Category >> Algorithms >> Interview  

Top 10 Algorithms for Coding Interview

PDF Version (updated on 1/16/2014)

The following are top 10 algorithms related topics for coding interviews. As understanding those concepts requires much more effort, this list below only serves as an introduction. They are viewed from a Java perspective and the following topics will be covered: String/Array/Matrix, Linked List, Tree, Heap, Graph, Sorting, Recursion vs. Iteration, Dynamic Programming, Bit Manipulation, Probability, Combinations and Permutations, and other problems that need us to find patterns.

1. String/Array/Matrix

First of all, String in Java is a class that contains a char array and other fields and methods. Without code auto-completion of any IDE, the following methods should be remembered.

toCharArray() //get char array of a String
Arrays.sort()  //sort an array
Arrays.toString(char[] a) //convert to string
charAt(int x) //get a char at the specific index
length() //string length
length //array size 
substring(int beginIndex) 
substring(int beginIndex, int endIndex)
Integer.valueOf()//string to integer
String.valueOf()/integer to string

Strings/arrays are easy to understand, but questions related to them often require advanced algorithm to solve, such as dynamic programming, recursion, etc.

Classic problems:
1) Evaluate Reverse Polish Notation
2) Longest Palindromic Substring
3) Word Break
4) Word Ladder
5) Median of Two Sorted Arrays
6) Regular Expression Matching
7) Merge Intervals
8) Insert Interval
9) Two Sum
9) 3Sum
9) 4Sum
10) 3Sum Closest
11) String to Integer
12) Merge Sorted Array
13) Valid Parentheses
14) Implement strStr()
15) Set Matrix Zeroes
16) Search Insert Position
17) Longest Consecutive Sequence
18) Valid Palindrome
19) Spiral Matrix
20) Search a 2D Matrix
21) Rotate Image
22) Triangle
23) Distinct Subsequences Total
24) Maximum Subarray
25) Remove Duplicates from Sorted Array
26) Remove Duplicates from Sorted Array II
27) Longest Substring Without Repeating Characters
28) Longest Substring that contains 2 unique characters
29) Palindrome Partitioning
30) Reverse Words in a String

2. Linked List

The implementation of a linked list is pretty simple in Java. Each node has a value and a link to next node.

class Node {
	int val;
	Node next;
 
	Node(int x) {
		val = x;
		next = null;
	}
}

Two popular applications of linked list are stack and queue.

Stack

class Stack{
	Node top; 
 
	public Node peek(){
		if(top != null){
			return top;
		}
 
		return null;
	}
 
	public Node pop(){
		if(top == null){
			return null;
		}else{
			Node temp = new Node(top.val);
			top = top.next;
			return temp;	
		}
	}
 
	public void push(Node n){
		if(n != null){
			n.next = top;
			top = n;
		}
	}
}

Queue

class Queue{
	Node first, last;
 
	public void enqueue(Node n){
		if(first == null){
			first = n;
			last = first;
		}else{
			last.next = n;
			last = n;
		}
	}
 
	public Node dequeue(){
		if(first == null){
			return null;
		}else{
			Node temp = new Node(first.val);
			first = first.next;
			return temp;
		}	
	}
}

It is worth to mention that Java standard library already contains a class called "Stack", and LinkedList can be used as a Queue (add() and remove()). (LinkedList implements the Queue interface) If you need a stack or queue to solve problems during your interview, you can directly use them.

