Unatoč tome što sam postigao pristojne ocjene i na predavanju iz algoritma CS101 i na predavanju Strukture podataka na sveučilištu, ježim se pri pomisli da prođem kroz intervju za kodiranje koji se fokusira na algoritme.
Stoga sam proveo posljednja tri mjeseca smišljajući kako poboljšati svoje vještine kodiranja intervjua i na kraju sam dobio ponude od velikih tehnoloških tvrtki. U ovom postu podijelit ću uvide i savjete koje sam stekao putem. Iskusni kandidati također mogu očekivati pitanja o dizajnu sustava, ali to je izvan dosega ovog posta.
Mnogi algoritamski koncepti testirani u intervjuima za kodiranje nisu ono što obično koristim na poslu, gdje sam internetski inženjer. Prirodno, prilično sam zaboravio na ove algoritme i strukture podataka, koje sam naučio uglavnom tijekom svog brucoškog i drugog studija.
Stresno je morati proizvesti (radni) kôd u intervjuu, dok netko pažljivo proučava svaki vaš pritisak. Još je gore što vas se kao sugovornika potiče da glasno priopćite svom procesu razmišljanja ispitivača.
Nekad sam mislio da je istovremeno moći razmišljati, kodirati i komunicirati nemoguć podvig, sve dok nisam shvatio da većina ljudi jednostavno nije dobra u kodiranju intervjua kad prvi put započnu. Intervjuiranje je vještina u kojoj možete poboljšati učenjem, pripremom i vježbanjem za nju.
Nedavno traženje posla odvelo me na putovanje da poboljšam svoje vještine kodiranja razgovora. Front-end inženjeri vole raspravljati o tome kako je trenutni postupak zapošljavanja prekinut jer tehnički intervjui mogu uključivati vještine koje nisu povezane s front-end razvojem. Na primjer, pisanje algoritma za rješavanje labirinta i spajanje dvaju razvrstanih popisa brojeva. Kao osobni inženjer, mogu suosjećati s njima.
Nažalost, pravila postavljaju tvrtke, a ne kandidati. Velik je naglasak na općim računalnim konceptima kao što su algoritmi, obrasci dizajna, strukture podataka; temeljne vještine koje bi trebao posjedovati dobar softverski inženjer. Ako želite posao, morate igrati prema pravilima koje su postavili majstori igara - poboljšajte svoje vještine razgovora za kodiranje!
Ovaj je post strukturiran u sljedeća dva odjeljka. Slobodno prijeđite na odjeljak koji vas zanima.
- Analiza intervjua za kodiranje i kako se za njih pripremiti.
- Korisni savjeti i savjeti za svaku temu algoritma (nizovi, stabla, dinamičko programiranje, itd.), Zajedno s preporučenim LeetCodeovim praksama za pregled osnovnih pojmova i poboljšanje tih tema.
Sadržaj ovog posta može se naći u mom repo priručniku za tehnički intervju na GitHubu. Tamo će se vršiti ažuriranja. Zahtjevi za povlačenje prijedloga i ispravaka su dobrodošli!
yangshun / tehnički intervju-priručnik
tehnički intervju-priručnik -? Algoritmi i bihevioralni sadržaj za potresanje vašeg kodiranja intervjua.g ithub.com
Ako ste zainteresirani za Front End sadržaj, pogledajte odgovore na poznata Pitanja za intervju za posao.
yangshun / priručnik za intervju s prednjim dijelom
front-end-intervju-priručnik -? Gotovo cjeloviti odgovori na "Pitanja za intervju za posao" na g ithub.com
Odabir programskog jezika
Osobno, Python je moj de facto izbor za algoritme kodiranja tijekom intervjua. Sažet je i ima ogromnu biblioteku funkcija i struktura podataka. Jedan od glavnih razloga preporučujem Python je da se koristi u skladu API koji rade na različitim strukturama podataka, kao što su
for ... in ...i na kriške zapis na sekvence (nizovi, popise i torke). Dobivanje posljednjeg elementa u nizu je
arr[-1], a njegovo poništavanje jednostavno
arr[::-1]. Puno toga možete postići minimalnom sintaksom u Pythonu.
