answer:```cpp#include <iostream>#include <string>#include <vector>using namespace std;bool containsVowels(const string &s) { for (const char &c : s) { if (tolower(c) == 'a' || tolower(c) == 'e' || tolower(c) == 'i' || tolower(c) == 'o' || tolower(c) == 'u') { return true; } } return false;}void reverseString(string &s) { int len = s.length(); for (int i = 0; i < len / 2; i++) { swap(s[i], s[len - i - 1]); }}vector<string> reverseAndExcludeVowels(vector<string> &arr) { vector<string> result; for (int i = arr.size() - 1; i >= 0; i--) { reverseString(arr[i]); if (!containsVowels(arr[i])) { result.push_back(arr[i]); } } return result;}int main() { vector<string> myArray = {"cat", "apple", "dog", "tangerine"}; vector<string> reversedArray = reverseAndExcludeVowels(myArray); for (const string &s : reversedArray) { cout << s << endl; } return 0;}```

answer:Designing a serverless framework using AWS Lambda and API Gateway can present a variety of challenges throughout the design and implementation stages. Here is a step-by-step guide to setting up this framework, common challenges with their potential solutions, and the best practices for optimal performance and robust security:1. Define Your System Requirements and Constraints: Importance: To create a serverless framework that meets your business requirements as closely as possible. If not done correctly: It may lead to a system that doesn’t meet your requirements and expectations.2. Designing the System: - Think in terms of functions: AWS Lambda runs your code as discrete functions or units of work, hence model your software in terms of these packages. Overpacking a function may not fully use the benefits of serverless. - Hierarchy of AWS Lambda services: Watch out for this challenge. AWS services invoke Lambda functions based on event triggers. The suggested hierarchy is like this: AWS Route53 -> AWS CloudFront -> AWS WAF -> Regional API Gateway -> AWS Lambda -> AWS DynamoDB. - Asynchronous vs Synchronous invocation: Ascertain if your function should operate synchronously or asynchronously for the clients. - Connection pooling: Persistent connection to resources like a database might not work well with AWS Lambda as it scales and contracts. - Error handling: Decide how to handle failures of your Lambda function. 3. Set Up an AWS Account: Importance: An essential starting point to access all AWS services. If not done correctly: You might run into access problems or over-utilize resources leading to unexpected charges.4. Create a Serverless Application Locally: Importance: Faster development and allows for debugging before deployment to AWS. If not done correctly: Could lead to wasted effort, costs and potential bugs when you deploy straight to AWS.5. Create an Amazon S3 Bucket: Importance: To store deployment files and operational data. If not done correctly: Infrastructure failure could occur if deployment files are not available when needed.6. Deploy Your App: Importance: Take your locally-developed app to 'go live' on AWS infrastructure. If not done correctly: Mistakes in this step can lead to the app not functioning as expected, causing downtime and potential data loss.7. Create an API Gateway: Importance: To create, maintain and secure the communication between your clients and services. If not done correctly: It can compromise the communication between your clients and services leading to data loss or exposing sensitive information.8. Link Your Functions to the API Gateway: Importance: To ensure your front-end can communicate with your serverless back-end. If not done correctly: It can lead to communication failures and non-functioning end-points.9. Debugging: Importance: To avoid any outstanding bugs or issues. If not done correctly: It might lead to unwanted issues in production. 10. Continuous Integration and Continuous Delivery (CI/CD) Implementation: Importance: To automate the deployment process aiming to increase the speed of deployment and reliability. If not done correctly: It may lead to longer deployment times and potential bugs slipping through into production.11. Monitoring and Logging: Importance: To keep track of system health and troubleshoot any potential issues. If not done correctly: It can lead to unnoticed performance degradations and issues taking longer to resolve due to limited visibility.12. Security Settings and Policies: Importance: To safeguard your application and data. If not done correctly: Could result in a data breach.Depending upon the sequencing of these stages, they could create dependencies and affect the subsequent stages. For example, setting up the AWS account is the fundamental phase for everything else and trying to deploy your app before creating an S3 bucket could cause problems.

