# Arrays Interview Questions & Tips

Despite their simplicity, arrays in coding interviews can be surprisingly intricate. This article explores their various forms and patterns, helping candidates navigate common pitfalls and effectively demonstrate mastery of this essential data structure.

## What are Arrays?

Arrays are a fundamental data structure comprising a collection of elements. They represent a contiguous block of memory and are often used to store collections of data of the same type. If we know the address of an array in memory, we can calculate the address of each element by adding an offset to the base address. Arrays are very efficient with respect to memory usage and provide fast access to individual elements. They are so useful that most programming languages natively incorporate them.

Arrays are usually fixed in size and have a specific number of elements. Some languages like Ruby and JavaScript offer dynamic arrays that can grow or shrink in size. However, these dynamic arrays are still implemented under the hood as fixed-size arrays. When they reach capacity, new arrays are created with double the capacity, and the old array is copied over. This is an expensive operation. Therefore we use an array when we know the collection size in advance.

### Types of Arrays

Arrays come in different shapes and sizes. Let's use an analogy to understand the different types of arrays.

The simplest and most common type is the one-dimensional array, similar to a row of houses on the street. This type of array consists of elements stored in a contiguous block of memory, much like houses lined up side by side. Each house, like an array element, has its unique address or index. The 'length' of this street or array is simply the count of houses or elements it hosts.

Elevating complexity, a two-dimensional array mirrors a city grid. Streets and avenues form a grid, each housing numerous homes. Each home's location can be identified using its street and house number, similar to a two-dimensional array's pair of indices. The total count of houses across the city grid corresponds to the total elements in the array.

For a three-dimensional array, picture a towering skyscraper in the city grid. Each floor is its own grid of streets and houses. Every apartment (element) is located using a floor number, street number, and house number, much like multiple indices in a multidimensional array. The total number of apartments across all the floors reflects the total elements within the array. While you can have an array with an arbitrary number of dimensions, in coding interviews it is rare to see more than three dimensions used.

### Array Operations

Arrays are best used when accessing an element by its index. This is a constant time `O(1)`

operation. This is the primary benefit of arrays over other data structures like linked lists, where finding a specific element necessitates traversing the list, resulting in a linear time `O(n)`

operation. However, the insertion or deletion of elements might not be as efficient, given that all the elements to the right or left of the insertion or deletion point must be shifted. This is also a linear time `O(n)`

operation. Similarly, if you’re searching for an element in an unsorted array, you’ll have to examine the entire array, which is also a linear time `O(n)`

operation. However, the story changes if the array is sorted. We'll delve into this facet later in the article.

## Companies That Ask Array Questions

## When to Use Arrays in Interviews

An array, at its core, is a very simple data structure. However, its versatility lies in its simplicity. It's akin to human cells: simple in isolation, yet they form complex organisms when combined.

Arrays form the backbone of many interview questions, whether they revolve around sorting, searching, dynamic programming, or other algorithmic concepts. They are often employed in scenarios where storing and accessing elements in a sequential or ordered manner is required. This includes strings, which are fundamentally just arrays of characters under the hood. Arrays also prove helpful when there's a need for constant-time access to elements based on their index.

Here are some instances when you can use arrays in interviews.

### Iterating Over a Collection of Elements in a Specific Order

Arrays are the go-to data structure when you need to iterate over a collection of elements in a specific order. Since elements in an array are laid out contiguously and have a unique index, iterating over them in any given order (forward, backward, or even at irregular intervals) is quite straightforward.

Suppose you are given a coding challenge during an interview where you are asked to square every array element in place. Such operations can be performed efficiently thanks to arrays, as we can access and modify each element via its index.

Here's how you might implement this in Python:

```
def square_array(arr):
for i in range(len(arr)):
arr[i] = arr[i] * arr[i]
return arr
```

```
1def square_array(arr):
2 for i in range(len(arr)):
3 arr[i] = arr[i] * arr[i]
4 return arr
```

However, it's worth noting that when the order of elements doesn't matter, other data structures such as sets or maps can be more appropriate, offering unique benefits like constant-time lookups and insertions, depending on the specific scenario.

### Sorting a Collection of Elements

Sorting is a typical operation performed on arrays. In interview scenarios, understanding various sorting algorithms and their efficiencies is critical. An array can be an intuitive choice when we need to sort elements, whether integers or objects, in a specific order.