I Java je pristojan izbor. Ali budući da ćete u kodu morati neprestano deklarirati vrste, to znači unos dodatnih pritiskanja tipki. To će usporiti brzinu kodiranja i upisivanja. Ovaj će problem biti očigledniji kada tijekom razgovora na terenu morate pisati na ploči.
Razlozi za odabir ili ne odabir C ++ slični su Java. U konačnici, Python, Java i C ++ su pristojan izbor. Ako već neko vrijeme koristite Javu i nemate vremena za upoznavanje drugog jezika, preporučujem da se držite Jave umjesto da Python podignete od nule. To vam pomaže da izbjegnete upotrebu jednog jezika za posao, a drugog za intervjue. Uglavnom je usko grlo u razmišljanju, a ne u pisanju.
Review your CS101
If you have been out of college for some time, it is highly advisable to review the CS fundamentals. I prefer to review it as I practice. I scan through my notes from college and revise the various algorithms as I work on the algorithm problems from LeetCode and Cracking the Coding Interview.
This interviews repository by Kevin Naughton Jr. served as a quick refresher for me.
The Medium publication basecs by Vaidehi Joshi is also a great and light-hearted resource to recap on the various data structures and algorithms.
Mastery through practice
Next, gain familiarity and mastery of the algorithms and data structures in your chosen programming language.
Practice and solve algorithm questions in your chosen language. While Cracking the Coding Interview is a good resource, I prefer solving problems by typing code, letting it run, and getting instant feedback. There are various Online Judges, such as LeetCode, HackerRank, and CodeForces for you to practice questions online and to get used to the language. From my experience, LeetCode questions are most similar to the questions asked in interviews. HackerRank and CodeForces questions are more similar to questions in competitive programming. If you practice enough LeetCode questions, there is a good chance that you will either see or complete one of your actual interview questions (or some variant of it).
Learn and understand the time and space complexities of the common operations in your chosen language. For Python, this page will come in handy. Also, learn about the underlying sorting algorithm being used in the language’s
sort() function and its time and space complexities (in Python it’s Timsort, which is a hybrid). After completing a question on LeetCode, I usually add the time and space complexities of the written code as comments above the function body. I use the comments to remind myself to communicate the analysis of the algorithm after I have completed the implementation.
Read up on the recommended coding style for your language and stick to it. If you choose Python, refer to the PEP 8 Style Guide. If you choose Java, refer to Google’s Java Style Guide.
Learn about and be familiar with the common pitfalls and caveats of the language. If you point them out during the interview and avoid falling into them, you will earn bonus points and impress the interviewer, regardless of whether the interviewer is familiar with the language or not.
Gain a broad exposure to questions from various topics. In the second half of the article, I mention algorithm topics and the useful questions for each topic to practice. Do around 100 to 200 LeetCode questions, and you should be good.
Practice, practice, and more practice!
Phases of a coding interview
Congratulations, you are ready to put your skills to practice! In a coding interview, you will be given a technical question by the interviewer. You will write the code in a real-time, collaborative editor (phone screen) or on a whiteboard (on-site), and have 30 to 45 minutes to solve the problem. This is where the real fun begins!
Your interviewer will be looking to see that you meet the requirements of the role. It is up to you to show them that you have the skills. Initially, it may feel weird to talk while you code, as most programmers do not make a habit of explaining out loud their thoughts while they are typing code.
However, it is hard for the interviewer to know what you are thinking by just looking at your code. If you communicate your approach to the interviewer even before you start to code, you can validate your approach with them. This way, the two of you can agree on an acceptable approach.
Preparing for a remote interview
For phone screens and remote interviews, have a paper and pen or pencil to jot down any notes or diagrams. If you are given a question about trees and graphs, it usually helps if you draw examples of the data structure.
Use earphones. Make sure you are in a quiet environment. You do not want to be holding a phone in one hand and typing with the other. Try to avoid using speakers. If the feedback is bad, communication is made harder. Having to repeat yourself will just result in the loss of valuable time.
What to do when you get the question
Many candidates start coding as soon as they hear the question. That is usually a big mistake. First, take a moment and repeat the question back to the interviewer to make sure that you understand the question. If you misunderstand the question, then the interviewer can clarify.
Always seek clarification about the question upon hearing it, even if you think it is clear. You might discover that you have missed something. It also lets the interviewer know that you are attentive to details.
Consider asking the following questions.
- How big is the size of the input?
