Essential Recursive Algorithms and Backtracking Techniques
1) Factorial of n
Question
Compute n!.
Explain question
Return the product 1 * 2 * ... * n. The problem is naturally defined in terms of a smaller n.
Approach (in-depth)
If n is 0 (or 1) the answer is 1. Otherwise the factorial of n = n * factorial(n-1). The recursion reduces n by 1 on every call until the base case. No branching — just a single recursive call. This is linear recursion.
Recurrence relation
fact(n) = n * fact(n-1), with fact(0)=1.
Pseudocode
function fact(n):
if n == 0: return 1return Read More
Cobalt-60 and Linear Accelerators in Radiation Therapy
Ionizing Radiation Fundamentals
Capable of photons or other particles separating electrons from atoms upon contact. All physical processes involve mass transfer and/or energy processing.
Criteria for Useful Radioactive Sources (Radiophotons)
- Must provide radiation penetrating deep enough to react with the target area.
- Must provide a sufficient amount of energy where the volume is small (If the source has considerable thickness, it absorbs part of the radiation; if it does not, it does not absorb the
Organizational Decline Models and Bottom-Up Design Methodology
Organizational Decline and Organizational Death
Organizational Decline is the stage in the life cycle where an organization fails to anticipate, recognize, avoid, neutralize, or adapt to internal or external pressures that threaten its long-term survival. When the company generates few profits and makes too many investments, executives may decide to sell its assets or shut it down.
Greiner’s Model: Crises and Hindrances to Growth
Each growth stage is followed by a crisis. Further growth may be hindered
Read MoreEconomic Alternatives: Market Systems Without Capitalism
Designing a Non-Capitalist Market Economy
Yes, it is possible to imagine a market economy that is not capitalist, although implementing it in practice poses a complex challenge. To answer this properly, it is important to distinguish between market economy and capitalism—terms often confused but not synonymous.
Market Economy vs. Capitalism: Key Distinctions
- Market Economy: Based on the free interaction between supply and demand, where prices are set by the market and economic agents operate with
Participatory vs. Pluralistic Democratic Models
The Participatory Democratic Model
The basic principle of the modern reinterpretation of the participatory democratic model is that defining democracy solely around the protection of individual interests is insufficient. This idea must be balanced with the need for public participation. Such participation serves to ensure collective self-government and succeeds in creating a citizenry that is informed and committed to the public good. Collective deliberation on public affairs and civic self-government
Read MoreLanguage Learning Strategies: Techniques for Mastery
Direct Language Learning Strategies
I. Memory Strategies
A. Creating Mental Linkages
- Grouping (LR)
- Associating/Elaborating (LR)
- Placing new words into a context (A)
B. Applying Images and Sounds
- Using Imagery (LR)
- Semantic Mapping (LR)
- Using Keywords (LR)
- Representing Sounds in Memory (LRS)
C. Reviewing Well
- Structured Reviewing (A)
D. Employing Action
- Using physical response or sensation (LR)
- Using mechanical techniques (LRW)
II. Cognitive Strategies
A. Practicing
- Repeating (A)
- Formally practicing with sounds and
India’s Five-Year Plans: Economic Growth & Development
Objectives of Five-Year Plans
a. Growth or Increase in GDP
William Blake: Visionary Poet, Artist, and Engraver
William Blake: Poet, Artist, and Visionary
William Blake (born Nov. 28, 1757, London, Eng.—died Aug. 12, 1827, London) was an English engraver, artist, poet, and visionary.
Early Life and Divine Inspiration
Blake was born over his father’s modest hosiery shop at 28 Broad Street, Golden Square, London. His life and work were profoundly influenced by his spiritual beliefs.
In 1802, Blake wrote to his patron William Hayley, “I am under the direction of Messengers from Heaven Daily & Nightly.”
Read MoreCatholic Social Teaching: Foundations, History, and Application
What is Catholic Social Teaching (CST)?
Catholic Social Teaching (CST) is a set of reflections in modern times embracing different aspects of social life. It emerged in 1891 with the encyclical Rerum Novarum by Pope Leo XIII. It is a teaching also addressed to non-believers.
Doctrine and Texts
CST has two realities:
- Doctrine: The set of teachings that the Church reflects upon.
- Texts: Written documents that religious institutions create to spread the Word (the Gospel and Church teachings).
Sources of Catholic
Read MoreBiotechnology Fundamentals: Genetics, Recombinant DNA, and Therapeutics
Biotechnology: Definitions and Core Concepts
Definition: Biotechnology uses living organisms or their products to solve problems or create useful items.
Historical and Modern Techniques
Historical Uses
- Fermentation
- Selective breeding
- Antibiotics
Modern Techniques
- Gene cloning
- Genetic engineering
- Recombinant DNA
- CRISPR-Cas (Gene Editing)
- Synthetic genomes
Disciplines Involved
- Biology
- Chemistry
- Physics
- Mathematics
- Computer science and Bioinformatics
- Engineering
Applications of Biotechnology
- Disease-resistant crops
- Golden
