min-key and max-key

2023-06-08

In programming, it is a common to want to obtain the absolute extrema of a list based on a function that takes the values of the list.

For example in my traveling salesman program, I wanted the shortest path so the function is the length. An example of an implementation of this in C would look something like:

Path shortest-path (Path[] paths, size_t size) {    
    Path min_path = paths[0];
    double min_path_length = path_length(paths[0]);

    for (size_t i = 1; i < size; i++) {
        double possible_min = path_length(paths[i]);
        if (possible_min < min_path_length) {
            min_path_length = possible_min;
            min_path = paths[i];
        }
    }
    
    return min_path;
}

This is very messy because we need to keep track of two variables, min_path and min_path_length.

But Clojure gives us a quick and simple way to do this with min-key:

(defn shortest-path [paths]
  (apply min-key path-length paths))

path-length is passed in as the function that min-key should sort by, so min-key returns the path that had the minimum value when passed into path-length