Data Structures and Algorithms: In Depth DSA using Java

analyze algorithms by time and space complexity, using experimental and theoretical (mathematical) analysis to measure running time, count primitive operations, and derive order of growth.

Analyze order of growth as input size increases, ignoring constants, and explain how loop patterns—from no loops to nested loops—produce constant, linear, logarithmic, quadratic, cubic, and exponential growth.

Explore asymptotic analysis to measure algorithm performance by order of growth, focusing on big O, Omega, and Theta bounds, and analyzing best, worst, and average cases.

Explain how big-O notation bounds a function's growth as input size increases, using examples like 5n+4 to illustrate upper bounds and asymptotic order.

Explain how the big omega notation provides a lower bound, and show that f(n)=5n+4 is omega(n) since it grows at least as fast as n up to a constant factor.

Explore big theta notation by proving when f(n) lies between constants times a growth function g(n); for example, 5n+4 is theta(n), with suitable C1 and C2.

Explore the practical significance of asymptotic notations—big-O, Omega, and Theta—in algorithm performance. Use linear search as an example to illustrate worst-case, best-case, and average-case complexities and order of growth.

Analyze memory usage and space complexity, focusing on bytes and bits, data types, and arrays that determine an algorithm’s memory footprint.

Learn how recursion works, including base cases, recursive calls, and how a function calls itself until termination. See examples that compare recursion with iterative approaches.

Explore implementing iterative and recursive methods in Java to print the squares from n down to 1, compare their behavior, and analyze time complexity using recurrence relations.

Analyze the time complexity of recursive functions using recurrence relations, derive the recurrence from a square function, and prove linear time using the substitution method.

Explore solving a recurrence relation using the substitution method, derive T(n) = T(n-1) + n, sum of natural numbers, and conclude time complexity is O(n^2).

Explore tail and head recursion in Java through practical demos that compute squares, showing how placing the recursive call at the end versus the beginning changes execution and output.

Explore tree recursion in Java by implementing a three-recursion demo, tracing recursive calls, and analyzing time complexity using a recursion tree pattern.

Learn to compute the sum of N natural numbers using a recurrence relation. Compare with the closed-form formula n(n+1)/2 and explore iterative methods and complexity.

Demonstrates summing numbers from 1 to n in Java using a formula, an iterative loop, and recursion inside the SumNumbersDemo class, with main confirming n=5 yields 15.

Explain the factorial concept and its recurrence relation, with base cases factorial(0)=1 and factorial(1)=1, and implement a recursive factorial function with linear time complexity.

Develop factorial implementations in Java using iterative and recursive methods within a factorial demo class, then execute the main method to verify that factorial of five equals 120.

Explore the linear search algorithm, a sequential method that scans an array element by element to find a key, returning its index or -1, with worst-case time complexity O(n).

Implement a Java linear search algorithm with a method taking an array, its length, and a key, returning the index or -1, demonstrated in a main method with an array.

Learn the binary search algorithm, an efficient iterative method for finding a key in a sorted array, using left, right, and middle indices to achieve O(log n) time.

Learn to implement binary search in Java using an iterative approach, including left and right indices, mid calculation, and condition checks to return the index or -1.

Explore the recursive binary search algorithm, using left, right, and mid to halve the search range, returning the index or -1 when not found, with time complexity log n.

Learn how to implement binary search with recursion in Java in a hands-on lab, using a binary search recursive demo class that tests with a sample array and keys.

Explore sorting algorithms and their goal of arranging elements in ascending or descending order, including selection, insertion, bubble, quicksort, merge, shell, and heap sorts.

Explore stable and unstable sorting, focusing on how duplicates affect ordering and how stable sorts preserve the original order of equal elements when sorting in ascending order.

Explore how selection sort works by repeatedly selecting the minimum element from the unsorted portion and swapping it into its correct position, demonstrated with a step-by-step example.

Analyze the selection sort algorithm by selecting the smallest unsorted element in each round, swapping it into place, and examining its time complexity and instability.

Develop a Java program that implements the selection algorithm (selection sort) with a selection method, a display method, and a main method to show the original and sorted array.

Explore how insertion sort builds a sorted left side by taking one element at a time and inserting it into its proper position.

Explore the insertion sort algorithm, including how to insert each element into its proper position by shifting predecessors, and analyze its stability and time complexity (best and worst cases).

Learn to implement insurgents' algorithm (insertion sort) in Java by creating a class, a method insertionSaqr, and a display helper; run with an array to show original and sorted sequences.

Explore how bubble sort compares adjacent elements, swaps when the left one is greater, and bubbles the maximum value to the last position across successive passes.

Analyze the bubble sort algorithm and its complexity, understanding how swaps move the largest elements to the end, and examine its stability and best and worst-case performance.

