Introduction to Data Structures

C++

The C++ standard library data structures are designed to store any type of data. We put the desired data type within the <> brackets when declaring the data structure, as follows:

1vector<string> v;

This creates a vector structure that only stores objects of type string.

For our examples below, we will primarily use the int data type, but note that you can use any data type including string and user-defined structures.

Essentially, every standard library data structure supports the size() method, which returns the number of elements in the data structure, and the empty() method, which returns true if the data structure is empty, and false otherwise.

Arrays

You already know one of the simplest data structures: the array! In C++11, in addition to normal arrays, there exists an array class in the STL. For example, an array of ints can be initialized using the following line of code:

1array<int, 25> ar;

The array class supports the normal STL operations (such as .empty() or .size()) as well as the normal square-bracket access operator:

1ar[5] //access the element at the 5th index.

Java

Java default Collections data structures are designed to store any type of object. However, we usually don't want our data structures to only store one type of data, like integers or strings. We do this by putting the desired data type within the <> brackets when declaring the data structure, as follows:

1ArrayList<String> list = new ArrayList<String>();

This creates an ArrayList structure that only stores objects of type String.

For our examples below, we will primarily use the Integer data type, but note that you can have Collections of any object type, including Strings , other Collections, or user-defined objects.

Collections data types always contain an add method for adding an element to the collection, and a remove method which removes and returns a certain element from the collection. They also support the size() method, which returns the number of elements in the data structure, and the isEmpty() method, which returns true if the data structure is empty, and false otherwise.

Python

Python

Lists

The default way to store data in Python is using a list, which can automatically resize itself to accommodate more elements. We can add and delete elements at the end in $\mathcal{O}(1)$ time. A list can be initialized as follows:

1arr = []

Python lists are generic. This means that they can store any kind of data type, including objects. For example, the following code creates a dynamic array and adds the numbers $1$ through $10$ to it:

1for i in range(1, 11): # Note that range(i, j) includes i, but does not include j
2    arr.append(i)

In Python, we can give a dynamic array an initial size. The code below creates a dynamic array with $30$ zeroes.

1arr = [0] * 30

Iterating

We can use a regular for loop to iterate through all elements of a list.

1arr = [1, 7, 4, 5, 2]
2
3for i in range(len(arr)):
4    print(arr[i], end = " ")
5print()
6
7for element in arr:
8    print(element, end = " ")
9print()

We can also use iterators. An iterator allows you to traverse a container by pointing to an object within the container. iter(arr) returns an iterator pointing to the first element of the list arr.

1arr = [4, 2, 0, 0, 5]
2it = iter(arr)
3
4print(next(it)) # 4
5print(next(it)) # 2
6print(next(it)) # 0

Inserting and Erasing

1arr = []
2arr.append(2) # [2]
3arr.append(3) # [2, 3]
4arr.append(7) # [2, 3, 7]
5arr.append(5) # [2, 3, 7, 5]
6arr[1] = 4; # sets element at index 1 to 4 -> [2, 4, 7, 5]
7arr.pop(1) # removes element at index 1 -> [2, 7, 5]
8# this remove method is O(n); to be avoided
9arr.append(8) # [2, 7, 5, 8]
10arr.pop() # [2, 7, 5]

List Comprehensions

List comprehensions are extremely useful for simplifying a python for loop that modifies/creates a list into one expression. The general syntax is: [ expression for item in list if conditional ]

An example is provided in the code block below.

1# If a number is odd, add the number times 2 into the array
2old_list = [2, 5, 3, 1, 6]
3new_list = []
4for i in old_list:
5    if i % 2 == 1:
6        new_list.append(i * 2);
7print(new_list) # [10, 6, 2]
8# Simplified one liner with list comprehension
9# Recall the form [ expression for item in list if conditional ]
10# expression: i * 2

A very applicable use of list comprehensions for competitive programming in particular is creating an integer list from space separated input:

1# Example input: 5 3 2 6 8 1
2# Note that the conditional in the list comprehension is optional, and defaults to True if not provided
3arr = [int(x) for x in input().split()]
4print(arr) # [5, 3, 2, 6, 8, 1]

For more information on list comprehensions, including nesting them to create multidimensional lists, refer to the below resources.

