function palindromep that returns T if its input is a palindrome.

  7. Write make-palindrome that takes in a list and makes a palindrome out of it in a simple way. Given (YOU AND ME) as input it should return (YOU AND ME ME AND YOU).

  8. Write a crude program to compute the probability that an integer picked from M to N is a perfect square.

  1. Earlier, we started a simulation of a dice rolling game. Finish the simulator and run it with 100,000 tries at each game to estimate the probability of winning. Report which game is easier to win, and the difference in the estimated probability of winning when compared to the other game.

  2. Sets are said to be equal if they contain exactly the same elements. Order does not matter in a set, so the sets (RED BLUE GREEN) and (GREEN BLUE RED) are considered equal. However, the EQUAL predicate does not consider them equal, because it treats them as lists, not as sets. Write a SET-EQUAL predicate that returns T if two things are equal as sets. (Hint: If two sets are equal, then each is a subset of the other.)

  3. We are going to write a program that compares the descriptions of two objects and tells how many features they have in common. The descriptions will be represented as a list of features, with the symbol -VS- separating the first object from the second. Thus, when given a list:

    (large red shiny cube -vs- small shiny red four-sided pyramid)

    the program will respond with:

    (2  COMMON  FEATURES)

    The steps to writing this program are:

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