Gain insights into array and linked list-based implementations, delve into advanced structures like skiplists and trees, and explore template-based collections for efficient data optimization and retrieval.

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Data structures and algorithms are essential in computer science since they play a crucial role in efficient information retrieval and processing, dealing with files, storing contacts on phones, social networks and web searches.

In this course, you’ll learn about the array-based implementation of various linear data structures, stack, and queues. You’ll also learn about linked list-based implementation. Next, you’ll explore advanced data structures like skiplists and hashing. You’ll learn how to implement a variety of trees and graphs, and data structures related to bits of an integer. Toward the end of the course, you’ll learn the implementation of structures based on external storage.

After completing this course, you’ll be able to create reusable programs with template-based collections that can efficiently analyze how to optimize the storage and retrieval of very large amounts of data. Overall, this course will enhance your productivity and performance as a software developer.

Data Structures with Generic Types in C++

A `SkiplistSSet` uses a skiplist structure to implement the `SSet` interface. When used in this way, the list $L_0$ stores the elements of the SSet in sorted order.

# The `find()` method 
The `find(x)` method works by following the search path for the smallest value $y$ such that $y \ge x$:

Node < T > findPredNode(T x) {
  Node < T > u = sentinel;
  int r = h;
  while (r >= 0) {
    while (u.next[r] != null && compare(u.next[r].x, x) < 0)
      u = u.next[r]; // go right in list r
    r--; // go down into list r-1
  }
  return u;
}
T find(T x) {
  Node < T > u = findPredNode(x);
  return u.next[0] == null ? null : u.next[0].x;
}

Following the search path for $y$ is easy: when situated at some node, `u`, in $L_r$, we look right to `u.next[r].x`. If `x > u.next[r].x`, then we take a step to the right in $L_r$; otherwise, we move down into $L_{r−1}$. Each step (right or down) in this search takes only constant time; therefore, the expected running time of `find(x)` is $O(\log n).$

Before we can add an element to a `SkipListSSet`, we need a method to simulate tossing coins to determine the height, `k`, of a new node. We do so by picking a random integer, `z`, and counting the number of trailing $1$s in the binary representation of `z`:

> **Note:** The `pickHeight()` method does not exactly replicate the coin-tossing experiment since the value of `k` will always be less than the number of bits in an `int`. However, this will have a negligible impact unless the number of elements in the structure is much greater than $2^{32} = 4294967296.$

Overview

Array-Based Lists

Linked Lists

Skiplists

Hash Tables

Binary Trees

Random Binary Search Trees

Scapegoat Trees

Red-Black Trees

Heaps

Sorting Algorithms

Graphs

Data Structures for Integers

External Memory Searching

Wrap Up

SkiplistSSet: An Efficient SSet

The `find()` method

SkiplistSSet: An Efficient SSet

The find() method

The `find()` method