C++

Dynamic Arrays

Dynamic arrays (vector in C++) support all the functions that a normal array does, and can resize itself to accommodate more elements. In a dynamic array, we can also add and delete elements at the end in $\mathcal{O}(1)$ time.

For example, the following code creates a dynamic array and adds the numbers $1$ through $10$ to it:

1vector<int> v;
2for(int i = 1; i <= 10; i++){
3    v.push_back(i);
4}

In C++, we can give a dynamic array an initial size. The code below creates a dynamic array with $30$ zeroes.

1vector<int> v(30); // one way
2vector<int> v; v.resize(30); // another way

In array-based contest problems, we'll use one-, two-, and three-dimensional static arrays most of the time. However, we can also have static arrays of dynamic arrays, dynamic arrays of static arrays, and so on. Usually, the choice between a static array and a dynamic array is just personal preference.

Unspecified Behavior

1vi res{-1};
2int addElement() {
3    res.pb(-1);
4    return sz(res)-1;
5}
6
7void rec(int x) {
8    F0R(i,10) {
9        res[i] = addElement();
10        ps(i,res[i]);

Running the above code with C++17

g++ -std=c++17 bad.cpp -o bad && ./bad

gives the intended output:

0 1
1 2
2 3
3 4
4 5
5 6
6 7
7 8
8 9
9 10

But running with C++14

g++ -std=c++14 bad.cpp -o bad && ./bad

gives:

0 -1
1 -1
2 3
3 -1
4 5
5 6
6 7
7 -1
8 9
9 10

However, the code works correctly if you save the result of addElement() to an intermediate variable.

1void rec(int x) {
2    F0R(i,10) {
3        int tmp = addElement();
4        res[i] = tmp;
5        ps(i,res[i]);
6    }
7}

The problem is that res[i] = addElement(); only works if addElement() is evaluated before res[i] is. If res[i] is evaluated first, and then addElement() results in the memory for res being reallocated, then res[i] is invalidated. The order in which res[i] and addElement() are evaluated is unspecified (at least before C++17).

See this StackOverflow post for some discussion about why this is the case (also a similar issue here).

Iterating

One way to iterate through all elements of a static or dynamic array is to use a regular for loop.

1vector<int> v{1,7,4,5,2};
2for (int i = 0; i < int(size(v)); i++){
3    cout << v[i] << " ";
4}
5cout << endl;

We can also use iterators. An iterator allows you to traverse a container by pointing to an object within the container. However, they are not the same thing as pointers.

For example, v.begin() or begin(v) returns an iterator pointing to the first element of the vector v. Apart from the standard way of traversing a vector (by treating it as an array), you can also use iterators:

1for (vector<int>::iterator it = v.begin(); it != v.end(); ++it) {
2    cout << *it << " "; //prints the values in the vector using the iterator
3}

Here is another way to write this. auto (since C++11) automatically infers the type of an object:

1vector<int> v{1,7,4,5,2};
2for (auto it = begin(v); it != end(v); it = next(it)) {
3    cout << *it << " "; //prints the values in the vector using the iterator
4}

We can also use a for-each loop.

1for (int element : v) {
2    cout << element << " "; //prints the values in the vector
3}

Inserting and Erasing

Keep in mind that insertion and erasure in the middle of a vector are $\mathcal{O}(n)$.

1vector<int> v;
2v.push_back(2); // [2]
3v.push_back(3); // [2, 3]
4v.push_back(7); // [2, 3, 7]
5v.push_back(5); // [2, 3, 7, 5]
6v[1] = 4; // sets element at index 1 to 4 -> [2, 4, 7, 5]
7v.erase(v.begin() + 1); // removes element at index 1 -> [2, 7, 5]
8// this remove method is O(n); to be avoided
9v.push_back(8); // [2, 7, 5, 8]
10v.erase(v.end()-1); // [2, 7, 5]

Strings

Java

Dynamic Arrays

Dynamic arrays (ArrayList in Java) that support all the functions that a normal array does, and can repeatedly reallocate storage to accommodate more elements as they are added.