- How big is the range of values?
- What kind of values are there? Are there negative numbers? Floating points? Will there be empty inputs?
- Are there duplicates within the input?
- What are some extreme cases of the input?
- How is the input stored? If you are given a dictionary of words, is it a list of strings or a trie?
After you have sufficiently clarified the scope and intention of the problem, explain your high-level approach to the interviewer, even if it is a naive solution. If you are stuck, consider various approaches and explain out loud why it may or may not work. Sometimes your interviewer might drop hints and lead you toward the right path.
Start with a brute-force approach. Communicate it to the interviewer. Explain the time and space complexities and clarify why it is bad. It is unlikely that the brute-force approach will be the one that you will be coding. At this point, the interviewer will usually pop the dreaded, “Can we do better?” question. This means they arelooking for a more optimal approach.
This is usually the hardest part of the interview. In general, look for repeated work and try to optimize them by potentially caching the calculated result somewhere. Reference it later, rather than computing it all over again. I provide some tips on tackling topic-specific questions in detail below.
Only start coding after you and your interviewer have agreed on an approach and you have been given the green light.
Starting to code
Use a good style to write your code. Reading code written by others is usually not an enjoyable task. Reading horribly formatted code written by others is even worse. Your goal is to make your interviewer understand your code so that they can quickly evaluate if your code does what it is suppose to and if it solves a given problem. Use clear variable names and avoid names that are single letters, unless they are for iteration. However, if you are coding on a whiteboard, avoid using verbose variable names. This reduces the amount of writing you will have to do.
Always explain to the interviewer what you are writing or typing. This is not about reading, verbatim, to the interviewer the code you are producing. Talk about the section of the code you are currently implementing at a higher level. Explain why it is written as such, and what it is trying to achieve.
When you copy and paste in code, consider whether it is necessary. Sometimes it is, sometimes it is not. If you find yourself copying and pasting a large chunk of code spanning multiple lines, it is probably an indicator that you can restructure the code by extracting those lines into a function. If it is just a single line you copied, usually it is fine. However, remember to change the respective variables in your copied line of code where relevant. Copying and pasting errors are a common source of bugs, even in day-to-day coding!
After you have finished coding, do not immediately announce to the interviewer that you are done. In most cases, your code is usually not perfect. It may contain bugs or syntax errors. What you need to do is review your code.
First, look through your code from start to finish. Look at it as if it were written by someone else, and you are seeing it for the first time and trying to spot bugs in it. That’s exactly what your interviewer will be doing. Review and fix any issues you may find.
Next, come up with small test cases and step through the code (not your algorithm) with those sample input. Interviewers like it when you read their minds. What they usually do after you have finished coding is get you to write tests. It is a huge plus if you write tests for your code even before they prompt you to do so. You should be emulating a debugger when stepping through your code. Jot down or tell them the values of certain variables as you walk the interviewer through the lines of code.
If there are large duplicated chunks of code in your solution, restructure the code to show the interviewer that you value quality coding. Also, look out for places where you can do short-circuit evaluation.
Lastly, give the time and space complexities of your code, and explain why it is such. You can annotate chunks of your code with their various time and space complexities to demonstrate your understanding of the code. You can even provide the APIs of your chosen programming language. Explain any trade-offs in your current approach versus alternative approaches, possibly in terms of time and space.
If your interviewer is happy with the solution, the interview usually ends here. It is also common that the interviewer asks you extension questions, such as how you would handle the problem if the whole input is too large to fit into memory, or if the input arrives as a stream. This is a common follow-up question at Google, where they care a lot about scale. The answer is usually a divide-and-conquer approach — perform distributed processing of the data and only read certain chunks of the input from disk into memory, write the output back to disk and combine them later.
Practice with mock interviews
The steps mentioned above can be rehearsed over and over again until you have fully internalized them and they become second nature to you. A good way to practice is by partnering with a friend and taking turns to interview each other.
A great resource for preparing for coding interviews is interviewing.io. This platform provides free and anonymous practice interviews with Google and Facebook engineers, which can lead to real jobs and internships. By virtue of being anonymous during the interview, the inclusive interview process is unbiased and low risk. At the end of the interview, both the interviewer and interviewee can provide feedback to each other for the purpose of helping one another improve.
