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Taddeüs Kroes
uva
Commits
67bd7fb4
Commit
67bd7fb4
authored
Nov 22, 2011
by
Sander Mathijs van Veen
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Merge branch 'master' of vo20.nl:/git/uva
parents
7ce81fae
35c64294
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67bd7fb4
open
List
(* 1 *)
let
rec
nth
l
n
=
(* Walk through the list recursively, subtracting 1 off n each time and
* matching it with 0 to check of the nth element has been reached yet *)
match
l
with
|
[]
->
raise
(
Failure
"list index out of bounds"
)
|
h
::
t
->
if
n
=
0
then
h
else
nth
t
(
n
-
1
)
;;
(* 2 *)
let
heads
l
=
map
hd
l
;;
(* 3 *)
let
zip
l
m
=
(* Cut off a list l at length e *)
let
rec
cut
l
e
=
if
e
=
(
length
l
)
then
l
else
cut
(
rev
(
tl
(
rev
l
)))
e
in
(* Get the minimum of two integers *)
let
min
a
b
=
if
a
>
b
then
b
else
a
in
(* Cut off both lists at the length of the shortest list to equal their
* lengths, then use the native 'combine' function *)
let
len
=
min
(
length
l
)
(
length
m
)
in
combine
(
cut
l
len
)
(
cut
m
len
)
;;
(* 4 *)
let
rec
map
f
l
=
(* Apply f to the head, then map it to the tail recursively *)
match
l
with
|
[]
->
[]
|
h
::
t
->
f
h
::
map
f
t
;;
(* 5 *)
let
rec
reduce
f
z
l
=
(* Apply f to the head, and the reducement of the tail *)
match
l
with
|
[]
->
z
|
h
::
t
->
f
z
(
reduce
f
h
t
)
;;
(* 6 *)
let
rec
isSublist
l
s
=
(* Check if l starts with s, otherwise check the tail recursively *)
let
rec
startsWith
l
s
=
(
length
s
)
<=
(
length
l
)
&&
match
s
with
|
[]
->
true
|
h
::
t
->
h
=
(
hd
l
)
&&
startsWith
(
tl
l
)
t
in
match
l
with
|
[]
->
false
|
_
::
t
->
(
startsWith
l
s
)
||
(
isSublist
t
s
)
;;
(* 7 *)
let
rec
lookup
l
key
=
(* Match key to the first tuple and return the value-side of the tuple if
* matched. Otherwise, lookup in the rest of the tuples *)
match
l
with
|
[]
->
raise
(
Failure
"lookup"
)
|
h
::
t
->
let
k
,
v
=
h
in
if
k
=
key
then
v
else
lookup
t
key
;;
(* Challenge *)
let
rec
coin_permutation
l
n
=
(* Reduce the list using the fact that the the total number of coin
* permutations is equal to the number of permutations given a single coin,
* added to the number of permutations without that coin *)
match
l
with
|
[]
->
0
|
h
::
t
->
(
if
h
>
n
then
0
else
1
+
(
coin_permutation
t
(
n
-
h
)))
+
(
coin_permutation
t
n
)
;;
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