Design and Analysis of Algorithms Roadmap
A complete Gate Smashers DAA roadmap covering algorithm analysis, recurrence relations, sorting, greedy techniques, graph algorithms, dynamic programming, hashing, and advanced optimization methods.
Learning outline
Expand a stage, choose a topic and start its Gate Smashers lectures.
01Algorithm Analysis Foundations4 topics · 9 lectures0 / 9
▶Algorithms & Analysis Basics0 / 2 lectures
▶Asymptotic Notations0 / 2 lectures
▶Comparing Growth Rates0 / 3 lectures
▶Complexity Reference: Algorithms & Data Structures0 / 2 lectures
02Recurrence Relations5 topics · 13 lectures0 / 13
▶Writing & Solving Basic Recurrences0 / 2 lectures
▶Substitution Method: Advanced Forms0 / 3 lectures
▶Master Theorem0 / 3 lectures
▶Recursion Tree Method0 / 2 lectures
▶Min-Max Algorithm Analysis0 / 3 lectures
03Divide, Conquer & Sorting7 topics · 22 lectures0 / 22
▶Divide & Conquer with Quick Sort0 / 3 lectures
▶Merge Sort0 / 3 lectures
▶Bubble, Insertion & Selection Sort0 / 3 lectures
▶Radix, Counting & Bucket Sort0 / 3 lectures
▶Tree & Heap Foundations0 / 4 lectures
▶Heapify, Deletion & Heap Sort0 / 3 lectures
▶Bubble Sort Optimizations & Swap Analysis0 / 3 lectures
04Greedy & Graph Algorithms6 topics · 15 lectures0 / 15
▶Greedy Strategy & Fractional Knapsack0 / 2 lectures
▶Huffman Coding0 / 2 lectures
▶Job Sequencing & Optimal Merge Pattern0 / 2 lectures
▶Minimum Spanning Trees: Kruskal & Prim0 / 3 lectures
▶Shortest Paths: Dijkstra & Bellman-Ford0 / 5 lectures
▶BFS & DFS Traversal0 / 1 lectures
05Dynamic Programming4 topics · 9 lectures0 / 9
▶DP Foundations & 0/1 Knapsack0 / 3 lectures
▶TSP & Sum of Subsets0 / 2 lectures
▶Multistage Graph0 / 1 lectures
▶Floyd-Warshall: All-Pairs Shortest Paths0 / 3 lectures
06Hashing & Advanced Techniques4 topics · 11 lectures0 / 11
▶Hashing & Chaining0 / 3 lectures
▶Open Addressing: Linear, Quadratic & Double Hashing0 / 4 lectures
▶Topological Sorting0 / 2 lectures
▶Branch & Bound0 / 2 lectures
Topics covered in this roadmap
Use this stage-by-stage outline to understand the complete learning path before opening the interactive roadmap.
Algorithm Analysis Foundations
Algorithm Analysis Foundations
Start by learning what an algorithm is, how algorithms are evaluated, and how growth rates describe performance as input size increases. This stage builds the vocabulary used throughout DAA for reasoning about efficiency rather than only writing working code.
Algorithms & Analysis Basics
These lectures introduce the DAA syllabus, define algorithms, and distinguish theoretical analysis from empirical measurement. They establish the characteristics of a good algorithm and the purpose of analysing efficiency before implementation details dominate the discussion.
Asymptotic Notations
Asymptotic notation expresses upper, lower, and tight bounds on algorithm growth. These lectures cover Big O, Big Omega, Theta, and their important properties so complexity statements can be interpreted and manipulated correctly.
Comparing Growth Rates
Complexity functions can differ dramatically as input size grows, even when they look similar for small values. These videos compare common growth rates and solve exam-style ordering questions using substitution and simplification techniques.
Complexity Reference: Algorithms & Data Structures
A practical complexity reference connects asymptotic theory to familiar searching, sorting, and data-structure operations. These revision-oriented videos consolidate expected costs and make it easier to choose appropriate techniques under performance constraints.
Recurrence Relations
Recurrence Analysis
Recursive algorithms are analysed by expressing total work in terms of smaller subproblems. This stage develops recurrence formulation and three major solving approaches: substitution, the Master Theorem, and recursion trees.
Writing & Solving Basic Recurrences
These lectures explain how recurrences arise from recursive procedures such as binary search and how substitution expands them toward a base case. The emphasis is on translating code structure into a mathematical running-time relation.
Substitution Method: Advanced Forms
Substitution can also handle recurrences involving multiple branches, decrementing input, or non-constant additional work. These examples build pattern-recognition skills for deriving bounds step by step instead of relying on a single memorized formula.
Master Theorem
The Master Theorem provides a fast way to solve many divide-and-conquer recurrences of the form aT(n/b)+f(n). These lectures apply its cases to several examples, including less obvious recurrence forms that require careful transformation or interpretation.
Recursion Tree Method
Recursion trees visualize work done at each level of a recursive computation. By summing level costs and counting tree depth, they provide both an intuitive and mathematical route to the final time complexity.
Min-Max Algorithm Analysis
Finding both minimum and maximum values is a useful example for comparing straightforward iteration with divide-and-conquer. These lectures connect recurrence analysis to a concrete algorithm and show how comparison counts change under different approaches.
Divide, Conquer & Sorting
Divide, Conquer & Sorting
Divide-and-conquer solves a problem by splitting it, solving smaller instances, and combining their results. This stage applies that strategy to quick sort and merge sort, then broadens into comparison sorts, linear-time sorts, and heap-based sorting.
Divide & Conquer with Quick Sort
Quick sort partitions data around a pivot and recursively sorts the resulting regions. These videos introduce divide-and-conquer through quick sort and analyse how partition balance determines average and worst-case running time.
