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Iterative Approach: In this approach, we compose the functions iteratively from the last function to the first. This is because function composition works in reverse order, i.e., f(g(h(x))) means first apply h, then g, and finally f. We start with the input value x and apply each function in the function list from right to left.
Time Complexity: O(n) where n is the number of functions.
Space Complexity: O(1) since we are using a fixed amount of extra space.
This JavaScript solution uses an array of arrow functions. It applies them from the end of the array to the beginning to the value x.
Recursive Approach: This approach encapsulates the recursive function composition in a way that it applies the last function first and makes a recursive call to apply the rest. We either call the next composed function recursively until the base case, i.e., no functions left, is reached, or upon an empty function list, return the input as it is simply the identity function.
Time Complexity: O(n) where n is the number of functions.
Space Complexity: O(n) due to the recursive call stack.
1function recursiveCompose(functions, index, x) {
2 if (index < 0) return x;
3 return recursiveCompose(functions, index - 1, functions[index](x));
4}
5
6const functions = [
7 x => x + 1,
8 x => x * x,
9 x => 2 * x
10];
11const x = 4;
12console.log(recursiveCompose(functions, functions.length - 1, x));JavaScript implements recursive function application by iterating over an index, ensuring each is called recursively across function composition.