sorting std vector of strings without using default algorithm

The least painful way is to put approporiate leading zeroes into your file names (even writing a second script that takes the generated names and renames them may be easier than writing your own sort routine).

The second least painful way is to write your own sort predicate that does sorts _ delimited numbers as a number rather than lexicographically.

Here's a comparison that handles any number of numeric values embedded in the strings:

#include <cstdlib>
#include <cctype>
#include <iostream>

#ifdef  _MSC_VER
#define strtoll _strtoi64
#endif

int cmp(const char* lhs, const char* rhs)
{
    while (*lhs || *rhs)
    {
        if (isdigit(*lhs) && isdigit(*rhs))
        {
            char* l_end;
            char* r_end;
            long long l = strtoll(lhs, &l_end, 10);
            long long r = strtoll(rhs, &r_end, 10);
            if (l < r) return -1;
            if (l > r) return 1;
            lhs = l_end;
            rhs = r_end;
        }
        else
            if (*lhs != *rhs)
                return *lhs - *rhs;
            else
                ++lhs, ++rhs;
    }
    return *lhs - *rhs;
}

It's deliberately "C style" so it can be applied directly and efficiently to character arrays. It returns a negative number if lhs < rhs, 0 if they're equal, and a positive number if lhs > rhs.

You can call this from a comparison functor or lambda specified to std::sort.

You can have a custom comparator something like following :

struct Comp{

    auto get_num (const std::string& a)
    {
        auto it1 = std::find_if( a.begin(), a.end(), ::isdigit );
        auto it2 = std::find_if( a.begin(), a.end(), 
                               [](char x){ return x == '.' ;}) ;
        /* Do some checks here for std::string::npos*/
        auto pos1 = std::distance( a.begin(), it1) ;
        auto pos2 = std::distance( it1, it2) ;
        return std::stoi (a.substr( pos1, pos2 )) ;
    }

    bool operator () (const std::string& a, const std::string& b)
    {
        return get_num (a) < get_num (b) ;
    }

};

See demo here