Doing well in mock interviews will unlock the jobs page for candidates, and allow them to book interviews (also anonymously) with top companies like Uber, Lyft, Quora, Asana, and more. For those who are new to coding interviews, a demo interview can be viewed on this site. Note that this site requires users to sign in.
I have used interviewing.io, both as an interviewer and an interviewee. The experience was great. Aline Lerner, the CEO and co-founder of interviewing.io, and her team are passionate about revolutionizing the process for coding interviews and helping candidates improve their interview skills. She has also published a number of coding interview-related articles on the interviewing.io blog. I recommend signing up as early as possible with interviewing.io, even though its in beta, to increase the likelihood of receiving an invite.
Another platform that allows you to practice coding interviews is Pramp. Where interviewing.io matches potential job seekers with seasoned coding interviewers, Pramp takes a different approach. Pramp pairs you up with another peer who is also a job seeker. The two of you take turns assuming the roles of interviewer and interviewee. Pramp also prepares questions, and provides solutions and prompts to guide the interviewee.
Personally, I am not that fond of Pramp’s approach. Because when I do interviews, I ask questions that are familiar to me. Also, many users do not have the experience of being an interviewer, and that can result in a horrible interview experience. In one instance, my matched peer took on the role of the interviewer but he did not have the correct understanding of the question and attempted to lead me down the wrong path to solve the question. However, this is more of a problem of the candidate than the platform though.
Go forth and conquer
After doing a fair amount of questions on LeetCode and having enough practice doing mock interviews, go forth and put your new-found interviewing skills to the test. Apply to your favorite companies or, better still, get referrals from your friends working for those companies. Referrals tend to get noticed earlier and have a faster response rate than applying without a referral. Good luck!
Practical tips for coding questions
This section dives deep into practical tips for specific topics of algorithms and data structures, which appear frequently in coding questions. Many algorithm questions involve techniques that can be applied to questions of a similar nature.
The more techniques you have in your arsenal, the greater your chances of passing the interview. For each topic, there is also a list of recommended questions, which is valuable for mastering the core concepts. Some of the questions are only available with a paid subscription to LeetCode, which in my opinion is absolutely worth the money if it lands you a job.
Always validate input first. Check for inputs that are invalid, empty, negative, or different. Never assume you are given the valid parameters. Alternatively, clarify with the interviewer whether you can assume valid input (usually yes), which can save you time from writing code that does input validation.
Are there any time and space complexities requirements or constraints?
Check for off-by-one errors.
In languages where there are no automatic type coercion, check that concatenation of values are of the same type:
After you finish your code, use a few example inputs to test your solution.
Is the algorithm supposed to run multiple times, perhaps on a web server? If yes, the input can likely be pre-processed to improve the efficiency in each API call.
Use a mix of functional and imperative programming paradigms:
- Write pure functions as often as possible.
- Use pure functions because they are easier to reason with and can help reduce bugs in your implementation.
- Avoid mutating the parameters passed into your function, especially if they are passed by reference, unless you are sure of what you are doing.
- Achieve a balance between accuracy and efficiency. Use the right amount of functional and imperative code where appropriate. Functional programming is usually expensive in terms of space complexity because of non-mutation and the repeated allocation of new objects. On the other hand, imperative code is faster because you operate on existing objects.
- Avoid relying on mutating global variables. Global variables introduce state.
- Make sure that you do not accidentally mutate global variables, especially if you have to rely on them.
Generally, to improve the speed of a program, we can choose to either use an appropriate data structure or algorithm, or to use more memory. It’s a classic space and time trade off.
Data structures are your weapons. Choosing the right weapon for the right battle is the key to victory. Know the strengths of each data structure and the time complexity for its various operations.
Data structures can be augmented to achieve efficient time complexity across different operations. For example, a HashMap can be used together with a doubly-linked list to achieve O(1) time complexity for both the
put operation in an LRU cache.
HashMaps are probably the most commonly used data structure for algorithm questions. If you are stuck on a question, your last resort can be to enumerate through the possible data structures (thankfully there aren’t that many) and consider whether each of them can be applied to the problem. This has worked for me at times.
If you are cutting corners in your code, state that out loud to your interviewer, and explain to them what you would do outside of an interview setting (no time constraints). For example, explain that you would write a regex to parse a string rather than using
split , which does not cover all cases.