Classic Problems:
1) Add Two Numbers
2) Reorder List
3) Linked List Cycle
4) Copy List with Random Pointer
5) Merge Two Sorted Lists
6) Merge k Sorted Lists *
7) Remove Duplicates from Sorted List
8) Partition List
9) LRU Cache


3. Tree & Heap

Tree here is normally binary tree. Each node contains a left node and right node like the following:

class TreeNode{
	int value;
	TreeNode left;
	TreeNode right;
}

Here are some concepts related with trees:

  1. Binary Search Tree: for all nodes, left children <= current node <= right children
  2. Balanced vs. Unbalanced: In a balanced tree, the depth of the left and right subtrees of every node differ by 1 or less.
  3. Full Binary Tree: every node other than the leaves has two children.
  4. Perfect Binary Tree: a full binary tree in which all leaves are at the same depth or same level, and in which every parent has two children.
  5. Complete Binary Tree: a binary tree in which every level, except possibly the last, is completely filled, and all nodes are as far left as possible

Heap is a specialized tree-based data structure that satisfies the heap property. The time complexity of its operations are important (e.g., find-min, delete-min, insert, etc). In Java, PriorityQueue is important to know.

Classic problems:
1) Binary Tree Preorder Traversal
2) Binary Tree Inorder Traversal
3) Binary Tree Postorder Traversal
4) Word Ladder
5) Validate Binary Search Tree
6) Flatten Binary Tree to Linked List
7) Path Sum
8) Construct Binary Tree from Inorder and Postorder Traversal
9) Convert Sorted Array to Binary Search Tree
10) Convert Sorted List to Binary Search Tree
11) Minimum Depth of Binary Tree
12) Binary Tree Maximum Path Sum *
13) Balanced Binary Tree

4. Graph

Graph related questions mainly focus on depth first search and breath first search. Depth first search is straightforward, you can just loop through neighbors starting from the root node.

Below is a simple implementation of a graph and breath first search. The key is using a queue to store nodes.

breath-first-search

1) Define a GraphNode

class GraphNode{ 
	int val;
	GraphNode next;
	GraphNode[] neighbors;
	boolean visited;
 
	GraphNode(int x) {
		val = x;
	}
 
	GraphNode(int x, GraphNode[] n){
		val = x;
		neighbors = n;
	}
 
	public String toString(){
		return "value: "+ this.val; 
	}
}

2) Define a Queue

class Queue{
	GraphNode first, last;
 
	public void enqueue(GraphNode n){
		if(first == null){
			first = n;
			last = first;
		}else{
			last.next = n;
			last = n;
		}
	}
 
	public GraphNode dequeue(){
		if(first == null){
			return null;
		}else{
			GraphNode temp = new GraphNode(first.val, first.neighbors);
			first = first.next;
			return temp;
		}	
	}
}

3) Breath First Search uses a Queue

public class GraphTest {
 
	public static void main(String[] args) {
		GraphNode n1 = new GraphNode(1); 
		GraphNode n2 = new GraphNode(2); 
		GraphNode n3 = new GraphNode(3); 
		GraphNode n4 = new GraphNode(4); 
		GraphNode n5 = new GraphNode(5); 
 
		n1.neighbors = new GraphNode[]{n2,n3,n5};
		n2.neighbors = new GraphNode[]{n1,n4};
		n3.neighbors = new GraphNode[]{n1,n4,n5};
		n4.neighbors = new GraphNode[]{n2,n3,n5};
		n5.neighbors = new GraphNode[]{n1,n3,n4};
 
		breathFirstSearch(n1, 5);
	}
 
	public static void breathFirstSearch(GraphNode root, int x){
		if(root.val == x)
			System.out.println("find in root");
 
		Queue queue = new Queue();
		root.visited = true;
		queue.enqueue(root);
 
		while(queue.first != null){
			GraphNode c = (GraphNode) queue.dequeue();
			for(GraphNode n: c.neighbors){
 
				if(!n.visited){
					System.out.print(n + " ");
					n.visited = true;
					if(n.val == x)
						System.out.println("Find "+n);
					queue.enqueue(n);
				}
			}
		}
	}
}

Output:

value: 2 value: 3 value: 5 Find value: 5
value: 4

Classic Problems:
1) Clone Graph

5. Sorting

Time complexity of different sorting algorithms. You can go to wiki to see basic idea of them.

