In C++, sorting elements in a container like an array or a vector is a common task. By default, the C++ standard library provides sorting algorithms that work well for built-in types like integers or floats. However, when dealing with custom objects or user-defined types, the default sorting may not produce the desired results.

To achieve custom sorting, you can define your own comparison function or use lambda expressions. This allows you to define how elements should be sorted based on specific criteria.

Let’s say we have a class called Person, which has two attributes - name and age. We want to sort a vector of Person objects based on their age.

#include <iostream>
#include <vector>
#include <algorithm>

class Person {
public:
    std::string name;
    int age;
    
    Person(std::string name, int age) : name(name), age(age) {}
};

bool compareByAge(const Person& p1, const Person& p2) {
    return p1.age < p2.age;
}

int main() {
    std::vector<Person> people;
    people.push_back(Person("John", 25));
    people.push_back(Person("Emily", 30));
    people.push_back(Person("Adam", 20));

    // Sort based on age using compareByAge function
    std::sort(people.begin(), people.end(), compareByAge);

    // Print sorted list
    for (const auto& person : people) {
        std::cout << person.name << ", " << person.age << std::endl;
    }
    return 0;
}

In the code above, we define a comparison function compareByAge that takes two Person objects as parameters and returns true if the age of the first person is less than the age of the second person. This function acts as a custom sorting criterion.

We then use the std::sort algorithm function to sort the people vector based on the defined comparison function. Finally, we print the sorted list, which will be displayed in ascending order of age.

You can also achieve the same result using a lambda expression, which provides a concise way of defining small inline functions. The lambda expression can be passed directly as the third argument to std::sort:

std::sort(people.begin(), people.end(), [](const Person& p1, const Person& p2) {
    return p1.age < p2.age;
});

By defining a custom comparison function or using a lambda expression, you can sort your custom objects or user-defined types based on any criteria you desire. This allows for flexible and customizable sorting in C++.