Arrays and strings are considered sequences (a string is a sequence of characters). There are tips for dealing with both arrays and strings, which will be covered here.
Are there duplicate values in the sequence? Would they affect the answer?
Check for sequence out of bounds.
Be mindful about slicing or concatenating sequences in your code. Typically, slicing and concatenating sequences require O(n) time. Use start and end indices to demarcate a subarray or substring where possible.
Sometimes you traverse the sequence from the right side rather than from the left.
Master the sliding window technique that applies to many substring or subarray problems.
When you are given two sequences to process, it is common to have one index per sequence to traverse. For example, we use the same approach to merge two sorted arrays.
- Empty sequence
- Sequence with 1 or 2 elements
- Sequence with repeated elements
Is the array sorted or partially sorted? If it is either, some form of binary search should be possible. This usually means that the interviewer is looking for a solution that is faster than O(n).
Can you sort the array? Sometimes sorting the array first may significantly simplify the problem. Make sure that the order of array elements do not need to be preserved before attempting to sort it.
For questions where summation or multiplication of a subarray is involved, pre-computation using hashing or a prefix, suffix sum, or product might be useful.
If you are given a sequence and the interviewer asks for O(1) space, it might be possible to use the array itself as a hash table. For example, if the array has values only from 1 to N, where N is the length of the array, negate the value at that index (minus one) to indicate the presence of that number.
- Two Sum
- Best Time to Buy and Sell Stock
- Contains Duplicate
- Product of Array Except Self
- Maximum Subarray
- Maximum Product Subarray
- Find Minimum in Rotated Sorted Array
- Search in Rotated Sorted Array
- Container With Most Water
- Bits, Bytes, Building With Binary
Questions involving binary representations and bitwise operations are asked sometimes. You must know how to convert a number from decimal form into binary form, and vice versa, in your chosen programming language.
Some helpful utility snippets:
- Test kth bit is set:
num & (1 << k) != 0
- Set kth bit:
num |= (1 << k)
- Turn off kth bit:
num &= ~(1 << k)
- Toggle the kth bit:
num ^= (1 << k)
- To check if a number is a power of 2:
num & num - 1 == 0.
- Check for overflow/underflow
- Negative numbers
- Sum of Two Integers
- Number of 1 Bits
- Counting Bits
- Missing Number
- Reverse Bits
- Demystifying Dynamic Programming
Dynamic Programming (DP) is usually used to solve optimization problems. Alaina Kafkes has written an awesome post on tackling DP problems. You should read it.
The only way to get better at DP is with practice. It takes lots of practice to recognize that a problem can be solved by DP.
To optimize space, sometimes you do not have to store the entire DP table in memory. The last two values or the last two rows of the matrix will suffice.
- 0/1 Knapsack
- Climbing Stairs
- Coin Change
- Longest Increasing Subsequence
- Longest Common Subsequence
- Word Break Problem
- Combination Sum
- House Robber and House Robber II
- Decode Ways
- Unique Paths
- Jump Game
When comparing Euclidean distance between two pairs of points, using dx² + dy² is sufficient. It is unnecessary to square root the value.
To find out if two circles overlap, check that the distance between the two centers of the circles is less than the sum of their radii.
- From Theory To Practice: Representing Graphs
- Deep Dive Through A Graph: DFS Traversal
- Going Broad In A Graph: BFS Traversal
Be familiar with the various graph representations and graph search algorithms, and with their time and space complexities.
You can be given a list of edges and tasked to build your own graph from the edges to perform a traversal on. The common graph representations are
- Adjacency matrix
- Adjacency list
- HashMap of HashMaps
Some inputs look like they are trees, but they are actually graphs. Clarify this with your interviewer. In that case, you will have to handle cycles and keep a set of visited nodes when traversing.
