Notes, summaries, assignments, exams, and problems

Fundamental Sorting Algorithms in C

This document provides standard C implementations for three essential comparison-based sorting algorithms: Merge Sort, Quick Sort, and Heap Sort. These examples demonstrate the core logic and structure of each algorithm.

Merge Sort Implementation

Merge Sort is a stable, divide-and-conquer algorithm known for its consistent O(n log n) time complexity.

#include <stdio.h>

void merge(int a[], int l, int m, int r) {
    int i=l, j=m+1, k=0, b[100];
    while(i<=m && j<=r) {
        if(a[i]<a[j]) b[k++]=a[i++];
        else b[k++]=a[j++];
    }
    while(i<=m) b[k++]=a[i++];
    while(j<=r) b[k++]=a[j++];
    for(i=l,k=0;i<=r;i++,k++) a[i]=b[k];
}

void mergesort(int a[], int l, int

Ancient Indian Literature: Shruti and Smriti

The literature of ancient India is a vast and glorious treasure, forming the foundation of Indian civilization and deeply influencing global thought. It is traditionally categorized into two main groups: Shruti (that which is heard/revealed) and Smriti (that which is remembered/transmitted).

1. Vedic Literature (Shruti)

This is the oldest stratum of Indian literature, considered eternal knowledge revealed to ancient sages.

The Vedas

The four foundational texts of Hinduism:

• Rigveda: The oldest Veda, a collection of 1,028 hymns in praise of various deities.
• Yajurveda: Contains formulas for rituals and sacrifices.
• Samaveda: A collection of melodies and chants, mostly drawn from the Rigveda.
• Atharvaveda: Deals

Chapter 11 – Unemployment & Labor Markets

BLS Household Survey

• 60,000 households monthly

• Population: 333,287,557

  • Age 17+: 269,523,012

  • Children: 63,764,545

  • Civilian Noninstitutional Population: 263,973,000

  • Labor Force: 164,287,000

    • Employed: 158,291,000

    • Unemployed: 5,996,000

    • Not in Labor Force: 99,686,000

Key Formulas:

• Unemployment Rate (UR) = (Unemployed / Labor Force) × 100 → 3.7%

• Labor Force Participation Rate (LFPR) = (Labor Force / Civilian Noninstitutional Pop) × 100 → 62.2%

Alternate Measures of Unemployment (U1–U6):

• U3: Official unemployment rate

• Marginally attached: sought work in the past year but no longer looking

• Underskilled: working below qualifications or hours desired

• Involuntarily part-time: want full-time but work part-time

• US Unemployed

Core Business Definitions and Stakeholders

Key Business Products

• Goods: Physical products.
• Services: Non-physical products.
• Consumer Goods: Goods and services sold directly to ordinary people (consumers).
• Producer Goods: Goods and services sold to other businesses.

Types of Enterprise Ownership

Ownership determines who controls and benefits from the enterprise:

• Private Enterprise: Owned by individuals.
• Social Enterprise: A resource focused on objectives other than profit maximization.
• Public Enterprise: Owned and controlled by the government.

Understanding Stakeholders

Stakeholders are individuals or groups with an interest in the business's operations and success. Key stakeholders include:

• Local community
• Owners
• Suppliers
• Customers
• Government
• Employees
• Managers
• Shareholders

Roles

Municipal Bond Yield Calculations

Equivalent Taxable Yield (ETY)

A municipal bond carries a coupon rate of 6.00% and is trading at par.

Required Calculation 1: ETY for a 38% Tax Bracket

What would be the equivalent taxable yield of this bond to a taxpayer in a 38% combined tax bracket?

