Algorithm to split an array into P subarrays of balanced sum

Question

I have an big array of length N, let\'s say something like:

2 4 6 7 6 3 3 3 4 3 4 4 4 3 3 1

I need to split this array into P subarrays (in

Answer 1

I propose an algorithm based on backtracking. The main function chosen randomly select an element from the original array and adds it to an array partitioned. For each addition will check to obtain a better solution than the original. This will be achieved by using a function that calculates the deviation, distinguishing each adding a new element to the page. Anyway, I thought it would be good to add an original variables in loops that you can not reach desired solution will force the program ends. By desired solution I means to add all elements with respect of condition imposed by condition from if.

sum=CalculateSum(vector)
Read P
sigma=sum/P
initialize P vectors, with names vector_partition[i], i=1..P
list_vector initialize a list what pointed this P vectors
initialize a diferences_vector with dimension of P
//that can easy visualize like a vector of vectors
//construct a non-recursive backtracking algorithm
function Deviation(vector) //function for calculate deviation of elements from a vector
{
  dev=0
  for i=0 to Size(vector)-1 do
  dev+=|vector[i+1]-vector[i]|
  return dev 
}
iteration=0
//fix some maximum number of iteration for while loop
Read max_iteration
//as the number of iterations will be higher the more it will get  
//a more accurate solution
while(!IsEmpty(vector))
{   
   for i=1 to Size(list_vector) do
   {
       if(IsEmpty(vector)) break from while loop
       initial_deviation=Deviation(list_vector[i])
       el=SelectElement(vector) //you can implement that function using a randomized   
                               //choice of element
       difference_vector[i]=|sigma-CalculateSum(list_vector[i])|
       PutOnBackVector(vector_list[i], el)
       if(initial_deviation>Deviation(difference_vector))
          ExtractFromBackVectorAndPutOnSecondVector(list_vector, vector)
    }
    iteration++
    //prevent to enter in some infinite loop
   if (iteration>max_iteration) break from while loop    

} You can change this by adding in first if some code witch increment with a amount the calculated deviation. aditional_amount=0 iteration=0 while { ... if(initial_deviation>Deviation(difference_vector)+additional_amount) ExtractFromBackVectorAndPutOnSecondVector(list_vector, vector) if(iteration>max_iteration) { iteration=0 aditional_amout+=1/some_constant } iteration++ //delete second if from first version }