We were discussing the use of graphs in natural language processing: We said when we have diverse multiple features for a vector that depend on each other, one way to represent them is using conditional random fields. We can see this clearly in relational data that have two characteristics. First, each entity has a rich set of features and second there are statistical dependencies between the entites we wish to model. These relationships and dependencies between entities are naturally represented in graph.  Graph based models are have been used to represent the joint probability distribution p(y,x) where the variables y represent the attributes of the entities that we wish to predict and the input variables x represent our observed knowledge about the entities. However if we were to model joint distributions, then modeling the distribution p(x) can include complex dependencies. Modeling these dependencies among inputs can lead to intractable models, but ignoring them can lead to reduced performance. Therefore, a solution may be to directly model the conditional distribution p(y|x), which is sufficient for classification. This is what conditional random fields does. A conditional random field is simply a conditional distribution p(y|x) with an associated graphical structure. The  conditional dependencies among the input variable x now do not need to be represented explicitly and the input can assume to have rich input features.
Reference: Sutton and McCallum

#codingexercise

Given a list of integers, segregate positive and negative ones
int segregate(ref List<int> A,)
{
     int I = -1;
     for (int j = 0; j < n; j++)
     {
          if (A[j] < 0)
          {
            i++;
            swap(A,i,j);
          }
     }
      return i+1;
}
Now interleave the positive and negative alternatively in a segregated list

void interleave(ref List<int> A, int i , int j)// i = segregate(A), j = 0
{
  while ( i < n && j < i)
  {
          Swap(A, j, i);
           i++;
           j += 2;
  }
}
The same holds for interleaving with negative values first because in this case we merely start with j = 1