The formula for Equivalent Taxable Yield ($r$) is:

$$r = r_m / (1 - t)$$

• $r$: Equivalent Taxable Yield
• $r_m$: Municipal Bond Yield (6.00% or 0.06)
• $t$: Tax Rate (38% or 0.38)

Calculation:

$$0.06 / (1 - 0.38) = 0.096774 \rightarrow \mathbf{9.68\%}$$

Required Calculation 2: Municipal Yield Preference

An investor is in a 40% combined federal plus state tax bracket. If corporate bonds offer 7.75% yields, what yield must municipals offer for the investor to prefer them to corporate... Continue reading "Financial Calculations: Yields, Index Returns, and Security Pricing" »

Core OOP Definitions

Class and Object

• Class: A user-defined data structure that binds data members and operations (methods) into a single unit.
• Object: An instance of a class. Objects are used to perform actions or allow interactions based on the class definition.

Variables and Attributes

• Method: An action performed using the object's attributes.
• Attributes: Characteristics or properties of a class. Also known as instance variables (declared outside methods, belonging to one object). They are accessible through static and public methods.
• Class Variable: Declared using the static keyword; shared among all objects of the class.
• Local Variables: Declared inside methods, constructors, or blocks; they exist only while the method runs. They cannot be accessed

1. Nature and Scope of Accounting

Nature of Accounting

• Systematic Process: Identifying, recording, classifying, summarizing, and interpreting business transactions.
• Historical in Nature: Primarily records past events.
• Quantitative: Deals mostly with financial/monetary information.
• Dual Aspect: Based on the double-entry system (debit equals credit).
• Communication Tool: Provides information to stakeholders.

Scope of Accounting

• Financial Accounting: Recording and reporting of transactions (Profit & Loss, Balance Sheet).
• Cost Accounting: Ascertainment of cost, cost control, and decision-making.
• Management Accounting: Provides financial and non-financial information for planning and control.
• Tax Accounting: Deals with income tax, GST, and compliance.
• Auditing:

The Mechanism of Photosynthesis and Energy Conversion

Photosynthesis (pronounced FOH-tə-SINTH-ə-sis)^[1] is a system of biological processes by which photopigment-bearing autotrophic organisms, such as most plants, algae, and cyanobacteria, convert light energy—typically from sunlight—into the chemical energy necessary to fuel their metabolism. The term photosynthesis usually refers to oxygenic photosynthesis, a process that releases oxygen as a byproduct of water splitting.

Storing Chemical Energy and Maintaining the Atmosphere

Photosynthetic organisms store the converted chemical energy within the bonds of intracellular organic compounds (complex compounds containing carbon), typically carbohydrates like:

• Sugars (mainly glucose, fructose,

Cellular and Genetic Foundations

• Cells: The fundamental unit of life.
• Prokaryotes: Lack a nucleus; typically single-celled organisms.
• Eukaryotes: Possess a nucleus and organelles; can be multi- or single-celled.

Genetics is the study of heredity. DNA structure was revealed in 1953, based on the work of Rosalind Franklin.

• DNA: A double helix structure composed of four bases (Adenine–Thymine, Cytosine–Guanine).
• DNA organizes sequentially into histones, forming chromatin, which condenses into chromosomes (humans have 23 pairs).

DNA Replication and Mutational Forces

• Replication Process: Involves initiation (using helicase), elongation (using polymerase), and termination.
• Mutations: Errors during replication are the only source of new genetic variation.

Network Switches

Managed vs. Unmanaged Switches

Managed Switch: Configurable via software, supports security and communication settings. Used in large networks (enterprise, universities).

Unmanaged Switch: Fixed configuration, hardware-only, cannot be configured.

Ethernet & Speed

1. Fast Ethernet: 100 Mbps.
2. Gigabit Ethernet: 1 Gbps.

Ethernet Protocol

Divides data into frames, encapsulates IP addresses, performs error detection.

Ports

3. Console Port: Connects PC/laptop to configure switch.

Communication Modes

• Simplex (Half Duplex): One-way communication at a time.
• Duplex (Full Duplex): Two-way communication simultaneously.

Bandwidth

5. Maximum transmission speed of a network, determined by signal frequency range.

IP Addressing & Subnets

6. IP Address: Identifies