Array Reduce Transformation

Problem

Given an integer array nums, a reducer function fn, and an initial value init, return the final result obtained by executing the fn function on each element of the array, sequentially, passing in the return value from the calculation on the preceding element.

This result is achieved through the following operations: val = fn(init, nums[0]), val = fn(val, nums[1]), val = fn(val, nums[2]), ... until every element in the array has been processed. The ultimate value of val is then returned.

If the length of the array is 0, the function should return init.

Please solve it without using the built-in Array.reduce method.

Examples

Example 1

Input: 
nums = [1,2,3,4]
fn = function sum(accum, curr) { return accum + curr; }
init = 0
Output: 10
Explanation:
initially, the value is init=0.
(0) + nums[0] = 1
(1) + nums[1] = 3
(3) + nums[2] = 6
(6) + nums[3] = 10
The final answer is 10.

Example 2

Input: 
nums = [1,2,3,4]
fn = function sum(accum, curr) { return accum + curr * curr; }
init = 100
Output: 130
Explanation:
initially, the value is init=100.
(100) + nums[0] * nums[0] = 101
(101) + nums[1] * nums[1] = 105
(105) + nums[2] * nums[2] = 114
(114) + nums[3] * nums[3] = 130
The final answer is 130.

Example 3

Input: 
nums = []
fn = function sum(accum, curr) { return 0; }
init = 25
Output: 25
Explanation: For empty arrays, the answer is always init.

Constraints

• 0 <= nums.length <= 1000
• 0 <= nums[i] <= 1000
• 0 <= init <= 1000

Solution

Method 1 - Simple For-each Loop

Intuition

Simulate the reduce operation by iteratively applying the reducer function to the accumulator and each element, starting from the initial value.

Approach

Define a function that takes nums, fn, and init. Start with ans = init, then for each element, update ans = fn(ans, num). Return ans at the end. If nums is empty, return init immediately.

Code

JavaScript

function reduce(nums, fn, init) {
  let ans = init;
  for (const num of nums) {
    ans = fn(ans, num);
  }
  return ans;
}

Python

from typing import List, Callable

def reduce(nums: List[int], fn: Callable[[int, int], int], init: int) -> int:
    ans = init
    for num in nums:
        ans = fn(ans, num)
    return ans

Complexity

• ⏰ Time complexity: O(n)
• 🧺 Space complexity: O(1)

Method 2 - Using Array.forEach

Code

JS

var reduce = function(nums, fn, init) {
  let acc = init;
  nums.forEach((element) => {
    acc = fn(acc, element);
  });
  return acc;
};

TS

type Fn = (accum: number, curr: number) => number

function reduce(nums: number[], fn: Fn, init: number): number {
  let acc = init;
  nums.forEach((element: number) => {
    acc = fn(acc, element);
  });
  return acc;
};

Python

from typing import List, Callable

def reduce(nums: List[int], fn: Callable[[int, int], int], init: int) -> int:
    acc = init
    for num in nums:
        acc = fn(acc, num)
    return acc

Method 3 - Using array.reduce

This method employs the Array.reduce() function to iterate through each array element, progressively updating a cumulative value.

Code

JS

var reduce = function(nums, fn, init) {
  return nums.reduce((acc, element) => fn(acc, element), init);
};

Python

from functools import reduce as builtin_reduce
from typing import List, Callable

def reduce(nums: List[int], fn: Callable[[int, int], int], init: int) -> int:
    return builtin_reduce(fn, nums, init)

Method 4 - Python Using List Comprehension with Walrus Operator

Code

Python

from typing import List, Callable

def reduce(nums: List[int], fn: Callable[[int, int], int], init: int) -> int:
    acc = init
    [acc := fn(acc, num) for num in nums]
    return acc