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// I think <algorithm> is unused.
#include <algorithm>
#include <iostream>
#include <map>
#include <string>
#include <vector>

using namespace std;

// Consider std::pair instead on std::vector<std::string>.
// Consider std::unordered_map instead of std::map if you have access to it.
// Somme people would rather see this whole thing wrapped in a class with a
// overload on operator().  The reasoning being that the constructor of the
// map runs before main() which hurts program start time.
map< vector< string >, int > lev_cache;

// There is a perf argument for passing in 4 string iterators.  But that will
// make the code somewhat less obvious.  Also it will make it so the cache is
// only useful for a single top level call to levenshtein_distance.
int levenshtein_distance(string l1, string l2) {
        // I'm not crazy about this early out.  I'm not sure if it's a win for performance.
        if (l1 == l2) return 0;
        if (l1 == "" && l2 != "") return l2.length();
        if (l1 != "" && l2 == "") return l1.length();

        // You're looking for the element twice in the case it's found, consider instead.
        // std::map<std::pair<std::string, std::string>, int>::iterator it = lev_cache.find(std::make_pair(l1, l2));
        // if (it != lev_cache.end())
        //      return *it;
        vector< string > temp; temp.push_back(l1); temp.push_back(l2); //vector< string > temp = {l1, l2};
        if (lev_cache.count(temp) > 0) return lev_cache[temp];

        // Consider combining these and making them const where apropriate.
        // Consider making ll_1 and ll_2 chars.
        // const char l1_1 = l1[0];
        // const std::string l1_rest = l1.substr(1);
        // const char l2_1 = l2[0];
        // const std::string l2_rest = l2.substr(2);
        string l1_1, l1_rest, l2_1, l2_rest;
        l1_1 = l1.substr(0,1);
        l1_rest = l1.substr(1);
        l2_1 = l2.substr(0,1);
        l2_rest = l2.substr(1);
        if (l2_1 == l1_1) {
                        int d = levenshtein_distance(l1_rest, l2_rest);
                        // Looks like you're putting the wrong thing into the memorization table.  _rest, _rest should be in there from the recursive call.
                        // lev_cache[std::make_pair(l1, l2)] = d;
                        temp.clear(); temp.push_back(l1_rest); temp.push_back(l2_rest); //temp = {l1_rest, l2_rest};
                        lev_cache[temp] = d;
                        return d;
        }
        // Again it looks like you're putting the result of the recursive call into the table.  It's simpler to just put the result into the table.
        int m1 = levenshtein_distance(l1_rest, l2);
        temp.clear(); temp.push_back(l1_rest); temp.push_back(l2); //temp = {l1_rest, l2};
        lev_cache[temp] = m1;
        int m2 = levenshtein_distance(l1, l2_rest);
        temp.clear(); temp.push_back(l1); temp.push_back(l2_rest); //temp = {l1, l2_rest};
        lev_cache[temp] = m2;
        int m3 = levenshtein_distance(l1_rest, l2_rest);
        temp.clear(); temp.push_back(l1_rest); temp.push_back(l2_rest); //temp = {l1_rest, l2_rest};
        lev_cache[temp] = m3;
        return 1 + min(min(m1, m2), m3);
}

int main(int argc, char **argv)
{
        cout << "Distance: " << levenshtein_distance("the quick brown fox jumps over the lazy dog", "pack my box with five dozen liquor jugs") << "\n";
        //cout << "Distance: " << levenshtein_distance("the quick brown fox", "pack my box") << "\n";

        // return is technically not required for main (it's a special case), but I'd throw in return 0;
}

#if 0

#include <iostream>
#include <string>
#include <unordered_map>
#include <utility>

namespace std {
        template<>
        struct hash<std::pair<std::string, std::string> > {
                size_t operator()(const std::pair<std::string, std::string> &p) const {
                        return std::hash<std::string>()(p.first) ^ std::hash<std::string>()(p.second);
                }
        };
}

std::unordered_map<std::pair<std::string, std::string>, int> lev_cache;

int levenshtein_distance(std::string l1, std::string l2) {
        if (l1.empty())
                return l2.length();
        if (l2.empty())
                return l1.length();

        std::unordered_map<std::pair<std::string, std::string>, int>::iterator it = lev_cache.find(std::make_pair(l1, l2));
        if (it != lev_cache.end())
                return it->second;

        const char l1_1 = l1[0];
        const std::string l1_rest = l1.substr(1);
        const char l2_1 = l2[0];
        const std::string l2_rest = l2.substr(1);
        if (l2_1 == l1_1) {
                        const int d = levenshtein_distance(l1_rest, l2_rest);
                        lev_cache[std::make_pair(l1, l2)] = d;
                        return d;
        }

        const int d = 1 + std::min(std::min(levenshtein_distance(l1_rest, l2),
                                            levenshtein_distance(l1, l2_rest)),
                                   levenshtein_distance(l1_rest, l2_rest));
        lev_cache[std::make_pair(l1, l2)] = d;
        return d;
}

int main(int argc, char **argv)
{
        std::cout << "Distance: " << levenshtein_distance("the quick brown fox jumps over the lazy dog", "pack my box with five dozen liquor jugs") << "\n";

        return 0;
}

#endif