Graph search algorithms
- Common: Breadth first search (BFS), Depth first search (DFS)
- Uncommon: Topological sort, Dijkstra’s algorithm
- Rare: Bellman-Ford algorithm, Floyd-Warshall algorithm, Prim’s algorithm, and Kruskal’s algorithm
In coding interviews, graphs are commonly represented as 2-D matrices, where cells are the nodes and each cell can traverse to its adjacent cells (up, down, left, and right). Hence it is important to be familiar with traversing a 2-D matrix. When recursively traversing the matrix, always ensure that your next position is within the boundary of the matrix. More tips for doing DFS on a matrix can be found here. A simple template for doing DFS on a matrix appears something like this:
def traverse(matrix): rows, cols = len(matrix), len(matrix) visited = set() directions = ((0, 1), (0, -1), (1, 0), (-1, 0)) def dfs(i, j): if (i, j) in visited: return visited.add((i, j)) # Traverse neighbors for direction in directions: next_i, next_j = i + direction, j + direction if 0 <= next_i < rows and 0 <= next_j < cols: # Check boundary # Add any other checking here ^ dfs(next_i, next_j) for i in range(rows): for j in range(cols): dfs(i, j)
- Empty graph
- Graph with one or two nodes
- Disjoint graphs
- Graph with cycles
- Clone Graph
- Course Schedule
- Alien Dictionary
- Pacific Atlantic Water Flow
- Number of Islands
- Graph Valid Tree
- Number of Connected Components in an Undirected Graph
- Longest Consecutive Sequence
Interval questions are questions that give an array of two-element arrays (an interval). The two values represent a start and an end value. Interval questions are considered to be part of the array family, but they involve some common techniques. Hence, they have their own special section.
An example of an interval array:
[[1, 2], [4, 7]].
Interval questions can be tricky for those who do not have experience with them. This is because of the sheer number of cases to consider when interval arrays overlap.
Clarify with the interviewer whether
[1, 2] and
[2, 3] are considered overlapping intervals, because it affects how you will write your equality checks.
A common routine for interval questions is to sort the array of intervals by the start value of each interval.
Be familiar with writing code to check if two intervals overlap and to merge two overlapping intervals:
def is_overlap(a, b): return a < b and b < a def merge_overlapping_intervals(a, b): return [min(a, b), max(a, b)]
- Single interval
- Non-overlapping intervals
- An interval totally consumed within another interval
- Duplicate intervals
- Insert Interval
- Merge Intervals
- Meeting Rooms and Meeting Rooms II
- Non-overlapping Intervals
Like arrays, linked lists are used to represent sequential data. The benefit of linked lists is that insertion and deletion of code from anywhere in the list is O(1), whereas in arrays, the elements have to be shifted.
Adding a dummy node at the head and /or tail might help to handle many edge cases where operations have to be performed at the head or the tail. The presence of dummy nodes ensures that operations will never have be executed on the head or the tail. Dummy nodes remove the headache of writing conditional checks to deal with null pointers. Be sure to remove them at the end of the operation.
Sometimes linked lists problem can be solved without additional storage. Try to borrow ideas from the for reverse a linked list problem.
For deletion in linked lists, you can either modify the node values or change the node pointers. You might need to keep a reference to the previous element.
For partitioning linked lists, create two separate linked lists and join them back together.
Linked lists problems share similarities with array problems. Think about how you would solve an array problem and apply it to a linked list.
Two pointer approaches are also common for linked lists:
- Getting the kthfrom the last node: Have two pointers, where one is k nodes ahead of the other. When the node ahead reaches the end, the other node is k nodes behind.
- Detecting cycles: Have two pointers, where one pointer increments twice as much as the other. If the two pointers meet, it means that there is a cycle.
- Getting the middle node: Have two pointers. One pointer increments twice as much as the other. When the faster node reaches the end of the list, the slower node will be at the middle.
Be familiar with the following routines because many linked list questions make use of one or more of these routines in their solution.
- Count the number of nodes in the linked list
- Reverse a linked list in place
- Find the middle node of the linked list using fast or slow pointers
- Merge two lists together
- Single node
- Two nodes
- Linked list has cycle. Clarify with the interviewer whether there can be a cycle in the list. Usually the answer is no.
- Reverse a Linked List
- Detect Cycle in a Linked List
- Merge Two Sorted Lists
- Merge K Sorted Lists
- Remove Nth Node From End Of List
- Reorder List
If the code involves division or modulo, remember to check for division or modulo by 0 case.
When a question involves “a multiple of a number”, modulo might be useful.
Check for and handle overflow and underflow if you are using a typed language like Java and C++. At the very least, mention that overflow or underflow is possible and ask whether you need to handle it.
Consider negative numbers and floating point numbers. This may sound obvious, but when you are under pressure in an interview, many obvious points go unnoticed.