In a dynamic array, we can also add and delete elements at the end in $\mathcal{O}(1)$ time. For example, the following code creates a dynamic array and adds the numbers $1$ through $10$ to it:

1ArrayList<Integer> list = new ArrayList<Integer>();
2for(int i = 1; i <= 10; i++){
3    list.add(i);
4}

In array-based contest problems, we'll use one-, two-, and three-dimensional static arrays most of the time. However, we can also have static arrays of dynamic arrays, dynamic arrays of static arrays, and so on. Usually, the choice between a static array and a dynamic array is just personal preference.

Iterating

To iterate through a static or dynamic array, we can use either the regular for loop or the for-each loop.

1ArrayList<Integer> list = new ArrayList<Integer>();
2list.add(1); list.add(7); list.add(4); list.add(5); list.add(2);
3int[] arr = {1, 7, 4, 5, 2};
4for(int i = 0; i < list.size(); i++){ // regular
5    System.out.println(list.get(i));
6}
7for(int element : arr){ // for-each
8    System.out.println(element);
9}

Adding and Removing

We can add and remove at any index of a dynamic array in $\mathcal{O}(n)$ time.

1ArrayList<Integer> list = new ArrayList<Integer>();
2list.add(2); // [2]
3list.add(3); // [2, 3]
4list.add(7); // [2, 3, 7]
5list.add(5); // [2, 3, 7, 5]
6list.set(1, 4); // sets element at index 1 to 4 -> [2, 4, 7, 5]
7list.remove(1); // removes element at index 1 -> [2, 7, 5]
8// this remove method is O(n); to be avoided
9list.add(8); // [2, 7, 5, 8]
10list.remove(list.size()-1); // [2, 7, 5]

C++

Of course, both vector<vector<int>> and vector<array<int,2>> would suffice for this case, but a pair can also store two elements of different types.

C++ Pairs

• pair<type1, type2> p: Creates a pair p with two elements with the first one being of type1 and the second one being of type2.
• make_pair(a, b): Returns a pair with values a, b.
• {a, b}: With C++11 and above, this can be used as to create a pair, which is easier to write than make_pair(a, b).
• pair.first: The first value of the pair.
• pair.second: The second value of the pair.

Example:

1#include <bits/stdc++.h>
2using namespace std;
3
4int main() {
5    pair<string, int> myPair1 = make_pair("Testing", 123);
6    cout << myPair1.first << " " << myPair1.second << endl;
7    myPair1.first = "It is possible to edit pairs after declaring them";
8    cout << myPair1.first << " " << myPair1.second << endl;
9    pair<string, string> myPair2 = {"Testing", "curly braces"};
10    cout << myPair2.first << " " << myPair2.second << endl;

C++ Tuples

Of course, we can hold more than two values with something like pair<int,pair<int,int>>, but it gets messy when you need a lot of elements. In this case, using tuples might be more convenient.

• tuple<type1, type2, ..., typeN> t: Creates a tuple with N elements, i'th one being of typei.
• make_tuple(a, b, c, ..., d): Returns a tuple with values written in the brackets.
• get<i>(t): Returns the i'th element of the tuple t. Can also be used to change the element of a tuple.

This operation only works for constant i. Namely, it is not allowed to do something like the following since i is not constant:

1tuple<int,int,int> t{3,4,5};
2int i = 1; cout << get<i>(t);

• tie(a, b, c, ..., d) = t: Equals a, b, c, ..., d to the elements of the tuple $t$ accordingly.

Example:

1#include <bits/stdc++.h>
2using namespace std;
3
4int main() {
5    int a = 3, b = 4, c = 5;
6    tuple<int, int, int> t = tie(a, b, c);
7    cout << get<0>(t) << " " << get<1>(t) << " " << get<2>(t) << endl;
8    get<0>(t) = 7;
9    cout << get<0>(t) << " " << get<1>(t) << " " << get<2>(t) << endl;
10

Java

Java

We can create our own generic Pair class in Java:

1static class Pair<K, V> {
2    K first;
3    V second;
4
5    public Pair(K first_value, V second_value) {
6        first = first_value;
7        second = second_value;
8    }
9}

Then, we can use the Pair class as follows:

1Pair<Integer, String> p = new Pair(5, "hello");
2System.out.println(p.first + " " + p.second);

Python

Python Tuples

Use the link below (if you know of a better one, please let us know!) to learn about tuples.