Algorithm Average Time Worst Time Space
Bubble sort n^2 n^2 1
Selection sort n^2 n^2 1
Insertion sort n^2 n^2
Quick sort n log(n) n^2
Merge sort n log(n) n log(n) depends

* BinSort, Radix Sort and CountSort use different set of assumptions than the rest, and so they are not "general" sorting methods. (Thanks to Fidel for pointing this out)

Here are some implementations/demos, and in addition, you may want to check out how Java developers sort in practice.
1) Mergesort
2) Quicksort
3) InsertionSort.

6. Recursion vs. Iteration

Recursion should be a built-in thought for programmers. It can be demonstrated by a simple example.

Question:

there are n stairs, each time one can climb 1 or 2. How many different ways to climb the stairs?

Step 1: Finding the relationship before n and n-1.

To get n, there are only two ways, one 1-stair from n-1 or 2-stairs from n-2. If f(n) is the number of ways to climb to n, then f(n) = f(n-1) + f(n-2)

Step 2: Make sure the start condition is correct.

f(0) = 0;
f(1) = 1;

public static int f(int n){
	if(n <= 2) return n;
	int x = f(n-1) + f(n-2);
	return x;
}

The time complexity of the recursive method is exponential to n. There are a lot of redundant computations.

f(5)
f(4) + f(3)
f(3) + f(2) + f(2) + f(1)
f(2) + f(1) + f(2) + f(2) + f(1)

It should be straightforward to convert the recursion to iteration.

public static int f(int n) {
 
	if (n <= 2){
		return n;
	}
 
	int first = 1, second = 2;
	int third = 0;
 
	for (int i = 3; i <= n; i++) {
		third = first + second;
		first = second;
		second = third;
	}
 
	return third;
}

For this example, iteration takes less time. You may also want to check out Recursion vs Iteration.

7. Dynamic Programming

Dynamic programming is a technique for solving problems with the following properties:

  1. An instance is solved using the solutions for smaller instances.
  2. The solution for a smaller instance might be needed multiple times.
  3. The solutions to smaller instances are stored in a table, so that each smaller instance is solved only once.
  4. Additional space is used to save time.


The problem of climbing steps perfectly fit those 4 properties. Therefore, it can be solve by using dynamic programming.

public static int[] A = new int[100];
 
public static int f3(int n) {
	if (n <= 2)
		A[n]= n;
 
	if(A[n] > 0)
		return A[n];
	else
		A[n] = f3(n-1) + f3(n-2);//store results so only calculate once!
	return A[n];
}

Classic problems:
1) Edit Distance
2) Longest Palindromic Substring
3) Word Break
4) Maximum Subarray

8. Bit Manipulation

Bit operators:

OR (|) AND (&) XOR (^) Left Shift (<<) Right Shift (>>) Not (~)
1|0=1 1&0=0 1^0=1 0010<<2=1000 1100>>2=0011 ~1=0

Get bit i for a give number n. (i count from 0 and starts from right)

public static boolean getBit(int num, int i){
	int result = num & (1<<i);
 
	if(result == 0){
		return false;
	}else{
		return true;
	}
}

For example, get second bit of number 10.

i=1, n=10
1<<1= 10
1010&10=10
10 is not 0, so return true;

Classic Problems:
1) Find Single Number
2) Maximum Binary Gap

9. Probability

Solving probability related questions normally requires formatting the problem well. Here is just a simple example of such kind of problems.

There are 50 people in a room, what's the probability that two people have the same birthday? (Ignoring the fact of leap year, i.e., 365 day every year)

Very often calculating probability of something can be converted to calculate the opposite. In this example, we can calculate the probability that all people have unique birthdays. That is: 365/365 * 364/365 * 363/365 * ... * 365-n/365 * ... * 365-49/365. And the probability that at least two people have the same birthday would be 1 - this value.

public static double caculateProbability(int n){
	double x = 1; 
 
	for(int i=0; i<n; i++){
		x *=  (365.0-i)/365.0;
	}
 
	double pro = Math.round((1-x) * 100);
	return pro/100;
}

calculateProbability(50) = 0.97

10. Combinations and Permutations

The difference between combination and permutation is whether order matters.

