Task: Longest common subsequence
C++: #include <stdint.h>
#include <string>
#include <memory>                       
#include <iostream>
#include <deque>
#include <unordered_map>                
#include <algorithm>                    
#include <iterator>                     

using namespace std;

class LCS {
protected:
  
  class Pair {
  public:
    uint32_t index1;
    uint32_t index2;
    shared_ptr<Pair> next;

    Pair(uint32_t index1, uint32_t index2, shared_ptr<Pair> next = nullptr)
      : index1(index1), index2(index2), next(next) {
    }

    static shared_ptr<Pair> Reverse(const shared_ptr<Pair> pairs) {
      shared_ptr<Pair> head = nullptr;
      for (auto next = pairs; next != nullptr; next = next->next)
        head = make_shared<Pair>(next->index1, next->index2, head);
      return head;
    }
  };

  typedef deque<shared_ptr<Pair>> PAIRS;
  typedef deque<uint32_t> THRESHOLD;
  typedef deque<uint32_t> INDEXES;
  typedef unordered_map<char, INDEXES> CHAR_TO_INDEXES_MAP;
  typedef deque<INDEXES*> MATCHES;

  uint32_t FindLCS(MATCHES& indexesOf2MatchedByIndex1, shared_ptr<Pair>* pairs) {
    auto traceLCS = pairs != nullptr;
    PAIRS chains;
    THRESHOLD threshold;

    
    
    
    
    uint32_t index1 = 0;
    for (const auto& it1 : indexesOf2MatchedByIndex1) {
      if (!it1->empty()) {
        auto dq2 = *it1;
        auto limit = threshold.end();
        for (auto it2 = dq2.rbegin(); it2 != dq2.rend(); it2++) {
          
          auto index2 = *it2;

          
          
          
          
          
          limit = lower_bound(threshold.begin(), limit, index2);
          auto index3 = distance(threshold.begin(), limit);

          
          
          
          
          
          
          
          
          
          auto preferNextIndex2 = next(it2) != dq2.rend() &&
            (limit == threshold.begin() || *prev(limit) < *next(it2));

          
          
          
          
          if (preferNextIndex2) continue;

          if (limit == threshold.end()) {
            
            threshold.push_back(index2);
            
            limit = prev(threshold.end());
            if (traceLCS) {
              auto prefix = index3 > 0 ? chains[index3 - 1] : nullptr;
              auto last = make_shared<Pair>(index1, index2, prefix);
              chains.push_back(last);
            }
          }
          else if (index2 < *limit) {
            
            
            *limit = index2;
            if (traceLCS) {
              auto prefix = index3 > 0 ? chains[index3 - 1] : nullptr;
              auto last = make_shared<Pair>(index1, index2, prefix);
              chains[index3] = last;
            }
          }
        }                                 
      }

      index1++;
    }                                     

    if (traceLCS) {
      
      auto last = chains.size() > 0 ? chains.back() : nullptr;
      
      *pairs = Pair::Reverse(last);
    }

    auto length = threshold.size();
    return length;
  }

  
  
  
  
  
  
  
  
  void Match(CHAR_TO_INDEXES_MAP& indexesOf2MatchedByChar, MATCHES& indexesOf2MatchedByIndex1,
    const string& s1, const string& s2) {
    uint32_t index = 0;
    for (const auto& it : s2)
      indexesOf2MatchedByChar[it].push_back(index++);

    for (const auto& it : s1) {
      auto& dq2 = indexesOf2MatchedByChar[it];
      indexesOf2MatchedByIndex1.push_back(&dq2);
    }
  }

  string Select(shared_ptr<Pair> pairs, uint32_t length,
    bool right, const string& s1, const string& s2) {
    string buffer;
    buffer.reserve(length);
    for (auto next = pairs; next != nullptr; next = next->next) {
      auto c = right ? s2[next->index2] : s1[next->index1];
      buffer.push_back(c);
    }
    return buffer;
  }

public:
  string Correspondence(const string& s1, const string& s2) {
    CHAR_TO_INDEXES_MAP indexesOf2MatchedByChar;
    MATCHES indexesOf2MatchedByIndex1;  
    Match(indexesOf2MatchedByChar, indexesOf2MatchedByIndex1, s1, s2);
    shared_ptr<Pair> pairs;             
    auto length = FindLCS(indexesOf2MatchedByIndex1, &pairs);
    return Select(pairs, length, false, s1, s2);
  }
};

Python: def lcs(xstr, ystr):
    
    if not xstr or not ystr:
        return ""
    x, xs, y, ys = xstr[0], xstr[1:], ystr[0], ystr[1:]
    if x == y:
        return str(lcs(xs, ys)) + x
    else:
        return max(lcs(xstr, ys), lcs(xs, ystr), key=len)