Merge Sort
Merge sort recursively divides the input and merges sorted halves. These lectures cover its working, pseudocode, and an exam-oriented question so both the algorithmic steps and the O(n log n) analysis are clear.
Bubble, Insertion & Selection Sort
Bubble, insertion, and selection sort are simple comparison-based methods that reveal important distinctions between best-case behaviour, stability, and in-place operation. Studying them makes later sorting trade-offs much easier to reason about.
Radix, Counting & Bucket Sort
Not every sorting algorithm must compare pairs of elements. Radix, counting, and bucket sort exploit assumptions about keys or value distribution to achieve near-linear performance in suitable settings.
Tree & Heap Foundations
Heap algorithms rely on structural properties of complete binary trees. These lectures review relevant tree types, introduce min-heaps and max-heaps, and explain heap insertion plus an exam-style heap question.
Heapify, Deletion & Heap Sort
Heapify restores the heap property efficiently and is the key operation behind bottom-up heap construction and heap sort. These videos derive O(n) heap construction, explain deletion, and show how repeated root removal produces a sorted sequence.
Bubble Sort Optimizations & Swap Analysis
These later playlist videos revisit bubble sort with shortcut reasoning, optimized stopping conditions, and pseudocode analysis. Together they clarify exactly when bubble sort can achieve linear best-case time and how to count swaps in structured inputs.
Greedy & Graph Algorithms
Greedy & Graph Algorithms
Greedy algorithms make locally best choices, while graph algorithms apply structured traversal and optimization rules to vertices and edges. This stage covers classic greedy problems and then moves into spanning trees, shortest paths, and graph traversal.
Greedy Strategy & Fractional Knapsack
The greedy technique chooses the best immediate option according to a defined criterion. Fractional knapsack demonstrates when this strategy is optimal because items may be split and selected by value-to-weight ratio.
Huffman Coding
Huffman coding builds an optimal prefix code by repeatedly combining the least frequent symbols or subtrees. The accompanying question reinforces how the greedy merge process determines code lengths and total encoding cost.
Job Sequencing & Optimal Merge Pattern
Job sequencing and optimal merge pattern are classic greedy problems with different selection rules. One maximizes profit under deadlines, while the other minimizes total merge cost by combining the smallest available files first.
Graph Algorithms
Graphs support traversal, connectivity, spanning-tree, and shortest-path problems. This grouping node separates graph-specific techniques from the earlier non-graph greedy problems and keeps their dependencies visually clear.
Minimum Spanning Trees: Kruskal & Prim
A minimum spanning tree connects all vertices of a connected weighted undirected graph with minimum total edge cost and no cycles. These lectures introduce spanning trees and compare Kruskal and Prim, the two standard greedy MST algorithms.
Shortest Paths: Dijkstra & Bellman-Ford
Single-source shortest-path algorithms compute minimum path costs from one source to the remaining reachable vertices. These videos cover Dijkstra in depth, explain its failure on negative weights, and contrast it with Bellman-Ford including pseudocode and time complexity.
BFS & DFS Traversal
Breadth-first search and depth-first search are the two fundamental systematic graph traversals. BFS explores layer by layer, while DFS follows a path deeply before backtracking, giving each method different natural applications.
Dynamic Programming
Dynamic Programming
Dynamic programming solves problems with overlapping subproblems and exploitable optimal substructure by storing reusable results. This stage develops the idea through knapsack, travelling salesman, subset problems, multistage graphs, and all-pairs shortest paths.
DP Foundations & 0/1 Knapsack
The 0/1 knapsack problem shows why a greedy ratio rule fails when items cannot be split. These lectures introduce dynamic programming, derive the knapsack recurrence, and relate the recursive formulation to its time complexity.
TSP & Sum of Subsets
Travelling salesman and subset-style problems demonstrate how dynamic programming can organize large combinational search spaces into states. These lectures focus on structured recurrence-based reasoning rather than blindly enumerating every possible solution.
Multistage Graph
A multistage graph divides a directed acyclic graph into ordered stages and computes an optimal route by reusing costs from later stages. It is a clean example of backward dynamic programming on graph structure.
Floyd-Warshall: All-Pairs Shortest Paths
Floyd-Warshall computes shortest paths between every pair of vertices by gradually allowing more intermediate vertices. These lectures explain its recurrence, work through an example, and derive its cubic time and quadratic space complexity.
Hashing & Advanced Techniques
Hashing & Advanced Techniques
The final technical stage covers fast key-based lookup, directed acyclic ordering, and state-space search using branch and bound. These topics extend DAA beyond the major design paradigms into practical and advanced problem-solving tools.
Hashing & Chaining
Hashing maps keys to table locations using a hash function so lookup can be very fast on average. These lectures introduce hash tables, explain collisions, and cover separate chaining as a method that stores colliding keys together.
Open Addressing: Linear, Quadratic & Double Hashing
Open addressing resolves collisions by probing alternative positions inside the hash table itself. These videos cover linear probing, quadratic probing, double hashing, and an exam-style question that exposes how probe sequences affect placement.
Topological Sorting
Topological sorting produces a linear order of a directed acyclic graph in which every directed dependency appears before the item that depends on it. The playlist covers both DFS-based ordering and Kahn’s indegree-based algorithm.
Branch & Bound
Branch and bound searches a structured state space while using bounds to discard branches that cannot improve the current best solution. These lectures introduce the method and apply it to 0/1 knapsack, connecting optimization search with pruning.
Completion
Design and Analysis of Algorithms Roadmap Complete
You have now covered the core analytical tools and major algorithm-design paradigms represented in the Gate Smashers DAA playlist. The next step is to revisit derivations, solve mixed problems without hints, and compare algorithms by correctness, complexity, and applicability.