How to generate conditions within constraints in Z3py - z3

Let us assume there are 5-time slots and at each time slot, I have 4 options to choose from, each with a known reward, for eg. rewards = [5, 2, 1, -3]. At every time step, at least 1 of the four options must be selected, with a condition that, if option 3 (with reward -3) is chosen at a time t, then for the remaining time steps, none of the options should be selected. As an example, considering the options are indexed from 0, both [2, 1, 1, 0, 3] and [2, 1, 1, 3, 99] are valid solutions with the second solution having option 3 selected in the 3rd time step and 99 is some random value representing no option was chosen.
The Z3py code I tried is here:
T = 6 #Total time slots
s = Solver()
pick = [[Bool('t%d_ch%d' %(j, i)) for i in range(4)] for j in range(T)]
# Rewards of each option
Rewards = [5, 2, 1, -3]
# Select at most one of the 4 options as True
for i in range(T):
s.add(Or(Not(Or(pick[i][0], pick[i][1], pick[i][2], pick[i][3])),
And(Xor(pick[i][0],pick[i][1]), Not(Or(pick[i][2], pick[i][3]))),
And(Xor(pick[i][2],pick[i][3]), Not(Or(pick[i][0], pick[i][1])))))
# If option 3 is picked, then none of the 4 options should be selected for the future time slots
# else, exactly one should be selected.
for i in range(len(pick)-1):
for j in range(4):
s.add(If(And(j==3,pick[i][j]),
Not(Or(pick[i+1][0], pick[i+1][1], pick[i+1][2], pick[i+1][3])),
Or(And(Xor(pick[i+1][0],pick[i+1][1]), Not(Or(pick[i+1][2], pick[i+1][3]))),
And(Xor(pick[i+1][2],pick[i+1][3]), Not(Or(pick[i+1][0], pick[i+1][1]))))))
if s.check()==False:
print("unsat")
m=s.model()
print(m)
With this implementation, I am not getting solutions such as [2, 1, 1, 3, 99]. All of them either do not have option 3 or have it in the last time slot.
I know there is an error inside the If part but I'm unable to figure it out. Is there a better way to achieve such solutions?

It's hard to decipher what you're trying to do. From a basic reading of your description, I think this might be an instance of the XY problem. See https://xyproblem.info/ for details on that, and try to cast your question in terms of what your original goal is; instead of a particular solution, you're trying to implement. (It seems to me that the solution you came up with is unnecessarily complicated.)
Having said that, you can solve your problem as stated if you get rid of the 99 requirement and simply indicate -3 as the terminator. Once you pick -3, then all the following picks should be -3. This can be coded as follows:
from z3 import *
T = 6
s = Solver()
Rewards = [5, 2, 1, -3]
picks = [Int('pick_%d' % i) for i in range(T)]
def pickReward(p):
return Or([p == r for r in Rewards])
for i in range(T):
if i == 0:
s.add(pickReward(picks[i]))
else:
s.add(If(picks[i-1] == -3, picks[i] == -3, pickReward(picks[i])))
while s.check() == sat:
m = s.model()
picked = []
for i in picks:
picked += [m[i]]
print(picked)
s.add(Or([p != v for p, v in zip(picks, picked)]))
When run, this prints:
[5, -3, -3, -3, -3, -3]
[1, 5, 5, 5, 5, 1]
[1, 2, 5, 5, 5, 1]
[2, 2, 5, 5, 5, 1]
[2, 5, 5, 5, 5, 1]
[2, 1, 5, 5, 5, 1]
[1, 1, 5, 5, 5, 1]
[2, 1, 5, 5, 5, 2]
[2, 5, 5, 5, 5, 2]
[2, 5, 5, 5, 5, 5]
[2, 5, 5, 5, 5, -3]
[2, 1, 5, 5, 5, 5]
...
I interrupted the above as it keeps enumerating all the possible picks. There are a total of 1093 of them in this particular case.
(You can get different answers depending on your version of z3.)
Hope this gets you started. Stating what your original goal is directly is usually much more helpful, should you have further questions.

