Lisp Programming (1062)

text (html, MIT press)
How to run your programs?
exercise 1: figure out the sum of squares of the minimum two arguments
- Write a procedure named 'sum-of-square-min-two' which accepts three arguments and will figure out the sum of squares of the minimum two arguments.
```
        $ scheme48
        > ,load ex1-sum-square-min-two.scm
        > 
        > (sum-of-square-min-two 1 2 3)
        5
        > (sum-of-square-min-two 1 2 -3)
        10
        > (sum-of-square-min-two 2 2 2)
        8
        > ,exit
        $ 
      
```
- Put your code in ~/scheme-1062/exer1
- Deadline: 2018/Mar/12 00:05 AM.
exercise 2: improving the good-enough?
- Refer to exercise 1.7
- Put your program under ~/scheme-1062/exer2
- Deadline 2018/Mar/18, 00:05 am
exercise 3: linear recursive and linear iterative
- Refer to exercise 1.11 but the formula is changed to
  f(n) = n if n < 3
  f(n) = 2*f(n-1) + f(n-2) + f(n-3) if n ≥ 3 and n is even
  f(n) = 2*f(n-1) - f(n-2) + f(n-3) if n ≥ 3 and n is odd
- Note that you have to write two procedures. One is written in recursive way and another in linear iterative way.
- Your program should be put under ~/scheme-1062/exer3
- Deadline: 2018/March/26 00:05 AM.
exercise 4: fast fibonacci
- Refer to exercise 1.19.
- Put your program under ~/scheme-1062/exer4.
- Deadline 2018/Apr/02, 00:05 am
exercise 5: calculating continued-fraction
- Refer to exercise 1.37.
- You have to write two procedures. One is (cont-frac n d k) and another is (pi epsilon).
- The "cont-frac" should be implemented in linear iterative way.
- To calculate pi, the sequence N_i is: 4, 1^2, 2^2, 3^2, ...
  and the sequence D_i is: 1, 3, 5, 7, ...
- To approximate pi, calculate (cont-frac n d 1), (cont-fract n d 2), .. until two consecutive values are close enough, that is, the distance between them is less than epsilon.
```
       $ scheme48
       > ,load ex5.scm
       > (cont-frac (lambda (i) 1.0) (lambda (i) 1.0) 100)
       0.6180339887498948
       > (pi 0.001)
       3.141463414634146
       > (pi 0.0001)
       3.1415888250921244
       > (pi 0.0000000000001)
       3.141592653589791
       > ,exit
       $ 
      
```
- Deadline: 2018 Apr 30 00:05 am
- Put your file(s) under ~/scheme-1062/exer5
exercise 6: representing a pair with a number
- Refer to exercise 2.5.
- Note the requirement of nonnegative is removed. Your method should accept two integers.
- Deadline: 2018 May 07 00:05
- Put your file(s) under ~/scheme-1062/exer6
exercise 7: mapping over trees
- Refer to exercise 2.31.
- Deadline: 2018 May 21 00:05
- Put your file(s) under ~/scheme-1062/exer7
exercise 8: enumerate a tree with sequence interface
- Rewrite (enum-tree T) with accumulate and map.
- Deadline: 2018 May 28 00:05
- Put your file(s) under ~/scheme-1062/exer8

exercise 9: enumerating tuples

Define a procedure, (enum-tuples list-1 list-2 .... list-k) which will generate a list of k-tuples. The tuples contains all combinations of elements from each list.

      $ scheme48
      > ,load ex9-enum-tuples.scm
      > 
      > (enum-tuples)
      ()
      > (enum-tuples '(x y z))
      ((x) (y) (z))
      > (enum-tuples '(a b c) '(hello world))
      ((a hello) (b hello) (c hello) (a world) (b world) (c world))
      > (enum-tuples '(1 2) '(h i j k))
      ((1 h) (2 h) (1 i) (2 i) (1 j) (2 j) (1 k) (2 k))
      > (enum-tuples '(hello ohio) '(101 39 11) '(good fine))  
      ((hello 101 good) (ohio 101 good) (hello 39 good) (ohio 39 good)
       (hello 11 good) (ohio 11 good) (hello 101 fine) (ohio 101 fine)
       (hello 39 fine) (ohio 39 fine) (hello 11 fine) (ohio 11 fine))
      > ,exit
      $

Deadline: 2018 June 04 00:05 am
Put your file(s) under ~/scheme-1062/exer9