fastest algorithm count number of 3 length AP in array

Question

I want to solve this CodeChef challenge:

Suppose We are given an array A of N(of range 100,000) elements. We are to find the count of all pairs of 3 such elements 1&

Answer 1

You can greatly cut execution time if you make a first pass over the list and only extract number pairs that it is possible to have an 3 term AP between (difference is 0 mod 2). And then iterating between such pairs.

Pseudo C++-y code:

// Contains information about each beginning point
struct BeginNode {
  int value;
  size_t offset;
  SortedList ends;  //sorted by EndNode.value
};

// Contains information about each class of end point
struct EndNode {
  int value;
  List offsets; // will be sorted without effort due to how we collect offsets
};

struct Result {
  size_t begin;
  size_t middle;
  size_t end;
};

SortedList nodeList;
foreach (auto i : baseList) {
  BeginNode begin;
  node.value = i;
  node.offset = i's offset; //you'll need to use old school for (i=0;etc;i++) with this
  // baseList is the list between begin and end-2 (inclusive)
  foreach (auto j : restList) { 
    // restList is the list between iterator i+2 and end (inclusive)
    // we do not need to consider i+1, because not enough space for AP
    if ((i-j)%2 == 0) { //if it's possible to have a 3 term AP between these two nodes
      size_t listOffset = binarySearch(begin.ends);
      if (listOffset is valid) {
        begin.ends[listOffset].offsets.push_back(offsets);
      } else {
        EndNode end;
        end.value = j;
        end.offsets.push_back(j's offset);
        begin.ends.sorted_insert(end);
      }
    }
  }
  if (begin has shit in it) {
    nodeList.sorted_insert(begin);
  }
}
// Collection done, now iterate over collection

List res;
foreach (auto node : nodeList) {
  foreach (auto endNode : node.ends) {
    foreach (value : sublist from node.offset until endNode.offsets.last()) {
      if (value == average(node.value, endNode.value)) {
        // binary_search here to determine how many offsets in "endNode.offsets" "value's offset" is less than.
        do this that many times:
          res.push_back({node.value, value, endNode.value});
      }
    }
  }
}

return res;