LeetCode #2629 — EASY

Function Composition

Build confidence with an intuition-first walkthrough focused on core interview patterns fundamentals.

The Problem

Problem Statement

Given an array of functions [f1, f₂, f₃, ..., f_n], 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

Step 01

Brute Force Baseline

Problem summary: 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.

Baseline thinking

Start with the most direct exhaustive search. That gives a correctness anchor before optimizing.

Pattern signal: General problem-solving

Example 1

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

Example 2

[x => 10 * x, x => 10 * x, x => 10 * x]
1

Example 3

[]
42

Core Insight

What unlocks the optimal approach

Start by returning a function that takes in a number and returns a number.
Call each of the functions in the correct order. Each time passing the output of the previous function into the next function.

Interview move: turn each hint into an invariant you can check after every iteration/recursion step.

Step 03

Algorithm Walkthrough

Iteration Checklist

Define state (indices, window, stack, map, DP cell, or recursion frame).
Apply one transition step and update the invariant.
Record answer candidate when condition is met.
Continue until all input is consumed.

Use the first example testcase as your mental trace to verify each transition.

Step 04

Edge Cases

Minimum Input

Single element / shortest valid input

Validate boundary behavior before entering the main loop or recursion.

Duplicates & Repeats

Repeated values / repeated states

Decide whether duplicates should be merged, skipped, or counted explicitly.

Extreme Constraints

Upper-end input sizes

Re-check complexity target against constraints to avoid time-limit issues.

Invalid / Corner Shape

Empty collections, zeros, or disconnected structures

Handle special-case structure before the core algorithm path.

Step 05

Full Annotated Code

Source-backed implementations are provided below for direct study and interview prep.

// Accepted solution for LeetCode #2629: Function Composition
// Auto-generated Java example from ts.
class Solution {
    public void exampleSolution() {
    }
}
// Reference (ts):
// // Accepted solution for LeetCode #2629: Function Composition
// type F = (x: number) => number;
// 
// function compose(functions: F[]): F {
//     return function (x) {
//         return functions.reduceRight((acc, fn) => fn(acc), x);
//     };
// }
// 
// /**
//  * const fn = compose([x => x + 1, x => 2 * x])
//  * fn(4) // 9
//  */

// Accepted solution for LeetCode #2629: Function Composition
// Auto-generated Go example from ts.
func exampleSolution() {
}
// Reference (ts):
// // Accepted solution for LeetCode #2629: Function Composition
// type F = (x: number) => number;
// 
// function compose(functions: F[]): F {
//     return function (x) {
//         return functions.reduceRight((acc, fn) => fn(acc), x);
//     };
// }
// 
// /**
//  * const fn = compose([x => x + 1, x => 2 * x])
//  * fn(4) // 9
//  */

# Accepted solution for LeetCode #2629: Function Composition
# Auto-generated Python example from ts.
def example_solution() -> None:
    return
# Reference (ts):
# // Accepted solution for LeetCode #2629: Function Composition
# type F = (x: number) => number;
# 
# function compose(functions: F[]): F {
#     return function (x) {
#         return functions.reduceRight((acc, fn) => fn(acc), x);
#     };
# }
# 
# /**
#  * const fn = compose([x => x + 1, x => 2 * x])
#  * fn(4) // 9
#  */

// Accepted solution for LeetCode #2629: Function Composition
// Rust example auto-generated from ts reference.
// Replace the signature and local types with the exact LeetCode harness for this problem.
impl Solution {
    pub fn rust_example() {
        // Port the logic from the reference block below.
    }
}

// Reference (ts):
// // Accepted solution for LeetCode #2629: Function Composition
// type F = (x: number) => number;
// 
// function compose(functions: F[]): F {
//     return function (x) {
//         return functions.reduceRight((acc, fn) => fn(acc), x);
//     };
// }
// 
// /**
//  * const fn = compose([x => x + 1, x => 2 * x])
//  * fn(4) // 9
//  */

// Accepted solution for LeetCode #2629: Function Composition
type F = (x: number) => number;

function compose(functions: F[]): F {
    return function (x) {
        return functions.reduceRight((acc, fn) => fn(acc), x);
    };
}

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

Step 06

Interactive Study Demo

Use this to step through a reusable interview workflow for this problem.

Custom checkpoints (one per line)

Press Step or Run All to begin.

Step 07

Complexity Analysis

Time

O(n)

Space

O(1)

Approach Breakdown

BRUTE FORCE

O(n²) time

O(1) space

Two nested loops check every pair or subarray. The outer loop fixes a starting point, the inner loop extends or searches. For n elements this gives up to n²/2 operations. No extra space, but the quadratic time is prohibitive for large inputs.

OPTIMIZED

O(n) time

O(1) space

Most array problems have an O(n²) brute force (nested loops) and an O(n) optimal (single pass with clever state tracking). The key is identifying what information to maintain as you scan: a running max, a prefix sum, a hash map of seen values, or two pointers.

Shortcut: If you are using nested loops on an array, there is almost always an O(n) solution. Look for the right auxiliary state.

Coach Notes

Common Mistakes

Review these before coding to avoid predictable interview regressions.

Off-by-one on range boundaries

Wrong move: Loop endpoints miss first/last candidate.

Usually fails on: Fails on minimal arrays and exact-boundary answers.

Fix: Re-derive loops from inclusive/exclusive ranges before coding.