Example 1:

Given 5 numbers - 1, 2, 3, 4 and 5, print out different sequence of the 5 numbers. 4 can not be the third one, 3 and 5 can not be adjacent. How many different combinations?

Example 2:

Given 5 banaba, 4 pear, and 3 apple, assuming one kind of fruit are the same, how many different combinations?

Class Problems:
1) Permutations
2) Permutations II
3) Permutation Sequence
4) Generate Parentheses

Some other problems need us to use observations to form rules to solve them:

1) Reverse Integer
2) Palindrome Number
3) Pow(x,n)
4) Subsets
5) Subsets II

Category >> Algorithms >> Interview  
  • Guest

    Well said.

  • ISuckatProgramming

    Having done more than 20 or more tech interviews during a job search recently, I’ve found the lists in this post to be very useful. Most companies like Google or Linkedin will first give you a phone screen and there you will encounter 2 or 3 questions of the variety found here. Once you survive that and get to the in person interview, then that’s where the REAL fun begins. You typically get much harder programming problems and have much less them to finish them. I guess most developers at Google or Facebook must be geniuses or something, I guess this is a good way to weed out all the people of only average intelligence. :(

  • Kenneth

    Yes Google and Facebook do ask these questions, but not for the reason you believed.

    I have friends in G and FB. They told me that they spent <1% of their time solving problems like "detecting cycle in linkedlist". It doesn't seem to be a wise thing to ask 90% of such questions interviews.

    The reason why they asked these questions was that they did know a better way to objectively evaluate candidate's real design and coding skills. So they fell back to the questions they were asked at school.

  • Guest

    In top software companies ( google, fb, amazon, ms, etcetera) you will face this kind if questions because what they want to see it’s not only if you can solve the problem but HOW did you solve it. That’s exactly what they want to evaluate, they want to see what questions you asked to understand the problem, how did you analyze it, how you decomposed the problem, how you transformed your analysis and ideas into code, how good is your code (readable, maintainable, flexible). So the questions are not all about algorithms but they are also about your skills

  • Walt Corey

    Knowing how they apply is a vastly different problem than how to implement them. As a previous poster wrote about never using a graph or never having to implement a RB tree that’s different than having an understanding of why they are important. It’s a 5 minute answer verses a 40 minute exercise.

  • Walt Corey

    that’s because the other 1,999 people didn’t care.

  • Walt Corey

    It absolutely can be but it can also blow a stack wide open. The goal is to have software that doesn’t program check at the customer’s site, not elegate to the eyes of the developer.

  • Walt Corey

    Not at all, those two scenarios are nothing alike. A student has absolutely no standing to question the professor. Professors generally have 90 semester hours in the subject the student maybe has 3 in. An interviewee with 20 years experience generally has 10 years or more experience than the person interviewing them.

  • Walt Corey

    Joe, you touched on the answer. These questions are asked by people who, otherwise don’t know how to interview a candidate. I’d go so far as to say it is a gotcha. That may be a tad unfair. I was also interviewed at a startup and one question was what is the second argument to a hashmap constructor. I answered I was pretty sure it was capacity but as I use a smart IDE I let the IDE prompt me for the parameters. I focus on solving the business problem not memorizing parameter sequences.

  • Walt Corey

    Apparently Facebook also tests developers ability to program while getting intoxicated, see “Social Network”. I agree 100% with Joe. I was once asked, either by Google or Amazon how’d I’d implement a stack in Java. I said I would instanciate an instance of the java Stack() object I didn’t get the job.

