Syllabus by chapter · অধ্যায়ভিত্তিক সিলেবাস

Sorting · 67 questions: Bubble Sort, Merge Sort; Feasible/Optimal Solution; Dijkstra's Shortest Path, Quicksort Complexity Analysis, Merge Sort — Worked Example and Complexity, Deriving the Merge Sort Recurrence T(n) = 2T(n/2) + n, Divide and Conquer Sorting (Merge Sort / Quick Sort)
Searching · 42 questions: Binary Search, Minimax Algorithm, Terminal State & Utility, Binary Search Using a Recursive Function, DFS vs BFS, DFS Limitations & Fixes, Binary Search — C/C++ Implementation
Greedy & Divide and Conquer · 23 questions: Huffman Coding, Kruskal's Algorithm, Block (Partitioned) Matrix Multiplication, Activity Selection (Maximum Non-Overlapping Intervals), Dynamic Programming vs. Divide and Conquer, Divide and Conquer vs Dynamic Programming
Dynamic Programming · 8 questions: Maximum Subarray Sum (Kadane's Algorithm), Dynamic Programming Explained with an Example, Fibonacci Number via Dynamic Programming, Time and Space Complexity of DP Fibonacci, Nested-Loop Complexity & Minimum Coin Change (DP)
Graph Algorithms · 23 questions: Dijkstra's Shortest Path Algorithm, Shortest Path (Dijkstra's Algorithm), Bellman-Ford & Negative-Weight Cycle Detection, DFS Time Complexity, Dijkstra's Algorithm, Tie-breaking by Alphabetical Order in Traversal
Complexity & Analysis · 22 questions: Polynomial-Time (Karp) Reduction, Recursive Function for F(n) = 1+2+...+n and Its Recurrence Relation, Big-O, Big-Omega and Big-Theta, Computing Algorithmic Complexity from Code, Fibonacci Sequence — Recursive vs Iterative Complexity, Nested Loop Output & Complexity Analysis
Mixed Topics · 66 questions: Regex for Odd Number of 1's, GCD Algorithm & Flowchart, Equilibrium Index of an Array, Regex for binary strings containing both 00 and 11, Generating Binary Strings without Consecutive 1s, Finding Odd Numbers from 1 to N

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Start learning: Asymptotic Analysis and Recurrences · অ্যাসিম্পটোটিক বিশ্লেষণ ও রিকারেন্স

Introduction

When we design an algorithm, the most important question an exam (and real life) asks is: how does the running time or memory grow as the input gets bigger? We do not care that one machine is faster than another, or that C is faster than Python — those are constant factors. We care about the shape of the growth: does the work double when the input doubles, or does it get four times bigger, or a million times bigger?

Asymptotic analysis is the mathematical language for describing this growth, and recurrences are the tool for finding the growth of recursive algorithms (like Merge Sort or Binary Search). Together they are the single most tested topic in the "Algorithms" section of BCS, Bank IT, and IT-officer written and MCQ exams. Almost every question about "time complexity", "Big-O", "order of growth", or "solve the recurrence" comes straight from here.

Learning Objectives

Define Big-O (O), Big-Omega (Ω), and Big-Theta (Θ) precisely and explain the intuition behind each.
Rank the common growth functions from slowest to fastest growing.
Compute the time complexity of loops, nested loops, and simple code fragments.
Distinguish best case, worst case, and average case, and relate them to O, Ω, Θ.
Set up a recurrence relation from a recursive algorithm.
Solve recurrences by the substitution method, the recursion-tree method, and the Master Theorem.
Avoid the classic exam traps (e.g. "Big-O means worst case").

Read the whole lesson free with an account · পুরো পাঠ পড়তে বিনামূল্যে সাইন আপ করুন

All 9 lessons · সব পাঠ

Asymptotic Analysis and Recurrences · অ্যাসিম্পটোটিক বিশ্লেষণ ও রিকারেন্স
Sorting Algorithms · সর্টিং অ্যালগরিদম
Searching and Divide-and-Conquer · সার্চিং এবং ডিভাইড-অ্যান্ড-কনকার
Greedy Algorithms · গ্রিডি অ্যালগরিদম
Dynamic Programming · ডাইনামিক প্রোগ্রামিং
Graph Algorithms: BFS, DFS, Shortest Path and MST · গ্রাফ অ্যালগরিদম: BFS, DFS, শর্টেস্ট পাথ এবং MST
Theory of Computation: Regex, Automata and Grammars · কম্পিউটেশন তত্ত্ব: রেগেক্স, অটোমেটা ও গ্রামার
Complexity Classes and AI Search Algorithms · জটিলতা শ্রেণি ও AI সার্চ অ্যালগরিদম
Elementary Algorithms and Flowcharts · প্রাথমিক অ্যালগরিদম ও ফ্লোচার্ট

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