30 Days of Javascript 8 - Function Composition

Given an array of functions [f1, f2, f3, …, fn], return a new function fn that is the function composition of the array of functions.

The function composition of [f(x), g(x), h(x)] is fn(x) = f(g(h(x))).

The function composition of an empty list of functions is the identity function f(x) = x.

You may assume each function in the array accepts one integer as input and returns one integer as output.

Example 1:

Input: functions = [x => x + 1, x => x * x, x => 2 * x], x = 4 Output: 65 Explanation: Evaluating from right to left … Starting with x = 4. 2 _ (4) = 8 (8) _ (8) = 64 (64) + 1 = 65 Example 2:

Input: functions = [x => 10 * x, x => 10 * x, x => 10 * x], x = 1 Output: 1000 Explanation: Evaluating from right to left … 10 _ (1) = 10 10 _ (10) = 100 10 * (100) = 1000 Example 3:

Input: functions = [], x = 42 Output: 42 Explanation: The composition of zero functions is the identity function

/**
 * @param {Function[]} functions
 * @return {Function}
 */
var compose = function (functions) {
  if (functions.length === 0) {
    return (x) => x; // Identity function
  }

  return functions.reduceRight((prevFn, nextFn) => {
    return (x) => nextFn(prevFn(x));
  });
};

/**
 * const fn = compose([x => x + 1, x => 2 * x])
 * fn(4) // 9
 */

The reduceRight method progressively composes the functions, starting from the rightmost function and moving towards the leftmost function.