I'm new to Prolog and I'm having trouble with the first part of my programming assignment:
Create a predicate split that that takes as input three parameters. The first and third parameters are lists and the second parameter is an element. You can think of the first parameter as being the input and the last two parameters being the output. The method computes all possible way of splitting a list into an element and the rest of the list. Here is an example run.
?- split([1,2,3,4,5],X,Y).
X = 1,
Y = [2, 3, 4, 5] ;
X = 2,
Y = [1, 3, 4, 5] ;
X = 3,
Y = [1, 2, 4, 5] ;
X = 4,
Y = [1, 2, 3, 5] ;
X = 5,
Y = [1, 2, 3, 4] ;
There are two rules in defining the predicate. The first rule simply gets the first element of the list and returns it as the second parameter and the rest of the list as the third parameter. The second rule generates the list by copying the first element of the list in the result (i.e., third parameter) and then recursively applying the method to the rest of the elements.
split([H|T], H, T).
split([H|T], X, [H|Y]) :-
split(T, X, Y).
There are two ways to take an element out of a list:
Take the head (the first element)
Set the head aside and take an element out of the tail (the rest of the list)
Notice that the predicate can run both ways; if the second and the third parameters are defined, it will yield all possible ways these two can be combined to form a list.
split(List,Elem,Rest) :- select(Elem,List,Rest).
| ?- select(X,[1,2,3],Y).
X = 1,
Y = [2,3] ? ;
X = 2,
Y = [1,3] ? ;
X = 3,
Y = [1,2] ? ;
no
and with split/3 ;
| ?- split([1,2,3,4],X,Y).
X = 1,
Y = [2,3,4] ? ;
X = 2,
Y = [1,3,4] ? ;
X = 3,
Y = [1,2,4] ? ;
X = 4,
Y = [1,2,3] ? ;
no
with Sicstus-prolog u need to export select from library/lists
:- use_module(library(lists)).
Related
I want to code this constraint.
d and a in the below code are the subsets of set S with the size of N. For example: (N=5, T=3, S=6), d=[1,2,2,3,1] (the elements of d are the first three digits of S and the size of d is N) and a=[6,4,5,6,4] (the elements of a are the three last digits of set S and the size of a is N).
In the constraint, s should start with d and end with a.
It should be like s[j=1]=1:6, s[j=2]=2:4, s[j=3]=2:5, s[j=4]=3:6, s[j=5]1:4.
I do not know how to deal with this set that depends on the other sets. Can you please help me to code my constraint correctly? The below code is not working correctly.
N = 5
T=3
S=6
Cap=15
Q=rand(1:5,N)
d=[1,2,2,3,1]
a=[6,4,5,6,4]
#variable(model, x[j=1:N,t=1:T,s=1:S], Bin)
#constraint(model, [j= 1:N,t = 1:T, s = d[j]:a[j]], sum(x[j,t,s] * Q[j] for j=1:N) <= Cap)
N, T, S = 5, 3, 6
Q = rand(1:5,N)
d = [1, 2, 2, 3, 1]
a = [6, 4, 5, 6, 4]
using JuMP
model = Model()
#variable(model, x[1:N, 1:T, 1:S], Bin)
#constraint(
model,
[t = 1:T, s = 1:S],
sum(x[j, t, s] * Q[j] for j in 1:N if d[j] <= s < a[j]) <= 15,
)
p.s. There's no need to post multiple comments and questions:
Coding arrays in constraint JuMP
You should also consider posting on the Julia discourse instead: https://discourse.julialang.org/c/domain/opt/13. It's easier to have a conversation there.
Let's say, for example, I have two arrayLists. One has strings in the form of:
[a, b, a, a, c, a, d, b, d, b]
The other has integers in the form of:
[1, 4, 2, 3, 5, 5, 6, 2, 5, 1]
In this case, "a" has/maps to values 1, 2, 3, and 5 (because "a" is at index 0, 2, 3, 5 in arrayList 1, and the values at index 0, 2, 3, 5 in arrayList 2 are 1, 2, 3, and 5). "b" has values 4, 2, and 1. "c" has value 5. "d" has values 6 and 5.
Now I want to create a Map from these two arrayLists in the form of:
[(a, 11), (b, 7), (c, 5), (d, 11)]
where the value each string key is matched with is the sum of all its corresponding values in arrayList 2.
Any pointers on an efficient way to go about implementing this in Java?
Thanks.
This kind of operation is, abstractly, "zipping". The stream of Java 8 works great here.
