What are C++ functors and their uses?

Question

I keep hearing a lot about functors in C++. Can someone give me an overview as to what they are and in what cases they would be useful?

Answer 1

A big advantage of implementing functions as functors is that they can maintain and reuse state between calls. For example, many dynamic programming algorithms, like the Wagner-Fischer algorithm for calculating the Levenshtein distance between strings, work by filling in a large table of results. It's very inefficient to allocate this table every time the function is called, so implementing the function as a functor and making the table a member variable can greatly improve performance.

Below is an example of implementing the Wagner-Fischer algorithm as a functor. Notice how the table is allocated in the constructor, and then reused in operator(), with resizing as necessary.

#include 
#include 
#include 

template 
T min3(const T& a, const T& b, const T& c)
{
   return std::min(std::min(a, b), c);
}

class levenshtein_distance 
{
    mutable std::vector > matrix_;

public:
    explicit levenshtein_distance(size_t initial_size = 8)
        : matrix_(initial_size, std::vector(initial_size))
    {
    }

    unsigned int operator()(const std::string& s, const std::string& t) const
    {
        const size_t m = s.size();
        const size_t n = t.size();
        // The distance between a string and the empty string is the string's length
        if (m == 0) {
            return n;
        }
        if (n == 0) {
            return m;
        }
        // Size the matrix as necessary
        if (matrix_.size() < m + 1) {
            matrix_.resize(m + 1, matrix_[0]);
        }
        if (matrix_[0].size() < n + 1) {
            for (auto& mat : matrix_) {
                mat.resize(n + 1);
            }
        }
        // The top row and left column are prefixes that can be reached by
        // insertions and deletions alone
        unsigned int i, j;
        for (i = 1;  i <= m; ++i) {
            matrix_[i][0] = i;
        }
        for (j = 1; j <= n; ++j) {
            matrix_[0][j] = j;
        }
        // Fill in the rest of the matrix
        for (j = 1; j <= n; ++j) {
            for (i = 1; i <= m; ++i) {
                unsigned int substitution_cost = s[i - 1] == t[j - 1] ? 0 : 1;
                matrix_[i][j] =
                    min3(matrix_[i - 1][j] + 1,                 // Deletion
                    matrix_[i][j - 1] + 1,                      // Insertion
                    matrix_[i - 1][j - 1] + substitution_cost); // Substitution
            }
        }
        return matrix_[m][n];
    }
};