Related

How can we reduce the size of the graph generated by Maximal Clique and remove the nodes of specific cliques?

I am using the networkx—find_cliques library for finding the maximal cliques in a graph. I want to reduce the size of this graph based on maximal cliques.
Here is the code:
from torch_geometric.utils.convert
import to_networkx from torch_geometric.data import Data
import networkx as nx
edge_list = torch.tensor([
[0, 1, 1, 2, 2, 2, 3, 4, 5, 6, 6, 6, 7, 7, 8 ], # Source Nodes
[1, 2, 3, 4, 5, 3, 9, 5, 6, 7, 8, 9, 8, 9, 9 ] # Target Nodes
], dtype=torch.long)
node_features = torch.tensor([
[-8, 1, 5, 8, 2, -3], # Features of Node 0
[-1, 0, 2, -3, 0, 1], # Features of Node 1
[1, -1, 0, -1, 2, 1], # Features of Node 2
[0, 1, 4, -2, 3, 4], # Features of Node 3
],dtype=torch.long)
data = Data(x=node_features, edge_index=edge_list, edge_attr=edge_weight)
G_directed = to_networkx(data)
G_undirected = G_directed.to_undirected()
no_cliques= nx.find_cliques(G, nodes=None)
print(No_cliques)
List of Maximal Cliques = {1,[1,2], 2,[2, 3, 4], 3,[4, 5, 6], 4,[6, 7], 5, [7, 8, 9, 10], 6, [10,3]}
In the next step, we reduce the size of the original graph in the coarsened graph as we consider one clique as one node and joint the edge based on this rule, joining two cliques if they are not disjoint. I want to remove such a clique whose node already appeared in other cliques. In the above example, the nodes of clique 6 are already assigned in cliques no 2 and 5. So in the new graph, this clique should be removed from the clique list.
For better understanding, I am posting the picture.
hierarchy of a graph as the coarsened graph at each level
I want to make this type of graph hierarchy based on maximal clique. Does anyone know about it? How can I do it?

How to remove array elements and append it to the front of the array in ruby without using any inbuilt methods?

I have an array say [1,2,3,4,5,6,7,8]. I need to take an input from the user and remove the last input number of array elements and append it to the front of the array. This is what I have achieved
def test(number, array)
b = array - array[0...(array.length-1) - number]
array = array.unshift(b).flatten.uniq
return array
end
number = gets.chomp_to_i
array = [1,2,3,4,5,7,8,9]
now passing the argument to test gives me the result. However, there are two problems here. first is I want to find a way to do this append on the front without any inbuilt method.(i.e not using unshift).Second, I am using Uniq here, which is wrong since the original array values may repeat. So how do I still ensure to get the correct output? Can some one give me a better solution to this.
The standard way is:
[1, 2, 3, 4, 5, 7, 8, 9].rotate(-3) #=> [7, 8, 9, 1, 2, 3, 4, 5]
Based on the link I supplied in the comments, I threw this together using the answer to that question.
def test(number, array)
reverse_array(array, 0, array.length - 1)
reverse_array(array, 0, number - 1)
reverse_array(array, number, array.length - 1)
array
end
def reverse_array(array, low, high)
while low < high
array[low], array[high] = array[high], array[low]
low += 1
high -= 1
end
end
and then the tests
array = [1,2,3,4,5,7,8,9]
test(2, array)
#=> [8, 9, 1, 2, 3, 4, 5, 7]
array = [3, 4, 5, 2, 3, 1, 4]
test(2, array)
#=> [1, 4, 3, 4, 5, 2, 3]
Which I believe is what you're wanting, and I feel sufficiently avoids ruby built-ins (no matter what way you look at it, you're going to need to get the value at an index and set a value at an index to do this in place)
I want to find a way to do this append on the front without any inbuilt method
You can decompose an array during assignment:
array = [1, 2, 3, 4, 5, 6, 7, 8]
*remaining, last = array
remaining #=> [1, 2, 3, 4, 5, 6, 7]
last #=> 8
The splat operator (*) gathers any remaining elements. The last element will be assigned to last, the remaining elements (all but the last element) are assigned to remaining (as a new array).
Likewise, you can implicitly create an array during assignment:
array = last, *remaining
#=> [8, 1, 2, 3, 4, 5, 6, 7]
Here, the splat operator unpacks the array, so you don't get [8, [1, 2, 3, 4, 5, 6, 7]]
The above moves the last element to the front. To rotate an array n times this way, use a loop:
array = [1, 2, 3, 4, 5, 6, 7, 8]
n = 3
n.times do
*remaining, last = array
array = last, *remaining
end
array
#=> [6, 7, 8, 1, 2, 3, 4, 5]
Aside from times, no methods were called explicitly.
You could create a new Array with the elements at the correct position thanks to modulo:
array = %w[a b c d e f g h i]
shift = 3
n = array.size
p Array.new(n) { |i| array[(i - shift) % n] }
# ["g", "h", "i", "a", "b", "c", "d", "e", "f"]
Array.new() is a builtin method though ;)

