Integer Linear Program as a feasability test

I am a beginner in Integer Linear Programs and I have a question about a problem that I am dealing. This problem tracks a configuration of a graph by unitary transformations on the graph and I want to minimize these number of transformations to achieve another configuration of the graph. As I only allow exactly one transformation per step, minimizing the number of transformations is the same as minimizing the number of steps.

But, I enter in the following problem: There is no internal property that can be tracked so that I can check if one or other state is closer or farther from the wanted configuration. That means that I can only check if a specific sequence of transformation is correct in a prior-of-execution defined step, for example, $T$. Then, what I am thinking in doing is testing a range of values for $T$, as there is a polynomial upper-bound for this value, in increasing order (bound in the number of steps). Then I recover the answer of the first $T$ that gives me any answer, as I know it will be a optimal answer.

My questions are:

  • This sort of is a feasibility test for a fixed $T$, as if the polytope exists, any answer will be a optimal answer, as they all have the same number of steps $T$. This approach is possible? In the sense that it can be calculated given a infinite amount of time? Because I am not sure what is the behavior of a IL program when there is no possible answer (ie. no polytope).
  • If yes, there is some existing technique to deal/optimize this type of situations without finding a specific property?

C ++ ERROR – [Error] ISO C ++ prohibits the comparison between pointer and integer [-fpermissive]

I am learning C ++ and have copied and modified a code from the Internet, but it shows the error when compiling – (error) ISO C ++ prohibits the comparison between pointer and integer (-fpermissive).


Include iostream

include stdio.h

Define SIZE 200

Character name (SIZE) (50);

Char (SIZE) (50);

int rg (SIZE) (50);

int cpf (SIZE) (50);

int tel (SIZE) (50);

int age (SIZE) (50);

int op;

Invalidate registration ();

void search ();

int main (void) {




Invalidate registration () {

static int linha;


    printf("nDigite o nome: ");

    scanf("%s", &nome(linha));

    printf("nDigite o sexo (F/M): ");

    scanf("%s", &sexo(linha));

    printf("nDigite o RG: ");

    scanf("%d", &rg(linha));

    printf("nDigite o CPF: ");

    scanf("%d", &cpf(linha));

    printf("nDigite a idade: ");

    scanf("%d", &idade(linha));

    printf("nDigite o telefone: ");

    scanf("%d", &tel(linha));

    printf("nDigite 1 para continuar ou 2 para sair: ");

    scanf("%d", &op);




void search () {

int cpfPesquisa;

int i;


    printf("nDigite o CPF que deseja buscar: ");

    scanf("%d", &cpfPesquisa);


Gender (i), cpf (i), rg (i), age (i), tel (i));



printf("nDigite 1 para continuar pesquisando: ");

scanf("%d", &op);



Why is it impossible to have a complex number with an integer as the real part and an approximate number as the imaginary part?

1/3 + 3. I
2 + 3. I

According to the code above, it seems impossible to have a complex number with an integer or an exact number as the real part and an approximate number as the imaginary part. The exact number as a real part is automatically and violently converted into an approximate number.

I looked it up in the official document and found no explanation.

Can anyone provide a documentation reference that explains this mechanism?

Integer in array returns zero

I use the EDD_Fees class to add an additional fee to products. I've already used this class and it works like magic, but now I can't figure out why the amount is zero (it seems to return zero). But if i echo shows the integer value.
Here is my full class code

$feeid_gen = date("Ydhis") . $download_id;
            function cencored_function() {
            // Additional Services Price START here
                    $cencored_fee = array(
            'amount'      => $int_val,
            'label'       => 'hbbl',    
            'id'          => $feeid_gen,    
            'no_tax'      => false,
            'type'        => 'fee',
            'download_id' => $download_id,
            'price_id'    => NULL   
            EDD()->fees->add_fee( $cencored_fee);
            /// Additional Services Price END here
            add_action( 'init', 'cencored_function' );
            cencored_function(); // Runned

haskell – closed form Fibonacci with integer

I implement the closed form of Fibonacci numbers.
I think I can use a custom data type without leaving it Integer.
It is no more efficient than the "standard" approach since I could not find an efficient way to calculate the performance of my custom number type.

But if I stick to this algorithm, I would be interested in best practices to write this.
In particular, I'm not sure about the use of Num for my FibNum and the use of fromJust.

module Fibo
    ) where

import Data.Maybe (fromJust)

-- use a data type similar to complex numbers. 
-- The only irrational number are multiples of sqrt 5 
-- which will cancel away in the closed form.
data FibNum = FibNum { int::Integer, sq5::Integer }
  deriving (Show)

instance Num FibNum where
  (+) (FibNum a1 b1) (FibNum a2 b2) = FibNum (a1+a2) (b1 + b2)
  (*) (FibNum a1 b1) (FibNum a2 b2) = FibNum intSide rootSide
    where intSide = a1*a2 + 5 * b1 * b2
          rootSide = a1*b2 + b1*a2
  negate (FibNum a b) = FibNum (negate a) (negate b)
  fromInteger n = FibNum (fromInteger n) 0
  -- no need for abs and sign for now
  abs _ = undefined
  signum _ = undefined

funit = FibNum 1 0
-- actual phi and psi are (1 + sqrt 5)/2 and (1 - sqrt 5)/2
-- I would prefer to avoid fractions so I divide at the end
fphi = FibNum 1 1
fpsi = FibNum 1 (negate 1)