Consider an example where you have an array of integers; the task is to sort this array in ascending order. Most languages provide a built-in function that can be used to sort arrays. In Python, we have both the `sort()`

and `sorted()`

functions available for this purpose. The `sort()`

method sorts the array in-place, meaning it modifies the original array:

```
def sort_elements(arr):
arr.sort()
return arr
```

```
1def sort_elements(arr):
2 arr.sort()
3 return arr
```

On the other hand, the `sorted()`

function returns a new sorted list from the elements of any sequence, leaving the original sequence unaffected. It's beneficial when you want to keep the original array intact and need a sorted version of it.

Read more about sorting algorithms in our Sorting guide.

### Searching for an Element in a Sorted Collection

When you are given a sorted collection, binary search may be an effective solution. Binary search is a divide-and-conquer algorithm used for searching in a sorted array. It halves the search space at every step, making it highly efficient with `O(log n)`

time complexity. It compares the target value to the middle element of the array; if they are unequal, the half in which the target cannot lie is eliminated, and the search continues on the remaining half until it is successful or the remaining half is empty.

Arrays are particularly useful when performing a binary search, as they provide constant-time access to the item in the middle of the array. Compare this to a linked list, where you'd have to traverse the list to find the middle element, which would take linear time.

```
def binary_search(arr, x):
low = 0
high = len(arr) - 1
mid = 0
while low <= high:
mid = (high + low) // 2
# If x is greater, ignore left half
if arr[mid] < x:
low = mid + 1
# If x is smaller, ignore right half
elif arr[mid] > x:
high = mid - 1
# x is present at mid
else:
return mid
# If we reach here, then the element was not present
return -1
```

```
1def binary_search(arr, x):
2 low = 0
3 high = len(arr) - 1
4 mid = 0
5
6 while low <= high:
7
8 mid = (high + low) // 2
9
10 # If x is greater, ignore left half
11 if arr[mid] < x:
12 low = mid + 1
13
14 # If x is smaller, ignore right half
15 elif arr[mid] > x:
16 high = mid - 1
17
18 # x is present at mid
19 else:
20 return mid
21
22 # If we reach here, then the element was not present
23 return -1
```

Binary search seems straightforward in concept, but questions on this topic come in various forms and complexities. Some problems ask you to find the first or last occurrence of a number, and others require you to find the smallest or largest number that meets a specific condition. Thus, it is essential to practice a diverse set of problems on binary search to recognize its patterns and application in different scenarios.

### Two Pointers

"Two Pointers" is a common technique for solving array problems, especially when dealing with sequential access or when there's a need to keep track of two places in the array simultaneously. The two pointers might move in the same direction, opposite directions, or one might remain stationary while the other moves; the specific pattern depends on the problem.

A classic example is reversing an array in-place. We position pointers at the start and end of the array and swap the corresponding elements. These pointers then converge towards the center, effectively reversing the array in-place.

Here's the Python code:

```
def reverse_array(arr):
start = 0
end = len(arr) - 1
while start < end:
arr[start], arr[end] = arr[end], arr[start]
start += 1
end -= 1
return arr
```

```
1def reverse_array(arr):
2 start = 0
3 end = len(arr) - 1
4
5 while start < end:
6 arr[start], arr[end] = arr[end], arr[start]
7 start += 1
8 end -= 1
9
10 return arr
```

It is worth nothing that this approach is applicable to strings as well. However, as strings are treated as immutable in many languages, including Python, we can't perform in-place operations on them directly. In such scenarios, we can convert the string to a list (which is mutable), perform the in-place reversal, and then convert it back to a string.

The utility of this technique is quite broad,for instance, in detecting palindromes or solving the two-sum problem. Mastery of this approach not only aids in array-related queries but also extends to solving linked list related problems, such as identifying the middle element or detecting a cycle within the list.

### Sliding Window Problems

Sliding window problems often require tracking a subset of an array. In these problems, you deal with a 'window' of elements, adjusting its size or shifting its position based on the problem's requirements, all while maintaining the desired property in this window.

