Combinatorics.cc

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/*
 * Combinatorics.cpp
 *
 * 03/04/2006 kasselmann@physik.rwth-aachen.de
 * 19/08/2007 giffels@physik.rwth-aachen.de
 *
 */
//framework
#include "FWCore/MessageLogger/interface/MessageLogger.h"
 
// Own header
#include "HeavyFlavorAnalysis/Skimming/interface/Combinatorics.h"
 
using namespace std;
 
// **************************************************************************
//  Class Constructor
// **************************************************************************
Combinatorics::Combinatorics(Int_t SetQuantity, Int_t SubsetQuantity)
    :
 
      m_SetQuantity(SetQuantity),
      m_SubsetQuantity(SubsetQuantity) {
  // Get permutations
  CalculatePermutations();
}
 
// **************************************************************************
//  Class Destructor
// **************************************************************************
Combinatorics::~Combinatorics() {}
 
// **************************************************************************
//  Get subset permutations
// **************************************************************************
vector<vector<UInt_t> > Combinatorics::GetPermutations() { return m_Permutations; }
 
// **************************************************************************
//  Calculate all subset permutations
// **************************************************************************
Int_t Combinatorics::CalculatePermutations() {
  if (m_SetQuantity < 1 || m_SubsetQuantity < 1 || (m_SetQuantity < m_SubsetQuantity)) {
    edm::LogWarning("Combinatorics") << "[Combinatorics] No valid choice of set or subset!" << endl;
    return -1;
  }
 
  Int_t* currentSubset = new Int_t[m_SubsetQuantity];
  Int_t* currentMapping = new Int_t[m_SetQuantity];
 
  initial_subset(m_SubsetQuantity, currentSubset);
  do {
    initial_permutation(m_SetQuantity, currentMapping);
    do {
      for (UShort_t i = 0; i < m_SubsetQuantity; i++) {
        m_Subset.push_back(currentSubset[currentMapping[i]]);
      }
      m_Permutations.push_back(m_Subset);
      m_Subset.clear();
    } while (next_permutation(m_SubsetQuantity, currentMapping));
  } while (next_subset(m_SetQuantity, m_SubsetQuantity, currentSubset));
 
  delete[] currentSubset;
  delete[] currentMapping;
 
  return 0;
}
 
// **************************************************************************
// Build initial permutation
// **************************************************************************
void Combinatorics::initial_permutation(int size, int* permutation) {
  for (int i = 0; i < size; i++) {
    permutation[i] = i;
  }
}
 
// **************************************************************************
// Build initial subset
// **************************************************************************
void Combinatorics::initial_subset(int k, int* subset) {
  for (int i = 0; i < k; i++) {
    subset[i] = i;
  }
}
 
// **************************************************************************
// Get next permutation if a next permutation exists
// **************************************************************************
Bool_t Combinatorics::next_permutation(int size, int* permutation) {
  int i, j, k;
  if (size < 2)
    return false;
  i = size - 2;
 
  while ((permutation[i] > permutation[i + 1]) && (i != 0)) {
    i--;
  }
  if ((i == 0) && (permutation[0] > permutation[1]))
    return false;
 
  k = i + 1;
  for (j = i + 2; j < size; j++) {
    if ((permutation[j] > permutation[i]) && (permutation[j] < permutation[k])) {
      k = j;
    }
  }
 
  // swap i and k
  {
    int tmp = permutation[i];
    permutation[i] = permutation[k];
    permutation[k] = tmp;
  }
 
  for (j = i + 1; j <= ((size + i) / 2); j++) {
    int tmp = permutation[j];
    permutation[j] = permutation[size + i - j];
    permutation[size + i - j] = tmp;
  }
 
  // return whether a next permutation exists
  return true;
}
 
// **************************************************************************
// Get next subset if a next subset exists
//
// n: the size of the set
// k: the size of the subset
// **************************************************************************
Bool_t Combinatorics::next_subset(int n, int k, int* subset) {
  int i;
  int j;
  int jsave;
  bool done;
 
  if (subset[0] < n - k) {
    done = false;
    jsave = k - 1;
    for (j = 0; j < k - 1; j++) {
      if (subset[j] + 1 < subset[j + 1]) {
        jsave = j;
        break;
      }
    }
    for (i = 0; i < jsave; i++)
      subset[i] = i;
    subset[jsave] = subset[jsave] + 1;
  } else {
    done = true;
  }
  // return whether a next subset exists
  return !done;
}
 
// **************************************************************************
//  Get all subset combinations
// **************************************************************************
vector<vector<UInt_t> > Combinatorics::GetCombinations() {
  if (m_Permutations.empty()) {
    LogDebug("Combinatorics") << "Nothing to do." << endl;
    return m_Combinations;
  }
 
  m_Combinations.push_back(m_Permutations.at(0));
 
  for (UInt_t i = 1; i < m_Permutations.size(); i++) {
    if (!EqualPermutation(m_Combinations.back(), m_Permutations.at(i))) {
      m_Combinations.push_back(m_Permutations.at(i));
    }
  }
  return m_Combinations;
}
 
