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2629. Function Composition

Description

Given an array of functionsΒ [f1, f2, f3,Β ..., fn], returnΒ a new functionΒ fnΒ that is the functionΒ composition of the array of functions.

TheΒ functionΒ compositionΒ ofΒ [f(x), g(x), h(x)]Β isΒ fn(x) = f(g(h(x))).

TheΒ functionΒ compositionΒ of an empty list of functions is theΒ identity functionΒ f(x) = x.

You may assume eachΒ functionΒ in the array accepts one integer as inputΒ and returns one integer as output.

Β 

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

Β 

Constraints:

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

Solutions

Solution 1

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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
 */

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