For example, if asked to find the maximum sum of any size k subarray, we could use a sliding window approach. Here's a simplified Python solution:

```
def max_sum_subarray(arr, k):
# Compute sum of the first window of size k
# arr[:k] slices the array from index 0 to k
window_sum = sum(arr[:k])
max_sum = window_sum
for i in range(k, len(arr)):
# Compute sum of next window of size k by
# removing the first element of the previous
# window and adding the next element
window_sum = window_sum - arr[i - k] + arr[i]
max_sum = max(max_sum, window_sum)
return max_sum
```

```
1def max_sum_subarray(arr, k):
2 # Compute sum of the first window of size k
3 # arr[:k] slices the array from index 0 to k
4 window_sum = sum(arr[:k])
5 max_sum = window_sum
6
7 for i in range(k, len(arr)):
8 # Compute sum of next window of size k by
9 # removing the first element of the previous
10 # window and adding the next element
11 window_sum = window_sum - arr[i - k] + arr[i]
12 max_sum = max(max_sum, window_sum)
13
14 return max_sum
```

### Implementing Other Data Structures

Arrays are often the foundational building blocks for more complex data structures. Their simplicity and efficient characteristics make them ideal for this role. For instance, stacks and queues, data structures that manage elements in a specific order, often use arrays to organize their elements. Arrays offer the advantage of efficient access, making them a popular choice for these structures.

Also, arrays are critical in depicting complex structures such as heaps and graphs. Graphs can be implemented using arrays through an adjacency matrix or list. Particularly with an adjacency list, arrays store adjacent vertices, offering a space-efficient method for representing sparse graphs. We'll learn more about implementing graphs using arrays later in this article.

## Common Mistakes in Interviews Featuring Arrays

Array-related questions can be trickier than they appear due to their simple structure, often causing interviewees to stumble. Arrays are a fundamental topic that also serves as a stepping stone to more advanced concepts. Consequently, understanding them thoroughly and being aware of common mistakes is vital. This section will highlight these common pitfalls and offer strategies to avoid them effectively.

### Off-by-One Errors and Array Out of Bounds

Off-by-one errors, also known as OBOEs, are among the most common errors. These typically happen when indexing arrays, especially in languages that use zero-based indexing, like Python and Java (There are a number of languages that use one-based indexing as well, such as Lua, R, Julia, COBOL, etc.) For example, suppose you are given an array; and you need to access the last element. It’s common to see mistakes like this:

```
def access_last_element(nums):
return nums[len(nums)] # Raises IndexError
```

```
1def access_last_element(nums):
2 return nums[len(nums)] # Raises IndexError
```

This code raises an IndexError because it attempts to access an index that is one past the end of the array. The correct approach is to subtract one from the length.

```
def access_last_element(nums):
return nums[len(nums) - 1] # Correct
```

```
1def access_last_element(nums):
2 return nums[len(nums) - 1] # Correct
```

In programming languages with static arrays, like C++ or Java, an array out of bounds is a common issue. However, Python's dynamic arrays (lists) mostly circumvent this issue. Still, you can encounter similar problems if you try to insert or update an element at an index that does not exist in the list.

```
def insert_at_index(nums, index, value):
nums[index] = value # Raises IndexError if index > len(nums) - 1
```

```
1def insert_at_index(nums, index, value):
2 nums[index] = value # Raises IndexError if index > len(nums) - 1
```

A better solution would be to use the `list.insert()`

method, which automatically handles these cases. If the provided index is beyond the current list length, the `insert()`

method appends the element to the end of the list.

```
def insert_at_index(nums, index, value):
nums.insert(index, value) # Inserts at correct index or appends if index > len(nums) - 1
```

```
1def insert_at_index(nums, index, value):
2 nums.insert(index, value) # Inserts at correct index or appends if index > len(nums) - 1
3
```

### Inadequate Complexity Analysis

Neglecting the analysis of time and space complexity is a common mistake. This can lead to suboptimal solutions or even solutions that exceed the time limit for larger inputs. For example, suppose you are given an array of numbers and asked to return an array of the same length where each element is the product of all numbers in the original array except the number at that index. The brute-force approach would look something like this:

```
def product_except_self(nums):
output = []
for i in range(len(nums)):
product = 1
for j in range(len(nums)):
if i != j:
product *= nums[j]
output.append(product)
return output
```

```
1def product_except_self(nums):
2 output = []
3 for i in range(len(nums)):
4 product = 1
5 for j in range(len(nums)):
6 if i != j:
7 product *= nums[j]
8 output.append(product)
9 return output
```