// **************************************************************************
// Returns true if two permutations of four "int" are equal
// (Equal means e.g.: 0123 = 1023 = 0132 = 1032)
// **************************************************************************
Int_t Combinatorics::EqualPermutation(const vector<UInt_t>& p1, const vector<UInt_t>& p2) {
  if (p1.size() != p2.size()) {
    edm::LogWarning("Combinatorics") << "[Combinatorics::EqualPermutation] permutations have different size!" << endl;
    return -1;
  }
 
  Float_t p1_sum = 0.0;
  Float_t p2_sum = 0.0;
 
  // Check whether permutations are equal (2^index)
  for (UInt_t i = 0; i < p1.size(); i++)
    p1_sum += (1 << p1.at(i));
  for (UInt_t i = 0; i < p2.size(); i++)
    p2_sum += (1 << p2.at(i));
 
  return (p1_sum == p2_sum ? 1 : 0);
}
 
// **************************************************************************
//  Get combinations: 4 out of n
//
//  (The order of the first and second two is not important!
//   0123 = 1023 = 0132 = 1032 are equal therefore)
// **************************************************************************
vector<vector<UInt_t> > Combinatorics::GetCombinations_2_2() {
  // combination vector returned
  vector<vector<UInt_t> > FinalCombinations;
 
  if (m_Permutations.empty()) {
    LogDebug("Combinatorics") << "[Combinatorics::GetCombinations_2_2] Nothing to do." << endl;
    return FinalCombinations;
  }
 
  // So far only for subsets of four indices
  if (m_SubsetQuantity != 4) {
    edm::LogWarning("Combinatorics") << "[Combinatorics::GetCombinations_2_2] Subset must be 4." << endl;
    return FinalCombinations;
  }
 
  // Skip specific permutations
  Skip_2_2(m_Permutations, FinalCombinations);
 
  return FinalCombinations;
}
 
// **************************************************************************
//  Get combinations: 4 out of n
//
//  (The order of the last two is important only:
//   0123 = 1023 are equal therefore)
// **************************************************************************
vector<vector<UInt_t> > Combinatorics::GetCombinations_2_0() {
  // combination vector returned
  vector<vector<UInt_t> > FinalCombinations;
 
  if (m_Permutations.empty()) {
    LogDebug("Combinatorics") << "[Combinatorics::GetCombinations_2_0] Nothing to do." << endl;
    return FinalCombinations;
  }
 
  // So far only for subsets of four indices
  if (m_SubsetQuantity != 4) {
    edm::LogWarning("Combinatorics") << "[Combinatorics::GetCombinations_2_0] Subset must be 4." << endl;
    return FinalCombinations;
  }
 
  // Skip specific permutations
  Skip_2_0(m_Permutations, FinalCombinations);
 
  return FinalCombinations;
}
 
// **************************************************************************
// Skip permutation from p1 if already existing in p2
// **************************************************************************
void Combinatorics::Skip_2_0(const vector<vector<UInt_t> >& p1, vector<vector<UInt_t> >& p2) {
  Bool_t Skip = kFALSE;
 
  p2.push_back(p1.at(0));
 
  for (UShort_t i = 1; i < p1.size(); i++) {
    for (UShort_t j = 0; j < p2.size(); j++) {
      if (EqualPermutation_2_0(p1.at(i), p2.at(j))) {
        Skip = kTRUE;
      }
    }
    if (!Skip)
      p2.push_back(p1.at(i));
 
    Skip = kFALSE;
  }
}
 
// **************************************************************************
// Skip permutation from p1 if already existing in p2
// **************************************************************************
void Combinatorics::Skip_2_2(const vector<vector<UInt_t> >& p1, vector<vector<UInt_t> >& p2) {
  Bool_t Skip = kFALSE;
 
  p2.push_back(p1.at(0));
 
  for (UShort_t i = 1; i < p1.size(); i++) {
    for (UShort_t j = 0; j < p2.size(); j++) {
      if (EqualPermutation_2_2(p1.at(i), p2.at(j))) {
        Skip = kTRUE;
      }
    }
    if (!Skip)
      p2.push_back(p1.at(i));
 
    Skip = kFALSE;
  }
}
 
// **************************************************************************
// Returns true if the two first digm_ of two permutations are equal
// e.g.: 0123 = 1023
// **************************************************************************
Int_t Combinatorics::EqualPermutation_2_0(const vector<UInt_t>& p1, const vector<UInt_t>& p2) {
  if (p1.size() < 2) {
    edm::LogWarning("Combinatorics") << "[Combinatorics::EqualPermutation_2_0] permutation has wrong size!" << endl;
    return -1;
  }
 