  • James
  • WJ

    You are right. Top Tech companies won’t ask these question from you (definitely, if YOU will apply there, a person will 25 years of experience). If they do ask these question, yeah!! You should probably walk out………Actually, these questions are asked by TOP Tech companies for Software Engineer roles (Fresh/mid/senior) under 10-15 year experience. Because they really want people who knows how to invent wheel. And most of the time developers will have to invent a wheel in such companies. A person with 25 years of experience shouldn’t apply for SDE roles. If you do….I would wonder….why you would. I think…… you better go for lead/architect positions. And then …yes!!! you won’t be asked such questions. Instead, companies will emphasis on design, your past experience plus your achievements, blogs, patents, your personal references, your links and your presence in IT industry. That’s what company like Google look for. I hope, you get it now!!

  • Aarohi Shirke

    For more IT interview questions you can check with skillgun @ http://skillgun.com truly helpful for your preparation

  • Drew

    I find it funny that there is so much bashing about how these problems don’t really tell the interviewer anything other than being able to jump through some hoops. I completely disagree with those sentiments. Having problems such as these while trivial for some, can quickly weed out those who don’t have fundamental understanding of basic data structure concepts or classic algorithms. Sure, there are libraries for such things to hide away the gory details, but if you blindly just use them without knowing when they apply, you get into bad habits. These classical problems also gives a common baseline in which to judge applicants. It’s not a perfect system, nothing is, but it’s unrealistic for employers to devise more relevant questions because in any new job, there is going to be a learning curve no matter how much someone prepares.

    Another thing to consider, these are computer science type of questions, applicable to a coder. Software Engineering is much more than just algorithms and encompasses the entire process of writing good software. I don’t believe this site advertises those type of questions because they can be much more subjective and open for great debate.

    One more thing. As someone who has programmed embedded systems, I’m not always afforded the luxury of using libraries for various business/legal reasons. Without the crutch of someone already doing the work for you, one must be knowledgeable enough to use classic algorithms and shape it to meet the necessary solution.

  • http://algorithmsandme.blogspot.in/ Jitendra Sangar

    A collection of problems asked in interviews
    http://algorithmsandme.blogspot.in/p/blog-page_27.html

  • Joe Pepersack

    No, they just hire me as a consultant at $200/hr.

  • Vinz

    Hi Joe,
    I am a Grad Student and preparing for the interviews..
    I completely agree with you, however in my past experience when i told the interviewer the similar answer just just posted ! he glared at me and then i got rejected :(

  • abossard

    I basically agree, it doesn’t make sense in most companies, to reinvent the square wheel all the time. I had an interview with a startup that asked my how to implement a Hash-table …. in the end they didn’t know anything about my problem solving skills and ended up explaining a Hash-table to me. Still they were interested in me taking the job.

    But for companies which are driven by algorithms, like Google or Facebook, it does make sense, to check whether the applicant know these things. Not to implement it by heart, but because the questions they asked are related to such algorithms. They don’t ask to implement a linked list, but they may asked how to detect a cycle in a linked list, or the start of the cycle. They want to see whether you can use the basic knowledge about algorithms to solve problems.

    To know the algorithms by heart is one part, but to apply that knowledge to solve trick-questions, that’s what they want to see.

    In the end, I know I’m not a good or bad programmer just by this knowledge, but I want that Job at Google :-)

  • Виктор Маслов

    Looks like you are making horrible bad code of totally boring and useless software for 25 years, because you didn’t even realize, that these questions aren’t about data structures implementation but about algorithms of work with them.

  • Paul

    Maybe that’s why you don’t work for a fortune 500 company.

  • John

    In an embedded field is ok to ask about these topics, as reinventing the wheel in embedded C is pretty usual, but for higher level applications these kind of questions don’t give any good qualifiers, apart from theoretical ones. E.g. would be a lot better if newbie C++ developers knew how to properly use containers and algorithms than knowing how to implement by hand a double linked list or a tree. A good example is this talk: http://channel9.msdn.com/Events/GoingNative/2013/Cpp-Seasoning

  • hardsoft

    When interviewing individuals for an embedded position, I might ask them to write a swap function because it is a simple and quick way to gauge their understanding of pointer operations and can lead into good conversation.

