Book Image

C++ Data Structures and Algorithm Design Principles

By : John Carey, Anil Achary, Shreyans Doshi, Payas Rajan
Book Image

C++ Data Structures and Algorithm Design Principles

By: John Carey, Anil Achary, Shreyans Doshi, Payas Rajan

Overview of this book

C++ is a mature multi-paradigm programming language that enables you to write high-level code with a high degree of control over the hardware. Today, significant parts of software infrastructure, including databases, browsers, multimedia frameworks, and GUI toolkits, are written in C++. This book starts by introducing C++ data structures and how to store data using linked lists, arrays, stacks, and queues. In later chapters, the book explains the basic algorithm design paradigms, such as the greedy approach and the divide-and-conquer approach, which are used to solve a large variety of computational problems. Finally, you will learn the advanced technique of dynamic programming to develop optimized implementations of several algorithms discussed in the book. By the end of this book, you will have learned how to implement standard data structures and algorithms in efficient and scalable C++ 14 code.
Table of Contents (11 chapters)


As we saw earlier, std::array is a really good improvement over C-style arrays. But there are some limitations of std::array, where it lacks functions for some frequent use cases while writing applications. Here are some of the major drawbacks of std::array:

  • The size of std::array must be constant and provided at compile time, and fixed. So, we can't change it at runtime.
  • Due to size limitations, we can't insert or remove elements from the array.
  • No custom allocation is possible for std::array. It always uses stack memory.

In the majority of real-life applications, data is quite dynamic and not a fixed size. For instance, in our earlier example of a hospital management system, we can have more doctors joining the hospital, we can have more patients in emergencies, and so on. Hence, knowing the size of the data in advance is not always possible. So, std::array is not always the best choice and we need something with dynamic size.

Now, we'll take a look at how std::vector provides a solution to these problems.

std::vector – Variable Length Array

As the title suggests, std::vector solves one of the most prominent problems of arrays – fixed size. std::vector does not require us to provide its length during initialization.

Here are some of the ways in which we can initialize a vector:

std::vector<int> vec;

// Declares vector of size 0

std::vector<int> vec = {1, 2, 3, 4, 5};

// Declares vector of size 5 with provided elements

std::vector<int> vec(10);

// Declares vector of size 10

std::vector<int> vec(10, 5);

// Declares vector of size 10 with each element's value = 5

As we can see from the first initialization, providing the size is not mandatory. If we don't specify the size explicitly, and if we don't infer it by specifying its elements, the vector is initialized with the capacity of elements depending on the compiler implementation. The term "size" refers to the number of elements actually present in the vector, which may differ from its capacity. So, for the first initialization, the size will be zero, but the capacity could be some small number or zero.

We can insert elements inside the vector using the push_back or insert functions. push_back will insert elements at the end. insert takes the iterator as the first parameter for the position, and it can be used to insert the element in any location. push_back is a very frequently used function for vectors because of its performance. The pseudocode of the algorithm for push_back would be as follows:


    if size < capacity

    // If vector has enough space to accommodate this element

    - Set element after the current last element = val

    - Increment size

    - return;

    if vector is already full

    - Allocate memory of size 2*size

    - Copy/Move elements to newly allocated memory

    - Make original data point to new memory

    - Insert the element at the end

The actual implementation might differ a bit, but the logic remains the same. As we can see, if there's enough space, it only takes O(1) time to insert something at the back. However, if there's not enough space, it will have to copy/move all the elements, which will take O(n) time. Most of the implementations double the size of the vector every time we run out of capacity. Hence, the O(n) time operation is done after n elements. So, on average, it just takes one extra step, making its average time complexity closer to O(1). This, in practice, provides pretty good performance, and, hence, it is a highly used container.

For the insert function, you don't have any option other than to shift the elements that come after the given iterator to the right. The insert function does that for us. It also takes care of reallocation whenever it is required. Due to the need to shift the elements, it takes O(n) time. The following examples demonstrate how to implement vector insertion functions.