This naive solution has a time complexity of `O(n^2)`

, which could be too slow for larger inputs. An optimal solution with a time complexity of `O(n)`

can be achieved by using two passes of the array: one pass to calculate the product of elements to the left of each element and a second pass to calculate the product of elements to the right of each element.

```
def product_except_self(nums):
n = len(nums)
output = [1] * n
left_product = right_product = 1
for i in range(n):
output[i] *= left_product
left_product *= nums[i]
output[~i] *= right_product
right_product *= nums[~i]
return output
```

```
1def product_except_self(nums):
2 n = len(nums)
3 output = [1] * n
4 left_product = right_product = 1
5 for i in range(n):
6 output[i] *= left_product
7 left_product *= nums[i]
8 output[~i] *= right_product
9 right_product *= nums[~i]
10 return output
```

### Mishandling Special Cases and Input Assumptions

Failing to handle special cases, like empty inputs, null values, or duplicate values, is a frequent pitfall. This can lead to unintended exceptions or incorrect outputs.

For instance, if you're writing a function to find the maximum element in an array and you do not consider the case where the array is empty, your function may throw an error.

```
def find_max(nums):
return max(nums) # Raises ValueError if nums is empty
```

```
1def find_max(nums):
2 return max(nums) # Raises ValueError if nums is empty
```

Similarly in JavaScript, the following code will return `-Infinity`

if the input array is empty:

```
function max_element(nums) {
return Math.max(...nums);
}
console.log(max_element([])); // prints -Infinity
```

```
1function max_element(nums) {
2 return Math.max(...nums);
3}
4
5console.log(max_element([])); // prints -Infinity
```

Another example, if you were asked to write a function that takes an array and returns a new array with duplicates removed, you might write something like this:

```
def remove_duplicates(nums):
return list(set(nums))
```

```
1def remove_duplicates(nums):
2 return list(set(nums))
```

This works well for most cases, but the solution doesn't preserve the original order of elements, which could be a requirement in some cases. This highlights the importance of asking clarifying questions about the input and output requirements before implementing your solution.

```
def remove_duplicates(nums):
seen = set()
result = []
for num in nums:
if num not in seen:
seen.add(num)
result.append(num)
return result
```

```
1def remove_duplicates(nums):
2 seen = set()
3 result = []
4 for num in nums:
5 if num not in seen:
6 seen.add(num)
7 result.append(num)
8 return result
```

### Misuse of Built-in Functions

Most programming languages have many helpful built-in functions and methods for working with arrays. However, it's crucial to understand their time complexities to avoid performance issues. One common misconception is thinking that searching for an element in an array (or list in Python) is an `O(1)`

operation when in reality it's `O(n)`

due to linear search.

A particularly common example of this misunderstanding involves the use of the `in`

keyword in Python, which is frequently used in array operations:

```
if x in my_list: # this might appear O(1), but it's actually O(n)!
pass
```

```
1if x in my_list: # this might appear O(1), but it's actually O(n)!
2 pass
3
```

Another example is the misuse of the `list.remove()`

function in Python, which has a time complexity of `O(n)`

because it has to shift all the elements after the removed element. If you are unaware of this, you might incorrectly assume it's an `O(1)`

operation, leading to inefficient code.

```
def remove_all_instances(nums, val):
while val in nums: # Each 'in' check is O(n) and 'remove' is also O(n)
nums.remove(val)
```

```
1def remove_all_instances(nums, val):
2 while val in nums: # Each 'in' check is O(n) and 'remove' is also O(n)
3 nums.remove(val)
```

To resolve this, you could use a different approach, such as filtering the array using list comprehension, which results in a single pass over the array (i.e., `O(n)`

):

```
def remove_all_instances(nums, val):
return [num for num in nums if num != val] # Single pass, hence O(n)
```

```
1def remove_all_instances(nums, val):
2 return [num for num in nums if num != val] # Single pass, hence O(n)
```

### Underutilizing Language Helpers

We have talked about misuse of built-in functions, but when to use them is also important to know. For example, suppose you are given an array of integers and asked to return the sum of all the elements. You might be tempted to write a for loop to iterate over the array and calculate the sum. However, Python has a built-in function called `sum()`

that does exactly that. Using this function is not only more concise, but it also results in better performance because it's implemented in C.

```
def sum_array(nums):
total = 0
for num in nums:
total += num
return total
# Can be written as
def sum_array(nums):
return sum(nums)
```

```
1def sum_array(nums):
2 total = 0
3 for num in nums:
4 total += num
5 return total
6
7# Can be written as
8
9def sum_array(nums):
10 return sum(nums)
```

Another example could be when you want to reverse an array. You could write a for loop to iterate over the array and swap the elements, but Python has built-in functions that let you do this in a single line. You can choose between in-place reversal with `my_list.reverse()`

or creating a new reversed list with `mylist[::-1]`

. Knowing the language helpers available to you and using them when appropriate is important.

