Function Composition

Problem Statement

The task requires creating a new function from a sequence of given arithmetic functions. This sequence of functions is expressed as an array where each element represents a function. The main goal is to perform function composition; where the output of one function becomes the input to the next one starting from the last function in the array.

For example, with functions [f(x), g(x), h(x)] in an array, the function composition will be f(g(h(x))), where h(x) is evaluated first, then g(h(x)), and finally f(g(h(x))). If there are no functions in the array, the program should return a default identity function that outputs the same integer passed to it, i.e., f(x) = x. This identity function ensures that there is a meaningful return value even when there are no operations to perform on x.

Each function in the array operates exclusively on integers, both accepting and returning an integer.

Examples

Example 1

Input:

functions = [x => x + 1, x => x * x, x => 2 * x]
x = 4

Output:

65

Explanation:

Evaluating from right to left:
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:

10 * 1 = 10
10 * 10 = 100
10 * 100 = 1000

Example 3

Input:

functions = []
x = 42

Output:

42

Explanation:

No functions to apply, so the identity function returns x unchanged.

Constraints

• -1000 <= x <= 1000
• 0 <= functions.length <= 1000
• All functions accept and return a single integer

Approach and Intuition

Function composition deals with chaining multiple functions together in a specific sequence. The output of one function becomes the input of the next, applied in reverse order from how they’re written in the array.

1. Identity Function Handling:

   • If functions is empty, return the input x unchanged.

2. Iterative Function Execution:

   • Start from the last function in the array.
   • Use a loop to apply each function one after the other.
   • Continuously update the value of x as you go.

3. Final Evaluation:

   • Once all functions have been applied, return the final value of x.

This guarantees proper chaining of operations and handles edge cases like an empty function array smoothly.

Solutions

var chainFunctions = function (fnList) {
  return function (value) {
    if (fnList.length === 0) return value;
    let result = value;

    for (const singleFn of fnList.reverse()) {
      result = singleFn(result);
    }

    return result;
  };
};