ruby Remove one element from array

I want to remove (only one) element by value from my array.
example :
x = [1,2,3,2]
x.remove(2)
result: x= [1,3]
But, i want to get [1,3,2].
thanks
As #7urkm3n mentioned in the comments, you can use x.delete_at to delete the first occurance
x.delete_at(x.index 2)
> x = [1,2,3,2]
=> [1, 2, 3, 2]
> x.delete_at(x.index 2)
=> 2
> x
=> [1, 3, 2]
You can use slice!(index, 1). You can get the 1st index of the element you want to delete by using index(element)
In your case you just have to do: x.slice!(x.index(2), 1) (or, as already mentioned, delete_at just providing the index)
You could write
x = [1,2,3,2]
x.difference([2])
#=> [1, 3, 2]
where Array#difference is as I've defined it my answer here. Because of the wide potential application of the method I've proposed it be added to the Ruby core.
Suppose
x = [1,2,3,2,1,2,4,2]
and you wished to remove the first 1, the first two 2's and the 4. To do that you would write
x.difference([1,2,2,4])
#=> [3, 1, 2, 2]
Note that
x.difference([1,2,2,4,4,5])
#=> [3, 1, 2, 2]
gives the same result.
To remove the last 1, the last two 2s and and the 4, write
x.reverse.difference([1,2,2,4]).reverse
#=> [1, 2, 3, 2]

Dividing elements of a ruby array into an exact number of (nearly) equal-sized sub-arrays [duplicate]

