reduce

Remember how, in class, we talked about map, which applies a function to every element of an array? Well, now we're going to write the companion function to map, which is called reduce. Just because such a notion is generally used in functional programming doesn't mean we can't build it in C$!$

What does reduce do$?$ It combines all of the elements in an array with a specified function, cumulatively. It maintains a current cumulative value and applies the function to the cumulative value and each element of the given array in turn, in order to produce a new accumulator value. You might have noticed that several functions from hw$2$ had a similar shape $--$ they had to look at each element of a numerical array in turn and update a running value. Can we abstract that behavior out somehow? We can! That's what reduce does.

Concretely, this is exactly analogous to functools.reduce in Python $3.$ And for your edification as a computer scientist, this is operation is often called "fold".

reduce will look like int reduce$($int $*$nums$,$ int len, int $(*$f$)($int$,$int$),$ int initial$).$

initial is the initial value of the cumulative value, and f is a pointer to a function that takes two ints and returns an int $--$ the new value for the cumulative function. When we're calling the function f$,$ imagine that its first parameter will be the current cumulative value, and the second parameter will be the next item in the input array, and the function f will return the new value for the cumulative value.

Why are we doing this? Well...