Consider a vector with the first five natural numbers:

std::vector<int> vec = {1, 2, 3, 4, 5};


Vector doesn't have a push_front function. It has the generic insert function, which takes the iterator as an argument for the position.

The generic insert function can be used to insert an element at the front, as follows:

vec.insert(int.begin(), 0);

Let's take a look a few more examples of the push_back and insert functions:

std::vector<int> vec;

// Empty vector {}


// Vector has one element {1}


// Vector has 2 elements {1, 2}

vec.insert(vec.begin(), 0);

// Vector has 3 elements {0, 1, 2}

vec.insert(find(vec.begin(), vec.end(), 1), 4);

// Vector has 4 elements {0, 4, 1, 2}

As shown in the preceding code, push_back inserts an element at the end. Additionally, the insert function takes the insertion position as a parameter. It takes it in the form of an iterator. So, the begin() function allows us to insert an element at the beginning.

Now that we have learned about the normal insertion functions, let's take a look at some better alternatives, available for vectors, compared to the push_back and insert functions. One of the drawbacks of push_back and insert is that they first construct the element, and then either copy or move the element to its new location inside the vector's buffer. This operation can be optimized by calling a constructor for the new element at the new location itself, which can be done by the emplace_back and emplace functions. It is recommended that you use these functions instead of normal insertion functions for better performance. Since we are constructing the element in place, we just need to pass the constructor parameters, instead of the constructed value itself. Then, the function will take care of forwarding the arguments to the constructor at the appropriate location.

std::vector also provides pop_back and erase functions to remove elements from it. pop_back removes the last element from the vector, effectively reducing the size by one. erase has two overloads – to remove the single element provided by the iterator pointing to it, and to remove a range of elements provided by the iterator, where the range is defined by defining the first element to be removed (inclusive) and the last element to be removed (exclusive). The C++ standard doesn't require these functions to reduce the capacity of the vector. It depends entirely on the compiler implementation. pop_back doesn't require any rearranging of elements, and hence can be completed very quickly. Its complexity is O(1). However, erase requires the shifting of the elements, and hence takes O(n) time. In the following exercise, we shall see how these functions are implemented.

Now, let's take a look at the example about removing elements from a vector in different ways:

Consider a vector with 10 elements – {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}:


// Vector has now 9 elements {0, 1, 2, 3, 4, 5, 6, 7, 8}


// vector has now 7 elements {1, 2, 3, 4, 5, 6, 7, 8}

vec.erase(vec.begin() + 1, vec.begin() + 4);

// Now, vector has 4 elements {1, 5, 6, 7, 8}

Now, let's take a look at some other useful functions:

  • clear(): This function simply empties the vector by removing all of the elements.
  • reserve(capacity): This function is used to specify the capacity of the vector. If the value specified as the parameter is greater than the current capacity, it reallocates memory and the new capacity will be equal to the parameter. However, for all other cases, it will not affect the vector's capacity. This function doesn't modify the size of the vector.
  • shrink_to_fit(): This function can be used to free up the extra space. After calling this function, size and capacity become equal. This function can be used when we are not expecting a further increase in the size of the vector.

Allocators for std::vector

std::vector resolves the drawback of std::array regarding custom allocators by allowing us to pass an allocator as a template parameter after the type of data.

To use custom allocators, we follow certain concepts and interfaces. Since a vector uses allocator functions for most of its behaviors related to memory access, we need to provide those functions as part of the allocator – allocate, deallocate, construct, and destroy. This allocator will have to take care of memory allocation, deallocation, and handling so as not to corrupt any data. For advanced applications, where relying on automatic memory management, mechanisms can be too costly, and where the application has got its own memory pool or similar resource that must be used instead of default heap memory, a customer allocator is very handy.

Therefore, std::vector is a really good alternative to std::array and provides a lot more flexibility in terms of its size, growth, and other aspects. Asymptotically, all the similar functions of an array have the same time complexity as a vector. We usually pay extra performance cost only for the extra features, which is quite reasonable. For an average case, the performance of a vector is not very far from an array. Hence, in practice, std::vector is one of the most commonly used STL containers in C++ because of its flexibility and performance.