  // Check whether permutations are equal
  if (((1 << p1.at(0)) + (1 << p1.at(1)) == (1 << p2.at(0)) + (1 << p2.at(1))) && p1.at(2) == p2.at(2) &&
      p1.at(3) == p2.at(3)) {
    return 1;
  }
  return 0;
}
 
// **************************************************************************
// Returns true if two permutations of four "int" are equal
// e.g.: 0123 = 1023 = 0132 = 1032
// **************************************************************************
Int_t Combinatorics::EqualPermutation_2_2(const vector<UInt_t>& p1, const vector<UInt_t>& p2) {
  // Returns true if two permutations of four "int" are equal
  // (equal means e.g.: 0123 = 1023 = 0132 = 1032)
 
  if (p1.size() != 4 && p2.size() != 4) {
    edm::LogWarning("Combinatorics") << "[Combinatorics::EqualPermutationTwoByTwo] permutation(s) have wrong size!"
                                     << endl;
    return -1;
  }
 
  // Check whether permutations are equal (2^index)
  if (((1 << p1.at(0)) + (1 << p1.at(1)) == (1 << p2.at(0)) + (1 << p2.at(1))) &&
      ((1 << p1.at(2)) + (1 << p1.at(3)) == (1 << p2.at(2)) + (1 << p2.at(3)))) {
    return 1;
  }
  return 0;
}
 
// **************************************************************************
// Returns true if two permutations of four are "equal"
// e.g.: 0123 = 1023
// **************************************************************************
Int_t Combinatorics::EqualPermutation_N_1(const vector<UInt_t>& p1, const vector<UInt_t>& p2) {
  // Returns true if two permutations of four "int" are equal
  // (equal means e.g.: 012 = 102)
 
  if (p1.size() != p2.size()) {
    edm::LogWarning("Combinatorics") << "[Combinatorics::EqualPermutationTwoByTwo] permutation(s) have wrong size!"
                                     << endl;
    return -1;
  }
 
  return (EqualPermutation(p1, p2) && p1.back() == p2.back() ? 1 : 0);
}
 
// **************************************************************************
//  Get combinations "N by 1"
// **************************************************************************
vector<vector<UInt_t> > Combinatorics::GetCombinations_N_1() {
  // Get combinations
  m_Combinations.clear();
  GetCombinations();
 
  // combination vector returned
  vector<vector<UInt_t> > FinalCombinations;
 
  if (m_Combinations.empty()) {
    LogDebug("Combinatorics") << "[Combinatorics::GetCombinationsThreeByOne] Nothing to do." << endl;
    return FinalCombinations;
  }
 
  for (UInt_t i = 0; i < m_Combinations.size(); i++) {
    vector<UInt_t> RotatingPermutation = m_Combinations.at(i);
    FinalCombinations.push_back(m_Combinations.at(i));
 
    for (UInt_t j = 1; j < RotatingPermutation.size(); j++) {
      FinalCombinations.push_back(Rotate(RotatingPermutation, j));
    }
  }
  return FinalCombinations;
}
 
// **************************************************************************
// Rotate permutation to the "left" by n digm_
// **************************************************************************
vector<UInt_t> Combinatorics::Rotate(const vector<UInt_t>& permutation, UInt_t digm_) {
  vector<UInt_t> p;
  vector<UInt_t> tmp;
 
  if (permutation.size() <= digm_) {
    edm::LogWarning("Combinatorics") << "[Combinatorics::Rotate] WARNING: More rotations than digm_ in permutation!"
                                     << endl;
  }
 
  // Save the first i digm_
  for (UInt_t i = 0; i < digm_; i++) {
    tmp.push_back(permutation.at(i));
  }
  for (UInt_t j = 0; j < permutation.size() - digm_; j++) {
    p.push_back(permutation.at(j + digm_));
  }
  for (UInt_t k = 0; k < digm_; k++)
    p.push_back(tmp.at(k));
 
  return p;
}
 
// **************************************************************************
//  Print one permutation
// **************************************************************************
void Combinatorics::Print(const vector<UInt_t>& p) {
  // Print permutations
  for (UShort_t i = 0; i < p.size(); i++) {
    LogDebug("Combinatorics") << (p.at(i));
  }
  LogDebug("Combinatorics") << endl;
}
 
// **************************************************************************
//  Print permutations
// **************************************************************************
void Combinatorics::Print(const vector<vector<UInt_t> >& p) {
  LogDebug("Combinatorics") << "**************" << endl;
  LogDebug("Combinatorics") << "Permutations: " << p.size() << endl;
 
  // Print permutations
  for (UShort_t i = 0; i < p.size(); i++) {
    for (UShort_t j = 0; j < (p.at(0)).size(); j++)
      LogDebug("Combinatorics") << (p.at(i)).at(j);
    LogDebug("Combinatorics") << endl;
  }
}