Implement the bubble sort algorithm in Java by building a demo class with a bubble start method, swapping adjacent elements, and displaying original and sorted arrays.

Learn how Shell sort uses decreasing gaps to compare and swap elements, moving them toward proper positions, until the final pass with a gap of one.

This lecture explains the shell sort algorithm and its analysis, using a gap sequence starting at n/2 and halving each round, performing insertion-like shifts and discussing complexity.

Implement the shell sort algorithm in Java with a public void shellStart method. Show gap halving and in-place insertion, plus a display method to print arrays before and after sorting.

Explore how merge sort uses divide and conquer to split a list into halves, recursively sort each half, and merge sorted sublists into one ordered sequence.

Merge sort uses a divide-and-conquer, recursive approach that splits an array by mid = floor((left + right)/2), sorts left and right subarrays, and merges them.

Learn how the merge algorithm combines two sorted subsects using a temporary array B with four parameters, left and rightmost indices, then copies the merged data back to original array.

Analyze the complexity of the merge sort algorithm by examining recursive division into halves and the merge step, showing a total running time of O(n log n).

Implement a Java merge sort by creating a class, writing a public void mergeSort method with left and right indices, and a merge routine, then display the sorted array.

Explain how quicksort uses a pivot and partitioning to sort by divide and conquer, recursively sorting left and right subarrays.

Examine the quicksort algorithm using a three-parameter approach (array, low, high), apply partitioning with a pivot, swap elements, and recursively sort left and right partitions in a divide-and-conquer framework.

Quicksort partitions data into two subsets and recursively sorts them, yielding n log n time, with worst-case n^2 when input is already sorted and the first element is pivot.

Implement quicksort in Java by building a quicksort class with partition and swap methods, demonstrating recursive sorting, array partitioning, and displaying results.

Summarize the time and space complexities of sorting algorithms, comparing comparison-based and index-based methods, and noting best, average, worst cases and stability.

Create a node class with element and next, where next references the following node, and initialize it with a constructor to build and link nodes into a linked list.

Explore how a linked list stores elements in nodes linked by next references, with head and tail pointers, and how to traverse from head to tail using next.

Learn to implement the append operation for a linked list: create a new node, update head and tail when empty, link nodes, and increment size with constant time complexity.

Learn to traverse and display a linked list from head to tail using next references until null, via a display method that prints each node's element.

Learn to implement a Java linked list by defining a node class and a list with head, tail, and size; add elements, compute length, check emptiness, and display.

Insert a new node at the beginning of a linked list by creating the node, updating head (and tail if empty), linking to the former head, and updating the size.

Learn to implement a method that inserts an element at beginning of a linked list in Java. Handle empty lists, update the head and size, and verify by displaying elements.

Insert a node at any position in the linked list by traversing from the head to the target position, linking the new node, updating the size, and analyzing time complexity.

Learn how to implement a method to insert an element at any position in a linked list, including position validation, node insertion, and size updates, with concrete examples.

Learn how to delete the first node of a linked list by updating the head to head.next, adjusting the size, and handling single-element cases with tail and null checks.

Learn how to implement a remove first method in a Java linked list to delete the head node, handle empty lists, update size, and return the removed element.

Delete the last node of a linked list by traversing from the head to the node before last. Update the tail and size, and return the deleted element.

Implement a remove last method in the list to delete the end element, handle empty lists, and update size. Traverse to last-but-one node, update pointers, and return the removed element.

Delete any element at a given position in a linked list by traversing to the node before and updating next pointer to the node after, and return the deleted element.

Implement a remove any method in a linked list to delete an element at a given position, handle invalid positions, traverse to the previous node, and return the removed element.

Learn how to search for an element in a linked list by traversing from head to tail, using a key, and returning the index or -1 with worst-case time complexity.

Implement a linked list search method in Java, traversing nodes from head, comparing each element to the key, and returning the zero-based index or -1 if not found.

Learn to write a Java method to insert elements into a linked list in sorted order, traversing to locate the insertion point, updating links, and increasing the list size.

Illustrate circular linked list by showing last node points to the first, creating a circular pattern with head and tail references; discuss single-node edge case where next points to itself.

Create a circular linked list by inserting nodes, updating head and tail, and linking the last node back to the first. Analyze the constant-time insertions and the overall time complexity.

Traverse a circular linked list from the head, printing each node’s value by advancing via next references until the length is reached, then analyze the traversal’s time complexity.

Learn to implement a circular linked list in Java, including creating nodes, maintaining head, last, and size, inserting at the end, and displaying elements via traversal.

Insert an element at the beginning of a circular linked list by creating a new node, linking it to the first node, updating head, and increasing size in O(1) time.