-- was originally planning to calculate the binomial coefficients
-- but seeing that I just need n relatively simple multiplications 
-- that seem like unnecessary complication
pow :: FibNum -> Integer -> FibNum
pow _ 0 = funit
pow x 1 = x
pow x n = x * pow x (n-1)

-- in the closed form the integer part is always 0
divR5 :: FibNum -> Maybe Integer
divR5 (FibNum 0 n) = Just n
divR5 _ = Nothing

fibo :: Integer -> Integer
fibo n = flip div p2 . fromJust $ divR5 nom
  where nom = pow fphi n - pow fpsi n
        p2 = 2^n

Maximizing the integer determines the intersection (with integer delta).

There are two sets of integers with different numbers of elements.

X= { x_0, x_1, ... x_n }, x_0 < x_1 < ... < x_n
Y= { y_0, y_1, ... y_m }, y_0 < y_1 < ... < y_m

And there is a function of a single integer, defined as

F(delta) = CountOfItems( Intersection( X, { y_0+delta, y_1+delta, ... y_m+delta) ) )

That is - I add delta Integer for each element of the Y and then count how many of the same integers there are X and the modified Y.

And then the problem - find delta that maximizes F(delta).

max( F(delta) ), where delta is integer

Is there a "mathematical" name for such a task and an optimal algorithm for it?
Of course I can use brute force here and enumerate all possible combinations - but it does not work for large n and m.

Polynomials – factorization problem and integer solutions

Find all pairs of Interger solutions ordered $ (x, y) $ so that $ 2 ^ x + 1 = y ^ 2 $

So I see that we can get $ 2 ^ x = (y + 1) (y-1) $ and from here we see that the right side must be a power of two. I found this problem online and it found the difference $ (y + 1) – (y-1) $ must be $ 2 $what I don't really see.

If we take the case $ 2 ^ 2 = (y + 1) (y-1) $, then the difference should not be the same $ 0 $?

Python – combinations of an integer list with product limit

In Python, the itertools module is a good tool for generating combinations of elements. In this case I want to generate all combinations (without repetition) with a subset of the specified length, but also with a product limit. For example, for a list of integers, I want all subsets of length 4 whose product is above a certain numeric limit, like below:

import functools, operator
LST = (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31 )
prod = lambda A : functools.reduce(operator.mul, A )

def combinations_with_limit( LST, length,lim ) : 
''':Description: LST - array of integers, 
    length = number of elements in each subset , 
    lim = product limit of each subset '''

    H = list(range(length))         # H - represents the index array
    B = ( LST(ii) for ii in H )     # B - the main array with elements
    while H(0) <= len(LST)-length  :
        for i in range( H(-1), len(LST)) :
            H = H(:-1) + (i)
            B = ( LST(ii) for ii in H )
            if prod(B) > lim :      ###  LIMIT THE OUTCOME PART . It skips the rest of the iteration
                H(-1) = len(LST) - 1
            elif prod(B) <= lim :
                yield B
            if H(-1) == len(LST) - 1 :    # We reset the index array here
                j = len(H)-1
                while H(j) == len(LST)-length+j :
                    j -=1
                H(j) +=1
                for l in range(j+1, len(H)) :
                    H(l) = H(l-1) +1

for i in combinations_with_limit(LST, 4 , 1000 ) :
    print(i ,end='  ' )

The output looks like this:

(2, 3, 5, 7)  (2, 3, 5, 11)  (2, 3, 5, 13)  (2, 3, 5, 17)  (2, 3, 5, 19) 
(2, 3, 5, 23)  (2, 3, 5, 29)  (2, 3, 5, 31)  (2, 3, 7, 11)  (2, 3, 7, 13)  
(2, 3, 7, 17)  (2, 3, 7, 19)  (2, 3, 7, 23)  (2, 5, 7, 11)  (2, 5, 7, 13) 

And that's right. All product subsets are below the requested limit. However, I think the code above is not elegant and has some loop inefficiency.

Do you have any ideas on how to improve it? Thanks a lot.

PHP – Round price to nearest integer as an optional fee

I wanted to add a feature to add an optional fee / surcharge to the checkout page and I found this answer.

Instead of a fixed fee, however, I would like the amount to be set as the difference between the total amount of the car and the next whole pound / dollar / euro / whatever. It always has to be rounded up. Even if the cart total is £ 23.14, there should be an option to add a £ 0.86 charge to the order. The same applies to orders worth $ 49.60. You should have the option to add $ 0.40.

How can I add this option to top up the order? Can it still be done with the product method? So far I have only added fees (percentages) that were not optional.