# 2629. Function Composition Solved Easy

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

## Constraints

* -1000 <= x <= 1000
* 0 <= functions.length <= 1000
* all functions accept and return a single integer

## 📝 Solution 1 – reduceRight (সবচেয়ে সংক্ষিপ্ত)
```js
/**
 * @param {Function[]} functions
 * @return {Function}
 */
var compose = function(functions) {
  return function(x) {
    return functions.reduceRight((acc, fn) => fn(acc), x);
  };
};
```

## 📝 Solution 2 – for লুপ (reverse করে)
```js
/**
 * @param {Function[]} functions
 * @return {Function}
 */
var compose = function(functions) {
  return function(x) {
    let result = x;
    for (let i = functions.length - 1; i >= 0; i--) {
      result = functions[i](result);
    }
    return result;
  };
};
```

## 📝 Solution 3 – for...of + slice().reverse()
```js
/**
 * @param {Function[]} functions
 * @return {Function}
 */
var compose = function(functions) {
  return function(x) {
    let result = x;
    for (const fn of functions.slice().reverse()) {
      result = fn(result);
    }
    return result;
  };
};
```

## 📝 Solution 4 – রিকার্সিভ (recursive)
```js
/**
 * @param {Function[]} functions
 * @return {Function}
 */
var compose = function(functions) {
  if (functions.length === 0) return x => x; // identity
  
  return function(x) {
    // প্রথম ফাংশন বাদ দিয়ে বাকি ফাংশনের কম্পোজিশন বানাচ্ছি
    const [first, ...rest] = functions;
    const composedRest = compose(rest);
    return first(composedRest(x));
  };
};
```

## ✅ উদাহরণ
```js
const functions = [x => x + 1, x => x * x, x => 2 * x];
const fn = compose(functions);

console.log(fn(4)); // Output: 65
```




## 🚀 কিভাবে কাজ করে:

- আমরা একটি নতুন ফাংশন রিটার্ন করি যা ইনপুট x নেয়।

- reduceRight ব্যবহার করে প্রতিটি ফাংশনকে ডান দিক থেকে বাঁ দিকে প্রয়োগ করি।

- প্রতিটি ফাংশনের আউটপুট পরের ফাংশনের ইনপুট হয়।