Programming Languages ML Programming Project Due 9/28/2001, 5:00 p.m.

Transcription

1 Programming Languages ML Programming Project Due 9/28/2001, 5:00 p.m. Functional Suite Instead of writing a single ML program, you are going to write a suite of ML functions to complete various tasks. You must write all of the required functions, plus any helper functions that are needed to get your main functions working. Lists and Sorting Write the following functions, that deal with lists: zip: 'a list * b list -> ('a * 'b) list input: an ordered pair of lists. output: a list of ordered pairs. For example: - zip ([1, 2, 3],["a", "b", "c"]); val it = [(1,"a"),(2,"b"),(3,"c")] : (int * string) list - zip ([false, true],[4,9]); val it = [(false, 4),(true, 9)] : ( bool * string) list zip should raise an exception if called with lists that are not of equal length unzip : ('a * 'b) list -> 'a list * 'b list input: a list of ordered pairs output: an ordered pair of lists unzip is (unsurprisingly) an inverse zip function. Some examples: - unzip [(1, true), (3, false)]; val it = ([1, 3], [true, false]) : int list * bool list - unzip [("a", 3), ("c", 2), ("b", 1)]; val it = (["a", "c", "b"], [3, 2, 1]) : sting list * int list split : 'a list -> 'a list * 'a list input: a list of anything output: an ordered pair of lists, which consist if the original list split into even and odd indices. Some examples: split [1,2,3,4,5]; val it = ([1,3,5],[2,4]) : int list * int list - split ["a", "b", "c", "d"]; val it = (["a", "c"], ["b", "d"]); merge : ('a * 'a -> bool) -> ('a list * 'a list) -> 'a list intput: a less than function, and an ordered pair of lists (each sorted according to the less than function) output: a single list, sorted according to the less than function

2 - merge (op <) ([1,3,5],[2,9,12]); val it = [1,2,3,5,9,12] : int list mergesort : ('a * 'a -> bool) -> 'a list -> 'a list input: a less-than function and a list of elements output: the list sorted according to the less-than function mergesort uses split and merge to sort a list. The let val <varname> = <expression> in <expression> end construct might be useful here, as well as the functions: fun first(x,_) = x; and fun second(_,x) = x; Some examples: - mergesort (op <) [5,4,3,2,1]; val it = [1,2,3,4,5] int list - mergesort (op >) [4,2,3,1,5]; val it = [5,4,3,2,1] int list Trees The following datatype can be used to store any binary tree datatype 'a btree = empty node of 'a * 'a btree * 'a btree; Each tree node is either empty, or stores some data element, a left subtree and a right subtree. Write the following functions that manipulate binary trees: numnodes : 'a btree -> int input: a general binary tree output: the total number of nodes in the tree Some examples: - numnodes empty; val it = 0 : int - numnodes (node("a", node("b", empty, node("e", empty empty)), empty)); val it = 3 : int - numnodes (node(4, empty, empty)); val it = 3 : int maxvalue : ('a * 'a -> bool) -> 'a btree -> 'a input: a less than function and a general binary tree (not necessarily a Binary Search Tree) output: the largest value in the tree, according to the less than function. - maxvalue (op <) (node(1, node(3, empty, node(4, empty empty)), empty)); val it = 4 : integer; - maxvalue (op >) (node(1, node(3, empty, node(4, empty empty)), empty)); val it = 1 : integer; preorder : 'a btree -> 'a list output: the nodes of the binary tree, in the order that they would be visited in a preorder traversal