### Using Array as a Queue

Arrays are efficient for accessing elements at specific indices but inefficient when removing or inserting elements at arbitrary positions. This is because these operations typically require shifting many elements, which is a linear time operation. For instance, using an array like a queue and popping from the front involves shifting all the remaining elements each time an element is popped, a `O(n)`

operation.

In Python, the `pop()`

method without any arguments efficiently removes the last element (`O(1)`

) because Python maintains a pointer to the end of the list. However, using `pop(0)`

to remove from the front leads to a linear-time operation (`O(n)`

), as all remaining elements need to be shifted to fill the gap left by the removed element.

```
def pop_front(nums):
return nums.pop(0) # Inefficient if nums is large
```

```
1def pop_front(nums):
2 return nums.pop(0) # Inefficient if nums is large
```

A better approach would be to use a data structure that supports efficient removal from the front, like a deque in Python.

```
from collections import deque
def pop_front(nums):
dq = deque(nums)
return dq.popleft() # Efficient
```

```
1from collections import deque
2
3def pop_front(nums):
4 dq = deque(nums)
5 return dq.popleft() # Efficient
6
```

Another example could be taken from JavaScript where built-in support for Queue is not available. In such cases, you can use an array as a queue, but you should be aware of the trade-offs and mention them to your interviewer. If they ask, you should know how to implement a Queue in JavaScript, which is efficient for both enqueue and dequeue operations.

### Array Resizing Misconceptions

In many programming languages, dynamic arrays or lists automatically resize when elements are appended beyond their current capacity. This, however, is not a constant time `O(1)`

operation as one might initially believe. When a resize occurs, what typically happens under the hood is the creation of a new, larger array, and all the elements from the old array are copied over to this new one.

```
def append_elements(nums, elements_to_add):
for element in elements_to_add:
nums.append(element) # Most of the time O(1), but sometimes O(n)
```

```
1def append_elements(nums, elements_to_add):
2 for element in elements_to_add:
3 nums.append(element) # Most of the time O(1), but sometimes O(n)
```

This example, although written in Python, mirrors the same principle in other languages that support dynamic arrays, such as JavaScript and Java (with `ArrayList`

). If you are unaware of this concept, you might wrongly assume that appending is always an `O(1)`

operation. It's worth noting that on average we can say it is an amortized `O(1)`

but this means occasionally we will pay a linear cost for this.

Being mindful of this underlying detail can help you write more efficient code and make better decisions about which data structures to use for specific problems. For instance, if you often need to add elements to an array, and the total number of elements is known in advance, it might be more efficient to preallocate the array with a fixed size if your language supports it. This knowledge can also assist in understanding the trade-offs between dynamic and static arrays.

### Limited Familiarity with Constructing Graphs Using Arrays

Graphs are a versatile and essential data structure in computer science, often used to model various real-world problems. They are typically represented in two common ways: adjacency matrices and adjacency lists. A common pitfall is not fully understanding how to construct and manipulate these graph representations using arrays.

An adjacency matrix, a 2D array, represents a finite graph. The matrix elements indicate whether pairs of vertices are adjacent or not in the graph. However, adjacency matrices can be inefficient for large graphs with many vertices but few edges due to the storage of many zero values.

```
# Graph represented as an adjacency matrix
# 0 1 2 3
graph = [[0, 1, 0, 0], #0
[1, 0, 1, 1], #1
[0, 1, 0, 1], #2
[0, 1, 1, 0]] #3
```

```
1# Graph represented as an adjacency matrix
2# 0 1 2 3
3graph = [[0, 1, 0, 0], #0
4 [1, 0, 1, 1], #1
5 [0, 1, 0, 1], #2
6 [0, 1, 1, 0]] #3
```

On the other hand, an adjacency list uses a more space-efficient approach, especially for sparse graphs. It comprises an array of lists. The array's index represents the node, and each entry in its list represents the nodes it's connected to.

```
# Graph represented as an adjacency list
graph = [[1],
[0, 2, 3],
[1, 3],
[1, 2]]
```

```
1# Graph represented as an adjacency list
2graph = [[1],
3 [0, 2, 3],
4 [1, 3],
5 [1, 2]]
```