    An embedded programmer needs to have a rock solid foundation in C or will have a steep learning curve.

    So technical questions can be useful to judge a candidates knowledge. If you walked out, I would (probably rightly) assume you are a primadonna who would end up writing slow, buggy, and unmaintainable code because you would not have the fundamentals to perform your job.

  • minus Seven

    This is true. But most companies don’t want to spend so time on evaluating candidates perfectly. These are just ways to weed out as many candidates as possible so that they can reduce the number of choices of potential hires.

    Still most companies insist on them and as an interview candidate it is important to know them enough to be able to solve them. Interviews are hardly perfect these days.

  • serge

    Design patterns are also solved problems. Do you want to hire someone who doesn’t know about them?

  • Johan Stén

    “Q. Other insights from the studies you’ve already done?

    A. On the hiring side, we found that brainteasers are a complete waste of time. How many golf balls can you fit into an airplane? How many gas stations in Manhattan? A complete waste of time. They don’t predict anything. They serve primarily to make the interviewer feel smart.”

    http://techcrunch.com/2013/06/22/the-technical-interview-is-dead/

  • Johan Stén

    Decades of programming experience here as well, highly technical at that. Low-level, technical, algorithmical stuff. I’ve never had any use for 99% of all the stuff that comes up in so called “competitive programming”. At best, this is masturbation. It’s not programming, it’s not what programming is about, it’s not what programmers spend their time on. It’s jerking off.

    I took part in a programming competition where the qualifying round was something akin to this. The final round however was a “real life” programing task, where you had spend hours, to ship code that actually did something useful. None of the “competitive programmer” types ended up anywhere near the top.

    Do I enjoy it? Highly. Does it have anything to do with what I get paid for? No.

  • kazoompa

    I am 100% with Joe. I’ve also done two decades of programming and never found most of the above questions too relevant. These days most people Google for the API’s or algorithms, you can’t know them all by heart or better still, some languages incorporate them in their grammar. Problem solving and the choosing the proper strategy is a lot more important.

  • Gabriel Ramírez

    great post! really

  • Wei Qiu

    For me, knowing about how to reinvent stuff is the only way to really understand how stuff works.
    These are the basics. Knowledge of them doesn’t make people awful programmers. Lacking knowledge of engineering does.

  • Wei Qiu

    Recursion is not hard to read. Recursion frequently leads to elegant and compact solutions. Check Sedgewick’s implementation of Left Leaning RB tree as an example. For me recursion is the most natural way to tackle hard problems. Recursion is generally more powerful than iteration. Iteration is just an extra optimization step when you get the solution right.

  • Le Trung Kien

    I don’t know why some people keep complaining about how big companies conduct interviews, as if they know the optimal way. It is very similar to students who do not contend with the way professors give exams.

  • chen gao

    I totally agree with you, but the problem is that if you only offer some questions about your company’s products or software, it’s really hard for them who have never done an internship in this company or never used these software. Maybe they only use these algorithm problems only to test wether this guy is qualified after a short training in the company.

  • Joe Pepersack

    Yes, the posted questions are VERY typical of the questions that get asked by clueless interviewers at second-rate organizations.

    And then they wonder why they hire programmers who write slow, buggy, and unmaintainable code. They scratch their heads why their products are delivered late, are unreliable, and won’t scale. They wonder why the top talent turns down their offers.

    This article is a shining example of how NOT to interview programmers and what questions NOT to ask. In all honesty, I’d walk out of an interview that asked these kind of questions, because it’s obvious to me that they have no clue what they’re doing. It speaks volumes about their corporate culture, and none of it is positive.

  • ryanlr

    Thanks a lot for your comments. I agree. But those questions are indeed asked during interviews. Hope the interviewers have the same point of view as you and ask better questions.