This question already has answers here:
How to chunk an array in Ruby
(2 answers)
Closed 4 years ago.
I need a way to split an array in to an exact number of smaller arrays of roughly-equal size. Anyone have any method of doing this?
For instance
a = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]
groups = a.method_i_need(3)
groups.inspect
=> [[1,2,3,4,5], [6,7,8,9], [10,11,12,13]]
Note that this is an entirely separate problem from dividing an array into chunks, because a.each_slice(3).to_a would produce 5 groups (not 3, like we desire) and the final group may be a completely different size than the others:
[[1,2,3], [4,5,6], [7,8,9], [10,11,12], [13]] # this is NOT desired here.
In this problem, the desired number of chunks is specified in advance, and the sizes of each chunk will differ by 1 at most.
You're looking for Enumerable#each_slice
a = [0, 1, 2, 3, 4, 5, 6, 7]
a.each_slice(3) # => #<Enumerator: [0, 1, 2, 3, 4, 5, 6, 7]:each_slice(3)>
a.each_slice(3).to_a # => [[0, 1, 2], [3, 4, 5], [6, 7]]
Perhaps I'm misreading the question since the other answer is already accepted, but it sounded like you wanted to split the array in to 3 equal groups, regardless of the size of each group, rather than split it into N groups of 3 as the previous answers do. If that's what you're looking for, Rails (ActiveSupport) also has a method called in_groups:
a = [0,1,2,3,4,5,6]
a.in_groups(2) # => [[0,1,2,3],[4,5,6,nil]]
a.in_groups(3, false) # => [[0,1,2],[3,4], [5,6]]
I don't think there is a ruby equivalent, however, you can get roughly the same results by adding this simple method:
class Array; def in_groups(num_groups)
return [] if num_groups == 0
slice_size = (self.size/Float(num_groups)).ceil
groups = self.each_slice(slice_size).to_a
end; end
a.in_groups(3) # => [[0,1,2], [3,4,5], [6]]
The only difference (as you can see) is that this won't spread the "empty space" across all the groups; every group but the last is equal in size, and the last group always holds the remainder plus all the "empty space".
Update:
As #rimsky astutely pointed out, the above method will not always result in the correct number of groups (sometimes it will create multiple "empty groups" at the end, and leave them out). Here's an updated version, pared down from ActiveSupport's definition which spreads the extras out to fill the requested number of groups.
def in_groups(number)
group_size = size / number
leftovers = size % number
groups = []
start = 0
number.times do |index|
length = group_size + (leftovers > 0 && leftovers > index ? 1 : 0)
groups << slice(start, length)
start += length
end
groups
end
Try
a.in_groups_of(3,false)
It will do your job
As mltsy wrote, in_groups(n, false) should do the job.
I just wanted to add a small trick to get the right balance
my_array.in_group(my_array.size.quo(max_size).ceil, false).
Here is an example to illustrate that trick:
a = (0..8).to_a
a.in_groups(4, false) => [[0, 1, 2], [3, 4], [5, 6], [7, 8]]
a.in_groups(a.size.quo(4).ceil, false) => [[0, 1, 2], [3, 4, 5], [6, 7, 8]]
This needs some better cleverness to smear out the extra pieces, but it's a reasonable start.
def i_need(bits, r)
c = r.count
(1..bits - 1).map { |i| r.shift((c + i) * 1.0 / bits ) } + [r]
end
> i_need(2, [1, 3, 5, 7, 2, 4, 6, 8])
=> [[1, 3, 5, 7], [2, 4, 6, 8]]
> i_need(3, [1, 3, 5, 7, 2, 4, 6, 8])
=> [[1, 3, 5], [7, 2, 4], [6, 8]]
> i_need(5, [1, 3, 5, 7, 2, 4, 6, 8])
=> [[1, 3], [5, 7], [2, 4], [6], [8]]

Calculate differences between array elements

Given a sorted array of n integers, like the following:
ary = [3, 5, 6, 9, 14]
I need to calculate the difference between each element and the next element in the array. Using the example above, I would end up with:
[2, 1, 3, 5]
The beginning array may have 0, 1 or many elements in it, and the numbers I'll be handling will be much larger (I'll be using epoch timestamps). I've tried the following:
times = #messages.map{|m| m.created_at.to_i}
left = times[1..times.length-1]
right = times[0..times.length-2]
differences = left.zip(right).map { |x| x[0]-x[1]}
But my solution above is both not optimal, and not ideal. Can anyone give me a hand?
>> ary = [3, 5, 6, 9, 14] #=> [3, 5, 6, 9, 14]
>> ary.each_cons(2).map { |a,b| b-a } #=> [2, 1, 3, 5]
Edit:
Replaced inject with map.
Similar but more concise:
[3, 5, 6, 9, 14].each_cons(2).collect { |a,b| b-a }
An alternative:
a.map.with_index{ |v,i| (a[i+1] || 0) - v }[0..-2]
Does not work in Ruby 1.8 where map requires a block instead of returning an Enumerator.

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