If the question asks to implement an operator such as power, squareroot, or division, and it is to be faster than O(n), binary search is usually the approach.
Some common formulas
- Sum of 1 to N = (n+1) * n/2
- Sum of GP = 2⁰ + 2¹ + 2² + 2³ + … 2^n = 2^(n+1)-1
- Permutations of N = N! / (N-K)!
- Combinations of N = N! / (K! * (N-K)!)
- Division by 0
- Integer overflow and underflow
- Pow(x, n)
- Integer to English Words
A matrix is a 2-dimensional array. Questions involving matrices are usually related to dynamic programming or graph traversal.
For questions involving traversal or dynamic programming, make a copy of the matrix with the same dimensions that are initialized to empty values. Use these values to store the visited state or dynamic programming table. Be familiar with this routine:
rows, cols = len(matrix), len(matrix) copy = [[0 for _ in range(cols)] for _ in range(rows)
- Many grid-based games can be modeled as a matrix. For example, Tic-Tac-Toe, Sudoku, Crossword, Connect 4, and Battleship. It is not uncommon to be asked to verify the winning condition of the game. For games like Tic-Tac-Toe, Connect 4, and Crosswords, verification has to be done vertically and horizontally. One trick is to write code to verify the matrix for the horizontal cells. Then transpose the matrix, reusing the logic used for horizontal verification to verify originally vertical cells (which are now horizontal).
- Transposing a matrix in Python is simply:
transposed_matrix = zip(*matrix)
- Empty matrix. Check that none of the arrays are 0 length.
- 1 x 1 matrix.
- Matrix with only one row or column.
- Set Matrix Zeroes
- Spiral Matrix
- Rotate Image
- Word Search
Recursion is useful for permutation, because it generates all combinations and tree-based questions. You should know how to generate all permutations of a sequence as well as how to handle duplicates.
Remember to always define a base case so that your recursion will end.
Recursion implicitly uses a stack. Hence all recursive approaches can be rewritten iteratively using a stack. Beware of cases where the recursion level goes too deep and causes a stack overflow (the default limit in Python is 1000). You may get bonus points for pointing this out to the interviewer. Recursion will never be O(1) space complexity because a stack is involved, unless there is tail call optimization (TCO). Find out if your chosen language supports TCO.
- Subsets and Subsets II
- Strobogrammatic Number II
Please read the above tips on sequence. They apply to strings too.
Ask about input character set and case sensitivity. Usually the characters are limited to lowercase Latin characters, for example a to z.
When you need to compare strings where the order isn’t important (like anagram), you may consider using a HashMap as a counter. If your language has a built-in
Counter class like Python, ask to use that instead.
If you need to keep a counter of characters, a common mistake is to say that the space complexity required for the counter is O(n). The space required for a counter is O(1) not O(n). This is because the upper bound is the range of characters, which is usually a fixed constant of 26. The input set is just lowercase Latin characters.
Common data structures for looking up strings efficiently are
- Trie/Prefix Tree
- Suffix Tree
Common string algorithms are
- Rabin Karp, which conducts efficient searches of substrings, using a rolling hash
- KMP, which conducts efficient searches of substrings
Use a 26-bit bitmask to indicate which lower case Latin characters are inside the string.
mask = 0 for c in set(word): mask |= (1 << (ord(c) - ord('a')))
To determine if two strings have common characters, perform
& on the two bitmasks. If the result is non-zero,
mask_a & mask_b > 0 , then the two strings have common characters.
An anagram is word switch or word play. It is the result of re-arranging the letters of a word or phrase to produce a new word or phrase, while using all the original letters only once. In interviews, usually we are only bothered with words without spaces in them.
To determine if two strings are anagrams, there are a few plausible approaches:
- Sorting both strings should produce the same resulting string. This takes O(nlgn) time and O(lgn) space.
- If we map each character to a prime number and we multiply each mapped number together, anagrams should have the same multiple (prime factor decomposition). This takes O(n) time and O(1) space.
- Frequency counting of characters will help to determine if two strings are anagrams. This also takes O(n) time and O(1) space.
A palindrome is a word, phrase, number, or other sequence of characters that reads the same backward and forward, such as madam or racecar.
Here are ways to determine if a string is a palindrome:
- Reverse the string and it should be equal to itself.