answer:WAR files (Web Application Archive) are not executable files in the same way an .exe or a .jar file can be. They are archive files that contain the components and resources of a web application like HTML files, Java classes, libraries, descriptors, and other resources. These components and resources need a server side environment like Apache Tomcat to function.Tomcat provides the "container" defined in the Java EE specification that implements the components used in the web application. It provides services like request handling from users, management of web sessions, deployment of the war files, and other necessary functionalities that a web application requires to function. So, it's not that you can execute the war file directly. Instead, you deploy the .war file into a web server like Tomcat, which can then run the application inside the .war file.To put it simply, the .war file is the application, and Apache Tomcat is the platform that runs the application. Without a server like Apache Tomcat, the .war file on its own can't do anything, it's just a bunch of files archived together.

answer:To solve the problem with the given constraints, efficiently we can use binary search technique. Follow the algorithm below to understand the approach.1. Initialize `low` and `high` pointers. * `low` is the minimum element in the given array. * `high` is the maximum among the given limit and the maximum element in the array. 2. While `low` <= `high`: a. Find `mid` = `low` + (`high` - `low`) / 2. b. For every `num` in `nums`, calculate the number of increments needed to make `num` equal to `mid`. c. If total count of increments is less than or equal to `mid`, it means we can make all the elements of the array at most `mid` in `mid` moves. So, update `high` = `mid` – 1. d. If total count of increments is greater than `mid`, update `low` = `mid` + 1. e. If at any stage, `mid` exceeds `L`, return -1. 3. Return `high`.Here is the Python code for the above approach:``` pythonfrom typing import Listclass Solution: def min_moves(self, nums: List[int], L: int) -> int: high = max(max(nums), L) low = min(nums) while low <= high: mid = low + (high - low) // 2 total = sum((mid - num) for num in nums) if total > mid or mid > L: return -1 if total <= mid: high = mid - 1 else: low = mid + 1 return high```Remember, the code above assumes that we can increment elements to a maximum value of `L` and decrement elements to a minimum value of 0. Ensure to handle the case of negative values in `nums` or `L` as per problem requirements.

answer:Here is a Python solution for the problem:```pythondef fib(n): if n <= 1: return n else: return (fib(n-1) + fib(n-2))num_terms = int(input("Enter how many terms the Fibonacci series should be computed until: "))if num_terms <= 0: print("Invalid input, please enter a positive number")else: print("Fibonacci sequence up to ", num_terms, ":") for i in range(num_terms): print(fib(i))```The function `fib` is a recursive function that calculates the Fibonacci number at a certain index. The Fibonacci sequence is defined such that each number is the sum of the two preceding ones, starting from 0 and 1. That's why in the recursive `fib` function, we return `n` if `n` is less or equal to 1, else we return the sum of `fib(n-1)` and `fib(n-2)`.We then ask the user to enter how many terms they want the Fibonacci sequence to be computed until. The entered number is stored in `num_terms`.If `num_terms <= 0` we print an error message. If `num_terms` is a positive number, we print each Fibonacci number up to the entered number of terms.

answer:Yes, you're correct. The implied volatility skew does decrease as the expiry increases. This is often referred to as the "term structure of volatility skew".The mathematical proofs of this phenomenon can be quite complex and involve stochastic calculus. Here are few references that discuss this property:1) "Stochastic Volatility for Leverage Effect and Smiling" by Jean-Pierre Fouque et al. (Chapter 3 and Chapter 6). This book is a good resource for understanding the mathematical theory of volatility skew and its term structure.2) "The Volatility Surface: A Practitioner's Guide" by Jim Gatheral. This book discusses implied volatility and skew in a very approachable and practical manner.3) "Pricing and Hedging of Derivative Securities" by Lars Tyge Nielsen. This book discusses the basic principles of derivative pricing and hedging, including the roles of volatility and skew.4) "Option Volatility & Pricing: Advanced Trading Strategies and Techniques" by Sheldon Natenberg. This popular book is often considered a foundational text in options trading. It covers implied volatility and skew in detail.5) "Volatility and Correlation: The Perfect Hedger and the Fox" by Riccardo Rebonato. This book discusses various models used to describe the behavior of financial markets, focusing in particular on the volatilities and correlations of financial quantities.There's also a number of academic research papers that formalize this property, though they can get quite technical. You might want to start with "Smile Asymptotics II" by Roger W. Lee, "The smile of Black–Scholes: asymptotics of the implied volatility" by Mirela Cirja and "Large maturity asymptotics of the implied volatility in stochastic volatility models" by Elisa Alos and Frederic Utzet.