Practice Question Strings

Duration: 3 min

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Inside: a video lesson and guided study material.

Module outline

  1. HPSC Interview Preparation: Interview Preparation
  2. Python Language: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis, DSA using Python
  3. Data Structure & Algorithms: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Algorithm Analysis, Sorting Algorithms, Minimum Spanning Trees, Time Complexity Analysis, Graph Theory, Shortest Path Algos
  4. Computer Networks: Introduction to CN, Data Communication, DLL: Access Control, DLL: Flow Control, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware basics, Network Security
  5. Computer System & Organisation: Basics of COA, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Control Unit Design, Programming the Basic Computer
  6. Database Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, SQL, File Organization & Indexing, Transaction Management, Concurrency Control
  7. Operating Systems: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Deadlock, Threads & Process Creation, Memory Management, Virtual Memory, Disc Scheduling
  8. Digital Logic & Circuits: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation
  9. Theory Of Computation: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Pushdown Automata & CFG, Turing Machines, Moore & Mealy Machines
  10. Compiler Design: Intro to Compilers, Lexical Analysis, Grammar & CFG, Syntax Analysis: Top-Down, Syntax Analysis: Bottom-Up, Semantic Analysis & SDT, Intermediate Code Gen, Code Optimization, Run Time Environment
  11. Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management, Data Warehousing & Mining
  12. Introduction to Emerging Trends: Emerging Tech Trends
  13. Digital Society & Cyber Law: Society, Law & Ethics
  14. HPSC PGT Previous Year Paper:
  15. HPSC Assistant Professor Previous Year Paper:
  16. Live Sessions: HPSC Live Sessions, EMRS TGT/PGT Live Class
  17. Full Mock Test:
  18. HPSC PGT - MOCK Test Series:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

The video presents a discrete mathematics problem concerning binary strings without consecutive zeros. The instructor defines $x_n$ as the count of such strings of length $n$ and asks to identify the correct recurrence relation from four options. He systematically calculates the first few terms ($x_0$ through $x_3$) by listing valid strings to verify the base cases. By testing these values against the given options, he eliminates incorrect formulas and identifies the Fibonacci-like recurrence $x_n = x_{n-1} + x_{n-2}$. Finally, he uses this recurrence to compute $x_5$, selecting the correct numerical answer from the provided choices.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor introduces the problem statement: finding the recurrence for binary strings of length $n$ with no consecutive 0s. He writes down the four options on the screen: $x_n = 2x_{n-1}$, $x_n = x_{\lfloor n/2 floor} + 1$, $x_n = x_{\lfloor n/2 floor} + n$, and $x_n = x_{n-1} + x_{n-2}$. He begins by determining base cases, writing $x_0 = 1$ for the empty string and $x_1 = 2$ for strings "0" and "1". He then lists valid strings for length 2 ("01", "10", "11") to find $x_2 = 3$. For length 3, he lists "010", "011", "101", "110", "111" to find $x_3 = 5$. He tests option (a) $x_n = 2x_{n-1}$ and finds it fails for $x_2$ since $3 eq 4$. He tests option (b) and (c) and finds they fail. He tests option (d) $x_n = x_{n-1} + x_{n-2}$, verifying $x_2 = x_1 + x_0$ ($3 = 2+1$) and $x_3 = x_2 + x_1$ ($5 = 3+2$), confirming it is the correct recurrence.

  2. 2:00 – 3:06 02:00-03:06

    The instructor proceeds to the second question asking for the value of $x_5$. He continues the sequence established by the recurrence relation $x_n = x_{n-1} + x_{n-2}$. He calculates $x_4$ by adding $x_3$ and $x_2$ ($5 + 3 = 8$). Then he calculates $x_5$ by adding $x_4$ and $x_3$ ($8 + 5 = 13$). He circles the value 13 on the board. He identifies 13 as the correct answer, corresponding to option (c), and marks it.

The lesson demonstrates a standard method for solving recurrence relation problems: calculating initial terms to identify the pattern. By explicitly listing small cases, the instructor validates the Fibonacci sequence structure inherent in the problem constraints. The progression from identifying the recurrence to applying it for a specific term ($x_5$) reinforces the practical application of the derived formula.

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