Sorting Interview Questions & Tips

By Jai Pandya | Last updated: July 24, 2023

What is Sorting?

Sorting, in computer science, is the process of arranging a collection of data in a specific order. This operation is fundamental to many practical scenarios, from ordering a list of contacts by name in your phone's contact list to sorting posts by date on a social media platform. Search engines, databases, and e-commerce websites extensively utilize sorting algorithms to provide faster and more efficient services.

From a coding interview perspective, a strong understanding of sorting algorithms demonstrates your problem-solving abilities, knowledge of time and space complexity, and ability to select the most efficient algorithm for a given situation.

At its core, sorting involves taking input data and writing a program that outputs it in a particular order. The input could be an array of numbers, a list of strings, or even complex data structures. The goal is to output this data sorted according to a specific rule, like ascending order for numbers or lexicographically for strings.

Types

Sorting algorithms can be broadly divided into two categories: comparison sorts and non-comparison sorts. Comparison sorts work by comparing elements and deciding their order based on the result; examples are Quick Sort, Merge Sort, and Heap Sort. On the other hand, non-comparison sorts do not make decisions based on comparing elements but on distributing the individual items (e.g., Counting Sort and Radix Sort).

While you should know all common sorting algorithms, from a coding interview perspective, you'll see quick sort, merge sort, and heap sort more often than others. Please note that while it's uncommon to be asked to implement these algorithms from scratch in a coding interview, the principles underlying these algorithms often inform the solutions to a variety of complex problems. Therefore, we'll focus on these three algorithms in this section.

Quick Sort

Quick Sort is a "divide and conquer" sorting algorithm known for its average-case performance. It selects a 'pivot' element from the array and partitions the other elements into two sub-arrays based on whether they are less than or greater than the pivot. The sub-arrays are then recursively sorted.

Time Complexity: The average and best case is O(n log n), but the worst case is O(n^2), when the smallest or largest element is always chosen as the pivot.

Space Complexity: O(log n) due to the stack space during recursive calls.

Let's see its implementation now:

def quick_sort(arr):
    quick_sort_helper(arr, 0, len(arr) - 1)

def quick_sort_helper(arr, start, end):
    if start >= end:
        return

pivot_index = partition(arr, start, end)
    quick_sort_helper(arr, start, pivot_index - 1)
    quick_sort_helper(arr, pivot_index + 1, end)

def partition(arr, start, end):
    pivot = arr[end]
    i = start
    for j in range(start, end):
        if arr[j] < pivot:
            arr[i], arr[j] = arr[j], arr[i]
            i += 1
    arr[i], arr[end] = arr[end], arr[i]
    return i

Merge Sort

Merge Sort is another "divide and conquer" sorting algorithm. It divides the unsorted list into N sublists, each containing one element (a list of one element is considered sorted). Then, it repeatedly merges these sublists to produce new sorted sublists until only one sublist remains.

Time Complexity: Merge Sort performs consistently well with a time complexity of O(n log n) in all cases.

Space Complexity: O(n), as it requires auxiliary space to store the temporary arrays.

Let's look at some example code:

def merge_sort(arr):
    if len(arr) <= 1:
        return arr

mid = len(arr) // 2
    left = arr[:mid]
    right = arr[mid:]

return merge(merge_sort(left), merge_sort(right))

def merge(left, right):
    result = []
    i = j = 0

while i < len(left) and j < len(right):
        if left[i] < right[j]:
            result.append(left[i])
            i += 1
        else:
            result.append(right[j])
            j += 1

result.extend(left[i:])
    result.extend(right[j:])
    return result

Heap Sort

Heap Sort uses a binary heap data structure to sort elements. A binary heap is a complete binary tree, which can be either a max heap or a min-heap. In a max heap, the parent node is always larger than or equal to its children, while in a min-heap, the parent node is less than or equal to its children. The binary heap data structure lets us quickly access the largest (max heap) or smallest (min-heap) element.

Heap Sort first builds a max heap from the input data, then continuously removes the maximum element from the heap and places it at the end of the sorted array.

Time Complexity: Heap Sort performs consistently with a time complexity of O(n log n) in all cases.

Space Complexity: O(1), as it does not require extra space beyond what is needed to store the input.

import heapq

def heap_sort(arr):
    heapq.heapify(arr)
    sorted_arr = []
    while arr:
        sorted_arr.append(heapq.heappop(arr))
    return sorted_arr

Stability of Sorting Algorithms

A sorting algorithm is "stable" if it maintains the original order of equal elements in the sorted output. Understanding the stability of a sorting algorithm is crucial when choosing the right one for your task. Merge Sort, Insertion Sort, and Bubble Sort are stable algorithms, while Heap Sort, Quick Sort, and Selection Sort are not.

In-Place Sorting Algorithms

An in-place sorting algorithm sorts the input data within the data structure containing it, using a fixed, small amount of extra space. These algorithms are beneficial when memory usage is a concern.

Quick Sort, Heap Sort, Insertion Sort, and Bubble Sort are examples of in-place sorting algorithms, while Merge Sort, Counting Sort, Radix Sort, and Bucket Sort require additional space, making them not in-place.

Cheat Sheet

When to Use Sorting in Interviews

In coding interviews, you may not often be asked to implement a sorting algorithm from scratch, but understanding the principles behind these algorithms can lead to an efficient solution. Understanding partitioning and how it segregates data based on a condition helps solve a broad range of problems and is a typical pattern in many coding interview questions.

Common Sorting interview Questions

HARD

1. Alien Dictionary - You are given a list of lexicographically sorted words from an alien language. This language has a unique order. Return the alphabetical order of all the letters found in the list of words.

MEDIUM

2. Container With the Most Water - Given n non-negative integers, find two lines that form a container that can hold the most amount of water.

3. Kth Smallest Element - Given an integer array and an integer k, return the kth smallest element in the array.

EASY

4. Reverse Words in a String - Given an input string s, reverse the order of the words without reversing the words themselves.