Problem : Function Composition | #2629 | LeetCode
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
Solution:
/**
* @param {Function[]} functions
* @return {Function}
*/
var compose = function (functions) {
return function (x) {
if (functions.length === 0) {
return x;
} else {
let result = x;
for (let i = functions.length - 1; i >= 0; i--) {
result = functions[i](result);
}
return result;
}
}
};
/**
* const fn = compose([x => x + 1, x => 2 * x])
* fn(4) // 9
*/
Explanation:
Let's break down the code step by step:
1. The code defines a function called `compose` which takes one parameter, `functions`. It's intended to create a new function by composing an array of functions together.
2. Inside the `compose` function, a new function is returned. This returned function takes one parameter, `x`, which is the input value to be processed by the composed functions.
3. The function checks if the `functions` array is empty by examining its length using `functions.length === 0`. If it's empty, it simply returns the input value `x` because there are no functions to apply.
4. If the `functions` array is not empty, the code initialises a variable `result` with the value of `x`. This variable will be used to accumulate the result of applying the composite functions.
5. It then enters a `for` loop that iterates through the `functions` array in reverse order, starting from the last function in the array and moving towards the first.
6. Inside the loop, each function in the `functions` array is applied to the `result`, and the updated value is stored back in the `result` variable. This effectively composes the functions in reverse order, with the last function being applied first.
7. After the loop has processed all the functions, the final `result` value represents the output of applying the composite functions to the input `x`.
8. The final `result` value is returned as the result of the function created by `compose`.
In summary, the `compose` function takes an array of functions and returns a new function that applies these functions to an input value `x`, composing them in reverse order. This allows you to create a single function that combines multiple functions to process input data. In the example provided, `compose` is used to create a new function `fn` that applies two functions: `x => x + 1` and `x => 2 * x`, resulting in the output `9` when `fn(4)` is called.