3 example: - preorder (node(2, node(1, empty, empty), node(3, empty, empty))); val it = [2,1,3] : int list postorder : 'a btree -> 'a list output: the nodes of the binary tree, in the order that they would be visited in a postorder traversal example: - postorder (node(2, node(1, empty, empty), node(3, empty, empty))); val it = [1,3,2] : int list inorder : 'a btree -> 'a list output: the nodes of the binary tree, in the order that they would be visited in an inorder traversal - inorder (node(2, node(1, empty, empty), node(3, empty, empty))); val it = [1,2,3] : int list insert: ('a * 'a -> bool) -> 'a btree -> 'a ->'a btree input: a less than function, a Binary Search Tree T, and an element e output: the binary search tree T with e inserted into the correct location - insert (op <) (node(2, node(1, empty, empty), node(3, empty, empty))) 4; val it = node(2, node(1, empty, empty), node(3, empty, node(4, empty, empty))) : int btree Note the ML interpreter may truncate the output when printed to the screen, just so that it can fit on one line. A # in the output is the ML interpreter's way of saying "...". It does not mean that the interpreter is returning a truncated value, just that the value is truncated when it is printed to the screen. So the interpreter may print out the following for the above output: val it = node(2, node(1, empty, empty), node(3, empty, # )) btreesort ('a * 'a -> bool) -> 'a list -> 'a list input: a less than function, and a list of elements output: the list of elements, sorted according to the less than function, using Binary Search Trees - btreesort (op <) [5,4,3,2,1]; val it = [1,2,3,4,5] int list - btreesort (op >) [4,2,3,1,5]; val it = [5,4,3,2,1] int list

4 Graphs Consider the following graph: a b c d We can represent this graph (among other ways) as an adjacency list, or as a set of edges: Adjacency list: [("a", ["b", "c", "d"]), ("b", ["c"]), ("c",[]), ("d",["c","b"])] Edge list: [("a","b"), ("b","c"), ("a","c"), ("a","d"), ("d","c"), ("d","b")] adjlist2edgelist: string * (string list) list -> string * string list input: an adjacency list representation of a graph output: an edge list representation of the graph - adjlist2edgelist [("a", ["b", "c", "d"]), ("b", ["c"]), ("c",[]), =("d",["c","b"])]; val it = [("a","b"), ("b","c"), ("a","c"), ("a","d"), ("d","c"), ("d","b")] : (string * string) list edgelist2adjlist: (string * string) list -> (string * (string list )) list input: an edge list representation of a graph output: an adjacency representation of a graph - edgelist2adjlist [("a","b"), ("b","c"), ("a","c"), ("a","d"), ("d","c"), =("d","b")]; val it = [("a", ["b", "c", "d"]), ("b", ["c"]), ("c",[]), =("d",[" c","b"])] : (string * string list) list Note that the item ("c",[]) is necessary! Programming Style Your code will need to have an introductory comment in the following format: (* <Your name> * CS 345 * Project 1 *)

5 Each of your functions should have a header comment that describes: The function's purpose What all the input parameters are (and any restrictions on the input parameters!!) What the function returns I should be able to use each function correctly after looking only at the header comment for that function. Remember that comments in ML are surrounded by (* and *) What to turn in A hardcopy of your ml source, with the code for all of the following functions (plus any helper functions): zip: 'a list * b list -> ('a * 'b) list unzip : ('a * 'b) list -> 'a list * 'b list split : 'a list -> 'a list * 'a list merge : ('a * 'a -> bool) -> ('a list * 'a list) -> 'a list mergesort : ('a * 'a -> bool) -> 'a list -> 'a list numnodes : 'a btree -> int maxvalue : ('a * 'a -> bool) -> 'a btree -> 'a preorder : 'a btree -> 'a list postorder : 'a btree -> 'a list inorder : 'a btree -> 'a list adjlist2edgelist: string * (string list) list -> string * string list edgelist2adjlist: (string * string) list -> (string * (string list )) list insert: ('a * 'a -> bool) -> 'a btree -> 'a ->'a btree btreesort ('a * 'a -> bool) -> 'a list -> 'a list note that you must use these exact names. You should also submit an electronic copy, copied to your submit directory. The filename of your electronic submission should be "prog1.ml". Do not use subdirectories in your submit directory, and be sure that the permissions are set correctly! Project Notes & Hints Note that you have 14 functions to write in 3 weeks which is ~5 functions / week, or a function every weekday. Start early, and work consistently for a pain-free assignment. Some of these functions are a little tricky, and will take some thinking time. The tree functions are probably the most straightforward, and the graph functions are probably the most tricky (though unzip might also take awhile to get completely correct).