Map<String, Integer> m = IntStream.range(0, stringList.size()) // indices
.boxed() // Stream<Integer>
.collect(Collectors.toMap(
stringList::get, // keyMapper
intList::get, // valueMapper
(x, y) -> x + y // mergeFunction for values when they have the same key
));
This code assumes that intList is the same size as, or longer than stringList. If intList can be shorter and you want to map the missing values to 0, you can modifiy the valueMapper from a method reference to a lambda.
Using Prolog:
Write a predicate dispnth to display the nth element of a list. You may assume that the input list always has n or more elements.
For Example:
?- dispnth([1, [2, 3], 4, 5], 2, X). should return X = [2, 3]
I have this so far:
dispnth([X|_], 0, X).
dispnth([_|Xs], N, X) :-
dispnth(N1, X, Xs),
N is N1 + 1.
First let's give the predicate a more descriptive name, say list_nth_element/3. Next you might like to consider an auxiliary predicate list_nth_element_/4 with an additional argument, that holds the current position. From your given example I assume that you start counting at 1, so that's going to be the start value for the fourth argument. Then the predicates might look something like this:
list_nth_element(L,N,E) :-
list_nth_element_(L,N,E,1).
list_nth_element_([X|Xs],N,X,N). % if the 2nd and 4th elements are equal X is the nth element
list_nth_element_([_X|Xs],N,E,P0) :- % if the 2nd and 4th arguments
dif(P0,N), % differ
P1 is P0+1, % increment current position
list_nth_element_(Xs,N,E,P1). % and recurse
So essentially the fourth argument is used as a position indicator that is being incremented until you reached the desired position. However, there is no need to have this additional argument in the actual predicates interface, so it is "hidden" in the auxiliary predicate's interface.
Querying this predicate yields your desired result:
?- list_nth_element([1, [2, 3], 4, 5], 2, X).
X = [2,3] ? ;
no
You can also ask things like Which element is at what position?
?- list_nth_element([1, [2, 3], 4, 5], N, X).
N = X = 1 ? ;
N = 2,
X = [2,3] ? ;
N = 3,
X = 4 ? ;
N = 4,
X = 5 ? ;
no
Let's say I have a vector of unique integers, for example [1, 2, 6, 4] (sorting doesn't really matter).
Given some n, I want to get all possible values of summing n elements of the set, including summing an element with itself. It is important that the list I get is exhaustive.
For example, for n = 1 I get the original set.
For n = 2 I should get all values of summing 1 with all other elements, 2 with all others etc. Some kind of memory is also required, in the sense that I have to know from which entries of the original set did the sum I am facing come from.
For a given, specific n, I know how to solve the problem. I want a concise way of being able to solve it for any n.
EDIT: This question is for Julia 0.7 and above...
This is a typical task where you can use a dictionary in a recursive function (I am annotating types for clarity):
function nsum!(x::Vector{Int}, n::Int, d=Dict{Int,Set{Vector{Int}}},
prefix::Vector{Int}=Int[])
if n == 1
for v in x
seq = [prefix; v]
s = sum(seq)
if haskey(d, s)
push!(d[s], sort!(seq))
else
d[s] = Set([sort!(seq)])
end
end
else
for v in x
nsum!(x, n-1, d, [prefix; v])
end
end
end
function genres(x::Vector{Int}, n::Int)
n < 1 && error("n must be positive")
d = Dict{Int, Set{Vector{Int}}}()
nsum!(x, n, d)
d
end
Now you can use it e.g.
julia> genres([1, 2, 4, 6], 3)
Dict{Int64,Set{Array{Int64,1}}} with 14 entries:
16 => Set(Array{Int64,1}[[4, 6, 6]])
11 => Set(Array{Int64,1}[[1, 4, 6]])
7 => Set(Array{Int64,1}[[1, 2, 4]])
9 => Set(Array{Int64,1}[[1, 4, 4], [1, 2, 6]])
10 => Set(Array{Int64,1}[[2, 4, 4], [2, 2, 6]])
8 => Set(Array{Int64,1}[[2, 2, 4], [1, 1, 6]])
6 => Set(Array{Int64,1}[[2, 2, 2], [1, 1, 4]])
4 => Set(Array{Int64,1}[[1, 1, 2]])
3 => Set(Array{Int64,1}[[1, 1, 1]])
5 => Set(Array{Int64,1}[[1, 2, 2]])
13 => Set(Array{Int64,1}[[1, 6, 6]])
14 => Set(Array{Int64,1}[[4, 4, 6], [2, 6, 6]])
12 => Set(Array{Int64,1}[[4, 4, 4], [2, 4, 6]])
18 => Set(Array{Int64,1}[[6, 6, 6]])
EDIT: In the code I use sort! and Set to avoid duplicate entries (remove them if you want duplicates). Also you could keep track how far in the index on vector x in the loop you reached in outer recursive calls to avoid generating duplicates at all, which would speed up the procedure.
