Design and Analysis of Algorithm Notes
Subject Overview
Design and Analysis of Algorithm formalizes algorithmic problem-solving — time/
Subject at a glance
4
Units
25
Topics
3
Credits
4
Infographics
Unit-wise Syllabus
4 units — open any unit for detailed topic-wise notes, diagrams and important exam questions
- Design and performance analysis of algorithms
- time and space complexity
- asymptotic notations (O, Ω, Θ)
- analysis of sequential search/bubble sort/selection sort/insertion sort/matrix multiplication
- recursion basics
- analysis of recursive algorithms
- Master's theorem
Case 1
f(n) smaller than n^(log_b a) → T(n) = Θ(n^(log_b a))
Case 2
f(n) equal to n^(log_b a) → T(n) = Θ(n^(log_b a) log n)
Case 3
f(n) larger → T(n) = Θ(f(n))
Merge sort example
T(n) = 2T(n/2) + n → Θ(n log n)
Study guide
Before designing an algorithm you must be able to judge it. You learn performance analysis, time and space complexity, asymptotic notations (O, Ω, Θ), analysis of searching and sorting algorithms and matrix multiplication, recursion and recurrence analysis with the Master's theorem. Practise solving recurrences with the Master's theorem; it is a guaranteed numerical question.
- General concept
- binary search
- finding maximum and minimum
- merge sort
- quick sort
- best/worst case analysis
- Strassen's matrix multiplication
- lower bound for comparison-based sorting
- 1Divide
Split the problem into smaller parts
- 2Conquer
Solve each part recursively
- 3Combine
Merge the partial solutions
Study guide
Divide and conquer breaks a problem into smaller parts, solves each and combines the results. You study binary search, finding maximum and minimum, merge sort, quick sort with best and worst cases, Strassen's matrix multiplication and the lower bound for comparison-based sorting. Write the recurrence for each algorithm and solve it.
- General concept
- general Knapsack problem
- minimum weight spanning trees via Prim's and Kruskal's algorithms
- Dijkstra's algorithm for single-source shortest paths
Builds
One growing tree from a start vertex
A forest that merges into a tree
Picks
Cheapest edge leaving the tree
Cheapest edge that forms no cycle
Best for
Dense graphs
Sparse graphs
Key structure
Priority queue
Union-find
Study guide
A greedy algorithm makes the best local choice at each step. You study the general idea, the fractional knapsack problem, minimum spanning trees using Prim's and Kruskal's algorithms and Dijkstra's single-source shortest paths. Trace Prim's and Kruskal's on the same graph and compare the steps.
- General concept
- Fibonacci series and binomial coefficient computation
- all-pairs shortest paths (Floyd-Warshall)
- 0/1 Knapsack problem
- finding connected components
- topological sorting
Decision
Best local choice, never revisited
Considers all subproblems
Optimal
Not always
Always, when the problem fits
Memory
Low
Stores a table of results
Example
Fractional knapsack
0/1 knapsack, Floyd-Warshall
Study guide
Dynamic programming solves overlapping subproblems once and stores the answers. You study Fibonacci numbers and binomial coefficients, all-pairs shortest paths (Floyd-Warshall), the 0/1 knapsack problem, connected components and topological sorting. Fill the DP table by hand for the knapsack problem; it shows exactly how the idea works.
Why Design and Analysis of Algorithm Matters
Algorithm design is the heart of computer science and the main topic of coding interviews at top technology companies. Understanding complexity and the standard paradigms lets you solve unfamiliar problems instead of memorising solutions.
How to Prepare for Design and Analysis of Algorithm
- Learn each technique with its standard example problems and complexities.
- Practise recurrence solving and Master's theorem problems daily.
- Compare greedy and dynamic programming on the knapsack problem to see when greedy fails.
- Solve at least one coding problem on each technique every week.
Design and Analysis of Algorithm: Frequently Asked Questions
What is the difference between greedy and dynamic programming?
A greedy algorithm commits to the best local choice at each step and never reconsiders, while dynamic programming considers all subproblems and stores results to guarantee an optimal answer.
Why is the Master's theorem useful?
It gives the time complexity of many divide-and-conquer recurrences quickly without expanding them step by step.