Finally, a matrix itself can be thought of as a graph in problems like Number of Islands or Rotting Oranges.

```
# Graph represented by each cell being a thought of as a "node"
# so (0,0) has three neighbors (0,1), (1,0), and (1,1)
graph = [[1, 1, 1],
[0, 0, 0],
[1, 0, 1],
[1, 1, 1]]
```

```
1# Graph represented by each cell being a thought of as a "node"
2# so (0,0) has three neighbors (0,1), (1,0), and (1,1)
3graph = [[1, 1, 1],
4 [0, 0, 0],
5 [1, 0, 1],
6 [1, 1, 1]]
```

## Clarifying Questions to Ask Your Interviewer About Arrays

### Using an In-place Algorithm

In-place operations refer to modifying the input data structure directly, instead of creating a new one. This tactic can significantly cut down the memory footprint of an algorithm, a distinct advantage when handling large data sets. However, in-place operations also modify the original data, which might not always be desirable. This is especially true if the original data is needed elsewhere in the program or if the problem requires maintaining the original input for future reference or backtracking purposes.

Therefore, if you see a problem that can be solved in-place, a good question to ask your interviewer could be:

"*Can I modify the original array to save space, or should I maintain the original input?*"

This shows that you know the trade-offs and are thinking about the problem holistically.

Pro tip: You can specifically ask "*if the data structure is thread-safe or if we want to have our function avoid side effects as we might in the functional programming paradigm.*" These tend to be the two main objections why we would not modify a data structure in-place and also provide an interviewer with good signal that you understand why direct modification isn't always a good idea.

### Proactive Edge-Case Handling and Understanding Input Specifics

When you are dealing with numbers, always ask about their nature. Understanding the specifics of numerical input is key to formulating a robust solution. *Are the numbers positive, negative, odd, or even, or could there be null values? What is the range of the numbers? Are there any other constraints?* It's essential to establish these details upfront or to state these assumptions at the beginning clearly. This habit can help avoid common errors, even the most glaring one – trying to solve the wrong problem.

Equally critical is the proactive exploration of edge cases. Think of zero values, empty arrays, or unexpected data types. It's not just about solving the problem but also about how you handle every possible scenario. Ignoring edge cases can indicate a lack of attention to detail, impacting your interview results.

### Memory Management

In real-world applications, you may need to handle arrays that are too large to fit into memory. You need to design a strategy to process such arrays in chunks, ensuring that only a manageable portion of the array is loaded into memory at any time. An example could be importing data from a large file.

You could ask, "*What is the maximum size of the array? Should I design the solution to handle very large arrays?*" These clarifications can help you understand the scale at which your solution will be applied.

### Algorithm Selection and Time-Space Complexity

Selecting the right algorithm is crucial to solving a problem effectively. This decision often involves trading off between time and space complexity. For example, if you're tasked with finding a target sum from any two numbers in an array, different approaches offer different trade-offs. A brute-force approach has `O(n^2)`

time complexity but doesn't require extra space. Using a hash table improves the time complexity to `O(n)`

but requires additional space.

You can ask your interviewer, "*Can I use extra space to speed up the computation?*" These clarifications can help guide your algorithm selection.

### Understanding the Problem's Characteristics / Is the Array Sorted?

A deep understanding of the problem's constraints and characteristics can guide you toward a more effective and efficient solution. An essential part of this is understanding the nature of the array you're working with. Is it sorted? Are there duplicates? Can it be sorted, and if so, does that offer any benefits for your specific problem?

Asking these questions can lead to insights that significantly optimize your solution. For example, if the array is already sorted, or if you have the freedom to sort it, you could use binary search for various operations, which is typically more efficient than linear search.

Take a problem where you need to find if a target value exists in an array. If the array is not sorted, you would typically resort to a linear search with a time complexity of `O(n)`

. However, if the array is sorted or can be sorted, you can utilize a binary search algorithm, which reduces the time complexity to `O(log n)`

.

### Understanding Data Structures: Arrays vs Linked Lists

A common question that comes up when discussing arrays is: "*Why are arrays commonly used in vector implementations despite the high cost of resizing?*" The answer lies in their efficiency for certain operations, especially accessing elements. However, the trade-off is the high cost during resizing, which involves copying all elements to a new array.