Learn to implement a public void insertFirst method for a circular linked list, inserting at the beginning, handling empty lists, updating links, and increasing size with a demonstration.

Insert a new node at any position in a circular linked list by traversing to the target, updating links correctly, increasing the size, and analyzing time complexity.

Implement a method to insert an element at any position in a circular linked list, validating bounds, traversing to the position, updating links, and increasing size with examples.

Delete an element at the beginning of a circular linked list using a remove first method that checks emptiness, updates head and tail, and decreases size in constant time.

Learn how to implement a removeFirst method to delete the element at the beginning of a circular linked list in Java, handling empty lists, head updates, and size.

Remove the last node in a circular linked list by traversing to the node before the tail, update the tail, reconnect to head, and return the deleted element.

Learn to implement a remove-last method for a circular linked list in Java. Handle empty lists, traverse to the last-but-one node, update pointers, retrieve the removed element, and update size.

Learn how to delete an element at any position in a circular linked list using a remove-any method, traversing to the node before the target, adjusting links, and updating size.

implement a remove-at-position method for a circular linked list, validating the position, traversing to the preceding node, unlinking the target, returning the removed element, and updating size.

Examine what a doubly linked list is, with nodes linking to next and previous elements, enabling efficient insertions and deletions, especially at the end, compared to a single linked list.

learn to define a node with element, next, and previous references, implement a constructor, and link nodes to form a doubly linked list.

Explore how a doubly linked list uses head and tail references, next and previous links, and null guards to traverse from head to tail and backward, with practical examples.

Demonstrates creating a doubly linked list by inserting nodes, initializing head and tail, updating next and previous references, and tracking size with constant time complexity.

Traverse a doubly linked list from head to tail by following the next references, displaying each element along the way. Analyze traversal time as proportional to the list size.

Implement a Java doubly linked list by defining a node with data, next, and previous, and a list with head, tail, and methods to add at end and display.

Insert at beginning of a doubly linked list by creating a new node, linking its next and previous, updating head (and tail if empty), and increasing size in O(1) time.

Learn to implement the insert-at-beginning operation for a doubly linked list in Java. Create a node, update head and tail for empty and nonempty cases, link nodes, and increase size.

Learn how to insert a node at any position in a doubly linked list by traversing to the target position and updating next and previous references, then increase size.

Demonstrates implementing a public void method to insert an element at any position in a doubly linked list, including validation, traversal to position-1, and pointer updates with size adjustment.

Remove the first node of a doubly linked list by updating the head to the next node, handling single-element cases, and returning the deleted element.

Delete the last node of a doubly linked list by using the tail and previous reference, update the tail, nullify the new tail's next, and decrease the size.

Delete element at arbitrary position in a doubly linked list by traversing to the node before, updating next and previous links, and reducing size, with O(n) time.

Learn to implement a remove-any method in a doubly linked list, validating positions, traversing to the target node, updating links, shrinking size, and returning the removed element.

Master the stack data structure and its last-in, first-out behavior with push, pop, and top operations. Implement stacks with arrays or linked lists for browser history, undo, and tag validation.

Explore implementing a stack with arrays, using last in, first out, and core operations push, pop, and top, including checks for full and empty states.

Implement a stack using an array in Java, including push, pop, top, isEmpty, isFull, and display operations, with a main method demonstrating element insertion, removal, and top lookup.

Explore implementing a stack with a linked list, performing push and pop at the head (or tail) to maintain last-in, first-out order, and evaluate the time complexity of these operations.

Learn how to implement a stack data structure using a linked list in Java, including push, pop, top, isEmpty, size, and display operations with a node-based design.

Explore queue data structure, a first in, first out collection, with NQ and dequeue operations at rear and front, plus front, size, and isEmpty, implemented via arrays or linked lists.

Implement queues using arrays to enforce fifo order, apply enqueue and dequeue operations, manage front and rear pointers, track size, and perform empty and full checks.

Learn to implement a queue in Java using an array, with front, rear, and size, and core operations enqueue, dequeue, isEmpty, isFull, plus display and a test main.

Build a queue with a linked list using head and tail references for enqueue at rear and dequeue from front. Insertions and front removals are O(1); tail removal is O(n).

This lecture teaches implementing a queue with a linked list in Java, featuring a node class, front and rear references, size tracking, and core operations enqueue, dequeue, and display.

Explore double ended queues, or deques, with insertions and deletions at both ends. Learn the dequeue adt's first, last, size, and isEmpty operations and their array or linked list implementations.

Learn to implement a double-ended queue (deque) using a linked list in Java, with front/rear insertions and removals, first/last retrievals, length checks, and a main demonstration.