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c++ lowerbound랑 upperbound 직접 구현하니까 1,2,3번 시간초과 납니다.

#include<iostream>
#include<vector>
#include<string>
#include<algorithm>
using namespace std;
bool compare(string a, string b)
{
    if (a.length() == b.length())
        return a < b;
    else
    {
        return a.length() < b.length();
    }
}
bool lower_compare(string a, string b)
{
    if (a.length() == b.length())
        return a > b;
    else
    {
        return a.length() > b.length();
    }
}
bool upper_compare(string a, string b)
{
    if (a.length() == b.length())
        return a >= b;
    else
    {
        return a.length() >= b.length();
    }
}
int myLowerBound(vector<string> words, string key)
{
    int left = 0;
    int right = words.size();
    int middle = 0;
    while (left < right)
    {
        middle = (left + right) / 2;
        if (lower_compare(key, words[middle]))
            left = middle +1;
        else
            right = middle;
    }
    return right;
}
int myUpperBound(vector<string> words, string key)
{
    int left = 0;
    int right = words.size();
    int middle = 0;
    while (left < right)
    {
        middle = (left + right) / 2;
        if (upper_compare(key, words[middle]))
            left = middle + 1;
        else
            right = middle;
    }
    return right;
}
vector<int> solution(vector<string> words, vector<string> queries)
{
    vector<int> answer;
    vector<string> rwords;
    sort(words.begin(), words.end(), compare);
    for (int i = 0; i < words.size(); ++i)
    {
        string temp = words[i];
        reverse(temp.begin(), temp.end());
        rwords.push_back(temp);
    }
    sort(rwords.begin(), rwords.end(), compare);
    for (int i = 0; i < queries.size(); ++i)
    {
        string query = queries[i];
        int start, end, pos;
        //vector<string>::iterator start, end;
        if (query[0] == '?')
        {
            reverse(query.begin(), query.end());
            pos = query.find("?");
            for (int i = pos; i < query.length(); ++i)
            {
                query[i] = 'a';
            }
            start = myLowerBound(rwords, query);
            //start = lower_bound(rwords.begin(), rwords.end(), query, compare);

            for (int i = pos; i < query.length(); ++i)
            {
                query[i] = 'z';
            }
            end = myUpperBound(rwords, query);
            //end = upper_bound(rwords.begin(), rwords.end(), query, compare);
        }
        else
        {
            pos = query.find("?");
            for (int i = pos; i < query.length(); ++i)
            {
                query[i] = 'a';
            }
            start = myLowerBound(words, query);
            //start = lower_bound(rwords.begin(), rwords.end(), query, compare);

            for (int i = pos; i < query.length(); ++i)
            {
                query[i] = 'z';
            }
            end = myUpperBound(words, query);
            //end = upper_bound(rwords.begin(), rwords.end(), query, compare);
        }
        answer.push_back(end - start);
    }
    return answer;
}

주석한대로 stl 라이브러리 쓰면 시간초과 안나는데
무슨 문제인가요??

작성중인 코드―solution.cpp
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#include<iostream>
#include<vector>
#include<string>
#include<algorithm>
using namespace std;
bool compare(string a, string b)
{
    if (a.length() == b.length())
        return a < b;
    else
    {
        return a.length() < b.length();
    }
}
bool lower_compare(string a, string b)
{
    if (a.length() == b.length())
        return a > b;
    else
    {
        return a.length() > b.length();
    }
}
bool upper_compare(string a, string b)
{
    if (a.length() == b.length())
        return a >= b;
    else
    {
        return a.length() >= b.length();
    }
}
int myLowerBound(vector<string> words, string key)
{
    int left = 0;
    int right = words.size();
    int middle = 0;
    while (left < right)
    {
        middle = (left + right) / 2;
        if (lower_compare(key, words[middle]))
            left = middle +1;
        else
            right = middle;
    }
    return right;
}
int myUpperBound(vector<string> words, string key)
{
    int left = 0;
    int right = words.size();
    int middle = 0;
    while (left < right)
    {
        middle = (left + right) / 2;
        if (upper_compare(key, words[middle]))
            left = middle + 1;
        else
            right = middle;
    }
    return right;
}
vector<int> solution(vector<string> words, vector<string> queries)
{
    vector<int> answer;
    vector<string> rwords;
    sort(words.begin(), words.end(), compare);
    for (int i = 0; i < words.size(); ++i)
    {
        string temp = words[i];
        reverse(temp.begin(), temp.end());
        rwords.push_back(temp);
    }
    sort(rwords.begin(), rwords.end(), compare);
    for (int i = 0; i < queries.size(); ++i)
    {
        string query = queries[i];
        int start, end, pos;
        if (query[0] == '?')
        {
            reverse(query.begin(), query.end());
            pos = query.find("?");
            for (int i = pos; i < query.length(); ++i)
            {
                query[i] = 'a';

            }
            start = myLowerBound(rwords, query);
            for (int i = pos; i < query.length(); ++i)
            {
                query[i] = 'z';
            }
            end = myUpperBound(rwords, query);
        }
        else
        {
            pos = query.find("?");
            for (int i = pos; i < query.length(); ++i)
            {
                query[i] = 'a';
            }
            start = myLowerBound(words, query);

            for (int i = pos; i < query.length(); ++i)
            {
                query[i] = 'z';
            }
            end = myUpperBound(words, query);
        }
        answer.push_back(end - start);
    }
    return answer;
}
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