Unlike arrays, linked lists, despite lacking efficient random access and causing cache locality issues, excel when frequent insertions and deletions occur. Understanding when to employ arrays versus linked lists, like in an LRU cache scenario, is a mark of mastery. It is crucial to recognize these nuances to make optimal problem-solving decisions.

## Conclusion

In essence, arrays are foundational data structures that are pivotal when dealing with fixed-size data sets. Indeed, arrays, in their simplicity, can present complex challenges that require careful navigation. By understanding common mistakes, one can deftly avoid pitfalls. Additionally, demonstrating mastery in an interview isn't just about solving problems - it involves asking the right clarifying questions and understanding the implications of algorithm choices. Mastery comes from deep understanding, keen attention to detail, and a practiced ability to apply this knowledge in diverse scenarios.

### Reverse Words in a String

Given an input string `s`, reverse the order of the words without reversing the words themselves.

### Binary Array Partition

Given an array Z of 0s and 1s, divide the array into 3 non-empty parts, such that all of these parts represent the same binary value.

### Top K Frequent Elements

Given a non-empty array of integers, return the k most frequent elements.

### Lucky Numbers in a Matrix

Given an m x n matrix of distinct numbers, return all lucky numbers in the matrix in any order.

### Number of Subarrays with Bounded Maximum

Given an integer array nums and two integers left and right, return the number of contiguous non-empty subarrays such that the value of the maximum array element in that subarray is in the range [left, right].

### Number of Islands

Given a 2D matrix, where "1" represents land and "0" represents water, count how many islands are present.

### Longest Substring Without Repeating Characters

Given a string s, find the length of the longest substring without repeating characters.

### 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.

### Build a Max Heap From an Array

Given an array of integers, transform the array in-place to a max heap.

### Two Sum

Given an array of integers, return the indices of the two numbers that add up to a given target.

### Reverse a Linked List

Given the head of a linked list, reverse the list and return the new head.

### Meeting Rooms

Given a list of meetings, represented as tuples with a start and an end time, determine the minimum number of rooms required to schedule all the meetings.

### Kth Smallest Element

Given an integer array and an integer k, return the kth smallest element in the array.

### Partition List

Given a list of integers L and a number K, write a function that reorganizes L into three partitions: elements less than K, elements equal to K, and elements greater than K. No additional lists may be used.

### Subarray Sum Equals K

Given an unsorted array of integers and an integer k, find the number of subarrays whose sum equals k.

### Find Peak Element in a 2D Array

Given a two-dimensional binary matrix where 1 represents water and 0 represents land, mutate the matrix in place and return the matrix with the highest peak maximized.

### Most Frequent Element in an Array

Given an array of integers, find the most frequent element in the array. Write a method that takes an array of integers and returns an integer. If there is a tie, you can just return any.

### Fruit into Baskets

Given a sequence of fruit trees represented as an array of strings. Return the maximum number of fruit trees you can pick from given you can only have one type of fruit in each basket and once you start picking you can't skip a tree and then keep picking.

### Split Array Largest Sum

Given an integer array nums and an integer k, split nums into k non-empty subarrays such that the largest sum of any subarray is minimized. Return the minimized largest sum of the split.

### Three Sum

Given an array of integers, return an array of triplets such that i != j != k and nums[i] + nums[j] + nums[k] = 0.

### Find the Missing Number in an Array

Given an unsorted array of unique integers (size n + 1) and a first array identical to the second array, missing one integer (size n), find and output the missing integer.

### Partition Equal Subset Sum

Given an array of positive numbers, determine if the array can be split such that the two partition sums are equal.

### Insert Delete getRandom O(1)

Design and implement an efficient sampler that works in average O(1) time complexity.

### Partition to K Equal Sum Subsets

Given an integer array nums and an integer k, return true if it is possible to divide this array into k non-empty subsets whose sums are all equal.

### Maximum Subarray

Given an integer array nums, find the subarray with the largest sum, and return its sum.

### K Largest Elements

Write an efficient program for printing k largest elements in an array. Largest elements are returned in order largest to smallest.

### Generate Parentheses

Given `n` pairs of parentheses, write a function to generate all combinations of well-formed parentheses.

## About the Author

Jai is a software engineer and a technical leader. In his professional career spanning over a decade, he has worked at several startups and companies such as SlideShare and LinkedIn. He is also a founder of a saas product used by over 10K companies across the globe. He loves teaching and mentoring software engineers. His mentees have landed jobs at companies such as Google, Facebook, and LinkedIn.

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