Merge Sorted Arrays

The problem

Given two sorted integer arrays, merge them into a single sorted array.

Because both sources are ordered, the absolute smallest remaining candidate is always standing at one of the two heads. Comparing those two values allows you to stream the merged output directly without sorting, and filling into spare buffer capacity from right to left prevents overwriting unprocessed items.

Full solution

Linear merge pass: two read pointers, always emit the smaller head, then copy whichever tail is left — O(n + m) time in one pass, using the sorted precondition that concatenate-and-sort throws away.

from typing import List


def merge_sorted_arrays(nums1: List[int], nums2: List[int]) -> List[int]:
    merged = []
    i, j = 0, 0
    while i < len(nums1) and j < len(nums2):
        # smallest remaining value always sits at one of the two heads
        if nums1[i] <= nums2[j]:
            merged.append(nums1[i])
            i += 1
        else:
            merged.append(nums2[j])
            j += 1
    merged.extend(nums1[i:])  # at most one of these tails is non-empty
    merged.extend(nums2[j:])
    return merged

function mergeSortedArrays(nums1, nums2) {
  const merged = [];
  let i = 0;
  let j = 0;
  while (i < nums1.length && j < nums2.length) {
    // smallest remaining value always sits at one of the two heads
    if (nums1[i] <= nums2[j]) {
      merged.push(nums1[i++]);
    } else {
      merged.push(nums2[j++]);
    }
  }
  // at most one of these tails is non-empty
  for (; i < nums1.length; i++) merged.push(nums1[i]);
  for (; j < nums2.length; j++) merged.push(nums2[j]);
  return merged;
}

The theory behind it

Arrays — the ground this problem stands on. All Arrays problems

What Arrays is

An array is a row of fixed boxes laid side by side in computer memory, like numbered lockers in a hallway. Because each box occupies identical space and sits directly next to its neighbors, jumping to locker zero or locker ten thousand takes the exact same tiny fraction of time. Every box holds an item of the same type, addressed by an offset number called an index.

When to reach for it

Reach for an array when items arrive in a known sequence and need immediate retrieval by position number. Problems asking for running totals, prefix accumulations, cyclic rotations, or in-place rearrangements signal array mechanics. Whenever constraints require constant-time random lookups or contiguous cache scans across fixed collections, a flat sequence is the default container.

How the pattern works

Visualize a tape with zero-indexed slots stretching from start to end. Keep track of write and read cursors when modifying contents without allocating helper buffers. For running computations, maintain an invariant such as having processed all elements left of the current index while pending elements wait to the right. When modifying entries in place, consider scanning backwards from the end so unread data is not overwritten.

What each operation costs

Which roles need this problem

Arrays is a core topic for these 25 roles — if you're targeting one of them, this problem is early in your path, not optional.

Secondary for 3 more roles, including Database Engineer, Bioinformatics Engineer, Networking Engineer.