  • Joe Pepersack

    I’ve interviewed with industry-leading companies.
    I’ve worked for industry-leading companies.
    I’ve interviewed candidates for industry-leading companies.

    The top companies want candidates who can SOLVE PROBLEMS EFFICIENTLY. They could care less if you know how to implement a breadth-first search, because that’s a solved problem. Even if you don’t have a suitable library for your platform, the expectation for a senior developer is that you can pick up a textbook and implement it.

    What they DO care about is if you know how to select the correct data structures and algorithms to solve a problem, and do so efficiently and professionally – which means means writing legible, maintainable code that follows best practices like code reuse.

    Re-implementing basic library functions would be a GUARANTEED way to fail an interview for a top company. If I give you an interview problem that requires you to count the number of distinct values in an input set, I’m testing you on your ability to recognize that you need to use a hash table, not on your ability to come up with an ad-hoc implementation of a hash table. Rolling your own hash table would be just as much of a fail as using the wrong data structure.

    Reinventing the wheel is bad engineering. If you hire engineers based on their ability to reinvent wheels, you are by definition hiring bad engineers.

  • ryanlr

    Large companies (e.g., Google, Facebook, or other similar levels) test developers’ knowledge of algorithm and data structure. That’s the essence of coding interview.

  • Joe Pepersack

    These are horrible – if typical – interview questions. Asking horrible programming questions will get you horrible programmers.

    I’ve been developing software professionally for 25 years. If someone asked me how I would implement a linked list, my answer would be “I wouldn’t. I’d a) develop in a language which supports lists natively or b) use a library.

    If your interview tests people on their ability to reinvent wheels, you’re going to get programmers who are good at reinventing wheels. You want your interview questions to test a candidate’s ability to solve problems and make smart design decisions. Reinventing the wheel is almost never a smart design decision.

  • Mambo

    So after asking all that stuff: how often in your professional career did you have to implement a linked list? Or graphs? Once? Twice? Nice things to ask, but not too practically relevant IMHO.

    Recursion can be useful, but what you don’t mention and don’t ask: how expensive is recursion? I’ve seen more than enough people coming from university trying to solve everything with recursion – resulting in bad to read, slow and memory expensive code. Every recursion creates a copy of the recursive function in memory(in most languages). And recursion almost always is slower than the iterative solution.

  • Fidel

    “Bin Sort” is lacking in the sorting algorithms, as well as “Radix sort”!! And “Heap Sort” as well.

    Besides, I would have put “Count Sort” after all the other methods, and after “Bin Sort” and “Radix Sort”, because the three of them (BinSort, Radix Sort and CountSort) use a different set of assumptions than the rest, and so they are not “general” sorting methods.

  • not-just-yeti

    Rather a nit-pick, but fwiw: what you call dynamic programming is really just “memoization”.

    DP is memoization plus an add’l optimization: don’t memoize the entire table of other-inputs; instead try to be clever and only keep some portion of that table, and calculate in a way that you only need refer to that portion. (For Fibonacci, that the DP version only keeps the last two elements of the array. In other problems, rather than keep an entire 2-D array you might keep just the last column of that array, or just the last three columns, if that’s as far as the recursion needs to go.)

  • Phil

    For #6, shouldn’t the line after
    f(3) + f(2) + f(2) + f(1)
    Be
    f(2) + f(1) + f(2) + f(2) + f(1)
    Then you’re done, because n <= 2 returns the value?

  • charles

    toCharyArray? I guess autocompletion might be useful.

  • http://www.artsgeek.net/ Hengfeng Luo

    for #9 probablity, C(50,2) * (1/365)*(1/365)

  • ryanlr

    Thousands of people have visited this page, you are the only one who points this out! Thank you.

  • jly

    For #9 Probability, I think there is a typo in the description. It should be 365/365 * … (the probability should be the product, not the sum)

  • Talgar

    Thank you !

  • GEEK

    I think the worst-case running time of counting sort is O(N+K), according to the book .