#include <functional>
#include <iostream>
#include <fstream>
#include <list>

#include <cmath>
#include <random>

#include "randutils/randutils.hpp"
#include "pcg-cpp/include/pcg_random.hpp"

using Rng = randutils::random_generator<pcg32>;
using Real = long double;

class Edge {
public:
  std::list<Real> weights;
  Real probability = 0;
};

class Face {
public:
  std::array<std::reference_wrapper<Edge>, 4> edges;

  Face(Edge& a, Edge& b, Edge& c, Edge& d) : edges({a, b, c, d}) {}
};

class AztecDiamond {
public:
  std::vector<Edge> edges;
  std::vector<std::vector<Face>> faces;

  AztecDiamond(unsigned n) : edges(pow(2 * n, 2)), faces(n) {
    for (unsigned i = 1; i <= n; i++) {
      faces[n - i].reserve(pow(i, 2));
      unsigned x0 = n - i;
      for (unsigned j = 0; j < pow(i, 2); j++) {
        unsigned x = 2 * (j % i);
        unsigned y = 2 * (j / i);
        faces[n - i].push_back(Face(
              edges[2 * n * (x0 + y) + x0 + x],
              edges[2 * n * (x0 + y) + x0 + x + 1],
              edges[2 * n * (x0 + y + 1) + x0 + x],
              edges[2 * n * (x0 + y + 1) + x0 + x + 1]
              ));
      }
    }
  }

  void computeWeights() {
    for (std::vector<Face>& fs : faces) {
      for (Face& f : fs) {
        Real w = f.edges[0].get().weights.back();
        Real x = f.edges[1].get().weights.back();
        Real y = f.edges[2].get().weights.back();
        Real z = f.edges[3].get().weights.back();

        Real cellFactor = w * z + x * y;

        f.edges[0].get().weights.push_back(z / cellFactor);
        f.edges[1].get().weights.push_back(y / cellFactor);
        f.edges[2].get().weights.push_back(x / cellFactor);
        f.edges[3].get().weights.push_back(w / cellFactor);
      }
    }

    // This process computes one extra weight per edge.
    for (Edge& e : edges) {
      e.weights.pop_back();
    }
  }

  void computeProbabilities() {
    for (auto it = faces.rbegin(); it != faces.rend(); it++) {
      for (Face& f : *it) {
        Real p = f.edges[0].get().probability;
        Real q = f.edges[1].get().probability;
        Real r = f.edges[2].get().probability;
        Real s = f.edges[3].get().probability;

        Real w = f.edges[0].get().weights.back();
        Real x = f.edges[1].get().weights.back();
        Real y = f.edges[2].get().weights.back();
        Real z = f.edges[3].get().weights.back();

        Real cellFactor = w * z + x * y;
        Real deficit = 1 - p - q - r - s;

        f.edges[0].get().probability = s + deficit * w * z / cellFactor;
        f.edges[1].get().probability = r + deficit * x * y / cellFactor;
        f.edges[2].get().probability = q + deficit * x * y / cellFactor;
        f.edges[3].get().probability = p + deficit * w * z / cellFactor;

        for (Edge& e : f.edges) {
          e.weights.pop_back();
        }
      }
    }
  }
};

int main(int argc, char* argv[]) {
  unsigned n = 100;
  unsigned m = 100;
  Real T = 1;

  int opt;

  while ((opt = getopt(argc, argv, "n:m:T:")) != -1) {
    switch (opt) {
    case 'n':
      n = atoi(optarg);
      break;
    case 'm':
      m = (unsigned)atof(optarg);
      break;
    case 'T':
      T = atof(optarg);
      break;
    default:
      exit(1);
    }
  }

  Rng r;
  AztecDiamond a(n);

  std::vector<Real> avgProbabilities(a.edges.size());

  for (unsigned i = 0; i < m; i++) {
    for (Edge& e : a.edges) {
      e.weights = {exp(- r.variate<Real, std::exponential_distribution>(1) / T)};
      e.probability = 0;
    }
    a.computeWeights();
    a.computeProbabilities();

    for (unsigned j = 0; j < a.edges.size(); j++) {
      avgProbabilities[j] += a.edges[j].probability;
    }
  }


  for (Real& x : avgProbabilities) {
    std::cout << x << " ";
  }
  std::cout <<std::endl;

  return 0;
}