I want a concise way of being able to solve it for any n.
Here is a concise solution using IterTools.jl:
Julia 0.6
using IterTools
n = 3
summands = [1, 2, 6, 4]
myresult = map(x -> (sum(x), x), reduce((x1, x2) -> vcat(x1, collect(product(fill(summands, x2)...))), [], 1:n))
(IterTools.jl is required for product())
Julia 0.7
using Iterators
n = 3
summands = [1, 2, 6, 4]
map(x -> (sum(x), x), reduce((x1, x2) -> vcat(x1, vec(collect(product(fill(summands, x2)...)))), 1:n; init = Vector{Tuple{Int, NTuple{n, Int}}}[]))
(In Julia 0.7, the parameter position of the neutral element changed from 2nd to 3rd argument.)
How does this work?
Let's indent the one-liner (using the Julia 0.6 version, the idea is the same for the Julia 0.7 version):
map(
# Map the possible combinations of `1:n` entries of `summands` to a tuple containing their sum and the summands used.
x -> (sum(x), x),
# Generate all possible combinations of `1:n`summands of `summands`.
reduce(
# Concatenate previously generated combinations with the new ones
(x1, x2) -> vcat(
x1,
vec(
collect(
# Cartesian product of all arguments.
product(
# Use `summands` for `x2` arguments.
fill(
summands,
x2)...)))),
# Specify for what lengths we want to generate combinations.
1:n;
# Neutral element (empty array).
init = Vector{Tuple{Int, NTuple{n, Int}}}[]))
Julia 0.6
This is really just to get a free critique from the experts as to why my method is inferior to theirs!
using Combinatorics, BenchmarkTools
function nsum(a::Vector{Int}, n::Int)::Vector{Tuple{Int, Vector{Int}}}
r = Vector{Tuple{Int, Vector{Int}}}()
s = with_replacement_combinations(a, n)
for i in s
push!(r, (sum(i), i))
end
return sort!(r, by = x -> x[1])
end
#btime nsum([1, 2, 6, 4], 3)
It runs in circa 4.154 μs on my 1.8 GHz processor for n = 3. It produces a sorted array showing the sum (which may appear more than once) and how it is made up (which is unique to each instance of the sum).
Extract all consecutive repetitions in a given list:
list1 = [1,2,2,3,3,3,3,4,5,5]
It should yield a list like this
[[2,2],[3,3,3,3],[5,5]]
I tried the code below. I know it is not the proper way to solve this problem but I could not manage how to solve this.
list1 = [1,2,2,3,3,3,3,4,5,5]
list2 = []
for i in list1:
a = list1.index(i)
if list1[a] == list1[a+1]:
list2.append([i,i])
print(list2)
You can use this to achieve it. There are "easier" solutions using itertools and groupby to get the same result, this is how to do it "by hand":
def FindInnerLists(l):
'''reads a list of int's and groups them into lists of same int value'''
result = []
allResults = []
for n in l:
if not result or result[0] == n: # not result == empty list
result.append(n)
if result[0] != n: # number changed, so we copy the list over into allResults
allResults.append(result[:])
result = [n] # and add the current to it
# edge case - if result contains elements, add them as last item to allResults
if result:
allResults.append(result[:])
return allResults
myl = [2, 1, 2, 1, 1, 1, 1, 2, 2, 2, 1, 2, 7, 1, 1, 1,2,2,2,2,2]
print(FindInnerLists(myl))
Output (works for 2.6 and 3.x):
[[2], [1], [2], [1, 1, 1, 1], [2, 2, 2], [1], [2], [7], [1, 1, 1], [2, 2, 2, 2, 2]]
Another way to do it:
list1 = [1, 2, 2, 3, 3, 3, 3, 4, 5, 5]
result = [[object()]] # initiate the result with object() as a placeholder
for element in list1: # iterate over the rest...
if result[-1][0] != element: # the last repeated element does not match the current
if len(result[-1]) < 2: # if there was less than 2 repeated elements...
result.pop() # remove the last element
result.append([]) # create a new result entry for future repeats
result[-1].append(element) # add the current element to the end of the results
if len(result[-1]) < 2: # finally, if the last element wasn't repeated...
result.pop() # remove it
print(result) # [[2, 2], [3, 3, 3, 3], [5, 5]]
And you can use it on any kind of a list, not just numerical.
This would work:
list1 = [1,2,2,3,3,3,3,4,5,5]
res = []
add = True
last = [list1[0]]
for elem in list1[1:]:
if last[-1] == elem:
last.append(elem)
if add:
res.append(last)
add = False
else:
add = True
last = [elem]
print(res)
Output:
[[2, 2], [3, 3, 3, 3], [5, 5]]