# Learn Data Structures by Practicing - Part I

The structure of this article is derived from here. However the organization of this wikipedia article is a mess. It need to be updated urgently in order not to mislead the newbies.

"Algorithm is to construct a proper structure, and insert data. "

---kulasama

Recomendation on hints: Use as few hints as possible.

## Data types

### Primitive types

Objectives: Knowing how the datum is stored, exploiting intrinsic features of it and avoid making mistakes.

* You should be able to declare, assign, read or print variables of these types.

* You should be able to apply all possible operators to variables of these types and predict the results.

* You should be able to predict the results of conversions between these types.

* You should know the limits of these types and should be able to predict the results of exceeding them.

#### Boolean

#### Character

#### Floating point

- Including single precision floats, double precision (IEEE 754) floats, etc.

#### Fixed-point numbers

- Integer, including signed and unsigned integer
- Reference, pointer, or handle

#### Enumerated types

Literatures

* *Hacker's Delight*, Henry S. Warren, Jr.

Excercises

* Given two 32-bit signed integers a and b, print how many bits changes when turning a to b.

* Hint: Hamming weight of a\underline\vee b

* Given a number of height in inches and a number of height in centimeters, tell whether they equal each other.

* Explain ASCII code 0, 9, 10, 13, and declare variables of them in charactor literals.

* How to process emojis?

* Given n integers, each of them appears twice except for one, which appears exactly once. Find that single one.

* Advanced: Given n integers, each of them appears three times except for one, which appears exactly once. Find that single one.

**Only premitive types are allowed in these excersices. **

### Composite types or non-primitive type

Objectives: Getting familiar with how multiple data are organized basically.

#### Array

#### Record, tuple, or structure

#### String

#### Union

#### Tagged union, variant, variant record, discriminated union, or disjoint union

Excercises

* Given a string of a heximal number (might not be an integer), print it in decimal form.

* Write a programm of encryption and decryption of Caesar ciphering.

* Name algorithms of string searching and compare their advantages and disadvantages.

* Implement a expression evaluator supporting decimal numbers (with or without seperator), + and -.

* Store sparse matrices with various methods and compare where they should be applied. (Note that some of them depends pointers or references)

* Dictionary of keys

* List of lists

* Coordinate list

* Compressed sparse row

* Compressed sparese column

* Diagnal

* Orthogonal linked list

* ELLPACK

* ELLPACK + Coordinates

* Implement a hash table.

* How do you hash the keys and how do you handle the conflictions?

* Hint: Consider there are n key-value pairs and the keys are respectfully k\ldots k+n, where k is an constant integer, try to design a structure storing and retrieving values by keys in O\left(1\right).

* What if the keys are 3*k, where k is in 1\ldots n?

* What if the keys are distinct integers?

* What if the keys are mostly distinct integers?

* What if the keys are strings?

## Basic data structures

Objective: Understanding the principles of basic data structures, and knowing when to use them.

### Linked list

- Singly linked list
- Doubly linked list
- XOR linked list

Excercises

* Use arrays to implement linked lists.

* Append a node into a given list.

* Insert a node after a given node.

* Remove a node from a given list.

* Empty a list.

* Use pointers or references to implement linked lists.

* Revert a given linked list(unless otherwise specified, linked lists refer to sigly linked list of number)

* Find n'th node from the end of a given linked list.

* Find the middle node of a given linked list.

* Sort a given linked list.

* If you get stucked on this problem, you may also try the following problems first.

* Find and delete a specified node in a given linked list.

* Swap two nodes on a given linked list.

* Implement **bubble sort** on linked lists.

* Given an ordered linked list, insert a new number without destroying its order.

* Implement **insertion sort** on linked lists.

* Given a linked list, divide them into two even halves.

* Given two ordered linked lists, merge them into one ordered linked list.

* Implement **merge sort** on linked lists.

* Given a linked list, divide them into two halves(might not be even) and meanwhile let each number in the first half be greater than all numbers in the second half.

* Implement **quick sort** on linked lists.

* Given a linked list(assume it is), tell whether there is a loop and find the entry of it.

* Given two linked list, tell whether and where they intersect each other. What if there can be loops?

### Stack

Excercises

* Use array to implement stacks.

* Push a node into a given stack.

* Pop a node from a given stack.

* Peak the top node of a given stack.

* Empty a given stack.

* Use pointers or references to implement stacks. Including the operations above.

* Implement undo/redo functionality(or back/forward navigation in explorer).

* Given a sequence of push operations and a sequence of pop operations, tell whether it can be valid.

* Implement a queue supporting `push()`

. `pop()`

and `getMin()`

.

* Without recursion, use backtracking to solve n queens problem.

* Based on the expression evaluator above, add \times and \div support.

* Based on the expression evaluator above, add brackets support.

### Queue

Excercises

* Use arrays to implement queue.

* Enqueue a node into a given queue.

* Dequeue a node from a given queue.

* Empty a queue.

* Use pointers or references to implement linked lists.

* Given a sequence of enqueue operations and a sequence of dequeue operations, tell whether it can be valid.

* Implement a queue supporting `enqueue()`

. `dequeue()`

and `getMin()`

.

* Hint: You may first think of implementing a queue with stacks.

* Implement a circular buffer. // *TODO: Better problem needed*

* Implement a message queue. // *TODO: Better problem needed*

### Tree

Excercises

* Explain binary tree, full binary tree, complete binary tree.

* Given the root node of a tree, print its pre-order traversal, in-order traversal, post-order traversal and level-order traversal.

* Same problem, without recursion.

* Given the post-order traversal and in-order traversal of a tree, print its pre-order traversal.

* Given a tree with a in-order traversal of which the data are in increasing order, i.e. BST, insert a new node while keeping this property.

* Implement a sorting algorithm with it (tree sort).

* Given n, how many structurally unique BST's (binary search trees) that store values 1\ldots n?

* Hint: Catalan Number.

* Analyze the complexity of BST, tell in which situation it behaves bad.

* Implement a binary heap.

* Consider a complete binary tree. Can it be properly stored in an array? How to get parent / child node of a given node?

* If every node of this tree either has no parent (it is the root! ) or the datum of its parent is larger than its, it is called a heap. Can you insert a new node, and keep its properties (complete binary tree, parent datum larger than children datum)?

* If the root node is removed, can you transform the rest nodes into a heap?

* Implement a sorting algorithm with it (heap sort).

* Given a tree (no root node specified), print its diameter.

* The diameter of a tree (T=\left(V, E\right)) is defined as max_{u,v\in V}\delta\left(u, v\right), which means, the length of longest path among all shortest paths between all vertices.

* Given a set of strings, find them in a text.

* Hint: Aho-Corasick algorithm

* Construct Huffman tree with a given set of nodes and their weights.

### Graph

- Store a graph with:
- Adjacency matrix
- Adjacency list

- Explain the possible meaning of powers of adjacency matrices.
- Generate minimum spanning tree of a given graph.
- Prim, Krustal, etc.

- Calculate shortest paths from a source node s to a target node t in a given graph.
- Hint: DFS, BFS, Bidirectional BFS, Dijkstra, Bellman-ford, etc.
- Compare their complexity and tell what kind of graphs fit them best.

- Calculate shortest paths from a source node s to every other node in a given graph.
- Calculate shortest paths from every node to every other node in a given graph.
- Floyd-Warshall

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