- Have two pointers at the start and end of the string. Move the pointers inward till they meet. At any point in time, the characters at both pointers should match.
The order of characters within the string matters, so HashMaps are usually not helpful.
When a question is about counting the number of palindromes, a common trick is to have two pointers that move outward, away from the middle. Note that palindromes can be even or odd length. For each middle pivot position, you need to check it twice: Once that includes the character and once without the character.
- For substrings, you can terminate early once there is no match.
- For subsequences, use dynamic programming as there are overlapping subproblems. Check out this question.
- Empty string
- Single-character string
- Strings with only one distinct character
- Longest Substring Without Repeating Characters
- Longest Repeating Character Replacement
- Minimum Window Substring
- Encode and Decode Strings
- Valid Anagram
- Group Anagrams
- Valid Parentheses
- Valid Palindrome
- Longest Palindromic Substring
- Palindromic Substrings
- Leaf It Up To Binary Trees
A tree is an undirected and connected acyclic graph.
Recursion is a common approach for trees. When you notice that the subtree problem can be used to solve the entire problem, try using recursion.
When using recursion, always remember to check for the base case, usually where the node is
When you are asked to traverse a tree by level, use depth first search.
Sometimes it is possible that your recursive function needs to return two values.
If the question involves summation of nodes along the way, be sure to check whether nodes can be negative.
You should be very familiar with writing pre-order, in-order, and post-order traversal recursively. As an extension, challenge yourself by writing them iteratively. Sometimes interviewers ask candidates for the iterative approach, especially if the candidate finishes writing the recursive approach too quickly.
In-order traversal of a binary tree is insufficient to uniquely serialize a tree. Pre-order or post-order traversal is also required.
Binary search tree (BST)
In-order traversal of a BST will give you all elements in order.
Be very familiar with the properties of a BST. Validate that a binary tree is a BST. This comes up more often than expected.
When a question involves a BST, the interviewer is usually looking for a solution which runs faster than O(n).
- Empty tree
- Single node
- Two nodes
- Very skewed tree (like a linked list)
- Maximum Depth of Binary Tree
- Same Tree
- Invert or Flip Binary Tree
- Binary Tree Maximum Path Sum
- Binary Tree Level Order Traversal
- Serialize and Deserialize Binary Tree
- Subtree of Another Tree
- Construct Binary Tree from Preorder and Inorder Traversal
- Validate Binary Search Tree
- Kth Smallest Element in a BST
- Lowest Common Ancestor of BST
- Trying to Understand Tries
- Implement Trie (Prefix Tree)
Tries are special trees (prefix trees) that make searching and storing strings more efficient. Tries have many practical applications, such as conducting searches and providing autocomplete. It is helpful to know these common applications so that you can easily identify when a problem can be efficiently solved using a trie.
Sometimes preprocessing a dictionary of words (given in a list) into a trie, will improve the efficiency of searching for a word of length k, among n words. Searching becomes O(k) instead of O(n).
Be familiar with implementing, from scratch, a
Trie class and its
remove , and
- Implement Trie (Prefix Tree)
- Add and Search Word
- Word Search II
- Learning to Love Heaps
If you see a top or lowest k mentioned in the question, it is usually a sign that a heap can be used to solve the problem, such as in Top K Frequent Elements.
If you require the top k elements, use a Min Heap of size k. Iterate through each element, pushing it into the heap. Whenever the heap size exceeds k, remove the minimum element. That will guarantee that you have the k largest elements.
- Merge K Sorted Lists
- Top K Frequent Elements
- Find Median from Data Stream
Coding interviews are tough. But fortunately, you can get better at them by studying and practicing for them, and doing mock interviews.
To recap, to do well in coding interviews:
- Decide on a programming language
- Study CS fundamentals
- Practice solving algorithm questions
- Internalize the Do’s and Don’ts of interviews
- Practice by doing mock technical interviews
- Interview successfully to get the job
By following these steps, you will improve your coding interview skills, and be one step closer (or probably more) to landing your dream job.
All the best!
The content for this post can be found in my Tech Interview Handbook repo on GitHub. Future updates will be posted there. Pull requests for suggestions and corrections are welcome!
tech-interview-handbook - ? Algorithms, front end and behavioral content for rocking your coding interview.github.com
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