C++ Algorithms for Binary Search and Prefix Sums
C++ Competitive Programming Solutions
This document contains several C++ solutions for common algorithmic problems involving prefix sums, binary search, and matrix manipulation.
1. Prefix Sum and Lower Bound Algorithm
#include <bits/stdc++.h>
using namespace std;
int main() {
int n;
long long k;
cin >> n >> k;
vector<long long> pref(n + 1, 0);
for (int i = 1; i <= n; i++) {
long long x;
cin >> x;
pref[i] = pref[i - 1] C++ Algorithms and Binary Search Implementation Codes
C++ Binary Search and Algorithms Collection
1. Binary Search Implementation
#include <iostream>
using namespace std;
int main(){
int n;
cin >> n;
int a[100000];
for (int i = 0; i < n; i++)
cin >> a[i];
int x;
cin >> x;
int l = 0, r = n - 1;
while (l <= r) {
int m = (l + r) / 2;
if (a[m] == x) {
cout << "Yes";
return 0;
}
if (a[m] < x)
l = m + 1;
Air Pollution, Solid Waste Management & Incineration Principles
Air Pollutants and Effects on Humans
Major Air Pollutants: Major air pollutants are classified as particulate matter (dust, smoke, fumes, mist), gaseous pollutants (SO2, NOx, CO, CO2, hydrocarbons), photochemical pollutants (ozone, PAN), and secondary pollutants formed by reactions in the atmosphere.
- Particulate Matter (PM10, PM2.5): Fine solid or liquid particles suspended in air, produced by combustion, industries, and vehicles.
- Sulphur Dioxide (SO2): Released from the burning of coal and fuel oil
American History Key Terms: From Colonization to the Constitution
Native Americans and Early European Colonization
- Bering Strait: Ice Age land bridge between Siberia and Alaska; early migration route into North America (15,000+ years ago).
- Cahokia: Large mound-building Native city near modern St. Louis (c. 600–1300); proof of sophisticated precolonial societies.
- Reasons Europeans came to the “New World”: Wealth/resources, competition for empire, Asian trade routes, conversion, and religious refuge → distinct colonies and economies.
- Christopher Columbus: Italian
Types of Strategic Costing and Their Relevance
Types of Strategic Costing and Their Relevance: Introduction
Strategic costing is the process of using cost information to support an organization’s long-term strategic objectives, competitive advantage, and value creation. Unlike traditional costing, which mainly focuses on determining product costs, strategic costing considers factors such as customer expectations, competition, product life cycle, quality, and business processes.
The major types of strategic costing include:
- Target Costing
- Activity-
Why is human resource needed for low esteem organizations
Role of ILOS: ILO =
International Labour Organization. It was founded in 1919 and became a specialized agency of the United Nations in 1946. It is a tripartite organization, meaning it brings together governments, employers and workers. Its main purpose is to promote social justice and decent work and to establish international rules that protect workers. The ILO creates Labour Standards, mainly through Conventions and Recommendations. These standards help countries make labour laws and policies
Comprehensive International Business Principles, Growth in India and Strategies
1. Define International Business. Explain its Nature, Scope and Importance
International business means business activities carried out across the borders of two or more countries. It includes the exchange of goods, services, technology, capital and knowledge. For example, an Indian company exporting medicines to another country is engaged in international business.
Nature and Features
- Cross-border activity: Buyers, sellers or business operations are located in different countries.
- Use of foreign currencies:
Algorithms Q&A: MST, Knapsack, and Backtracking
Q1. State Minimum Cost Spanning Trees Problem. Discuss Prim’s Algorithm to Solve This Problem and State Its Running Time.
Minimum Cost Spanning Tree (MCST/MST): Given a connected, weighted, undirected graph G = (V, E), a spanning tree connects all vertices using exactly |V| − 1 edges and contains no cycle. An MST is a spanning tree having minimum total edge weight: Cost(T) = Σ w(e), e ∈ T.
Prim’s Algorithm: A greedy algorithm that starts from any vertex and repeatedly adds the minimum-weight
Essential Business Management and Finance Key Concepts
Financial Objectives
- Survival
- Increase market share
- Profit
Private and Public Limited Companies
Private Limited Companies
- Advantages: Control can’t be lost, shareholders have limited liability
- Disadvantages: Profit is shared, can’t raise huge amounts of money
Public Limited Companies
- Advantages: Large amounts can be raised, shareholders have limited liability
- Disadvantages: Setting up is very expensive, outsiders can take control
Location
- Proximity to market: To keep transport costs down
- Proximity to competitors:
Advanced Statistical Modeling and Real-Time Stream Analytics
Regression Modeling: Linear and Multiple Regression
1. Definition
Regression modeling is a statistical technique used to study the relationship between a dependent variable and one or more independent variables. It is mainly used for prediction and estimating relationships between variables.
2. Simple Linear Regression
It uses one independent variable.
$$Y = \beta_0 + \beta_1X + \epsilon$$
where:
- $Y$ = dependent variable
- $X$ = independent variable
- $\beta_0$ = intercept
- $\beta_1$ = regression coefficient
- $\