1. Write a function called hwd_problem1 that takes two inputs: a vector v and a positive integer scalar n. You do NOT need to check these assumptions. The function needs to find the n consecutive elements in v whose sum is the maximum. It needs to return the sum and the index of the first of these elements. If there are multiple such n consecutive elements in v, it returns the first one, i.e, the one with the smallest index. Here is an example run:
1. Write a function called hwd_problem1 that takes two inputs: a vector v and a positive integer scalar n. You do NOT need to check these assumptions. The function needs to find the n consecutive elements in v whose sum is the maximum. It needs to return the sum and the index of the first of these elements. If there are multiple such n consecutive elements in v, it returns the first one, i.e, the one with the smallest index. Here is an example run:
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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How do I do number 1
![Sure, here's the transcription suitable for an educational website:
---
### 3. Problems
1. **Function - `hw4_problem1`**:
- **Inputs**: A vector `v` and a positive integer scalar `n`.
- **Objective**: Identify consecutive elements in `v` such that their sum is maximized.
- **Outputs**: The sum and the index of the first element in this segment. In case of ties, return the sum and index with the smallest initial index.
- **Example**:
```plaintext
>> [total ind] = hw4_problem1([1 2 3 4 5 4 3 2 1],3)
total = 13
ind = 4
```
2. **Function - `hw4_problem2`**:
- **Inputs**: A vector `v`.
- **Objective**: Determine if the elements of `v` are monotonically non-decreasing.
- **Outputs**: A logical true if the condition is satisfied, otherwise false. Indicates false if the input is not a vector.
3. **Function - `hw4_problem3`**:
- **Inputs**: A positive integer scalar `k`.
- **Objective**: Find the smallest prime number `p` less than 1000 such that `p+k` is also a prime. Return 0 if no such `p` exists.
- **Hints**: Utilize built-in functions like `primes` and/or `isprime`.
4. **Function - `hw4_problem4`**:
- **Calculation**:
\[
s = \sum_{k=1}^{n} \frac{1}{k} = 1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \ldots
\]
- **Objective**: Calculate the smallest `n` such that `s` exceeds `limit`. Return `n` and corresponding `s`.
- **Restriction**: Do not use for loops.
- **Examples**:
```plaintext
>> [n s] = hw4_problem4(1)
n = 2
s = 1.50000000000000
>> [n s] = hw4_problem4(2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F40a9514d-d7ca-4467-8320-3b6e9b54f257%2F1a342522-fa6c-4663-a497-65006a135688%2F3n8kcwj_processed.png&w=3840&q=75)
Transcribed Image Text:Sure, here's the transcription suitable for an educational website:
---
### 3. Problems
1. **Function - `hw4_problem1`**:
- **Inputs**: A vector `v` and a positive integer scalar `n`.
- **Objective**: Identify consecutive elements in `v` such that their sum is maximized.
- **Outputs**: The sum and the index of the first element in this segment. In case of ties, return the sum and index with the smallest initial index.
- **Example**:
```plaintext
>> [total ind] = hw4_problem1([1 2 3 4 5 4 3 2 1],3)
total = 13
ind = 4
```
2. **Function - `hw4_problem2`**:
- **Inputs**: A vector `v`.
- **Objective**: Determine if the elements of `v` are monotonically non-decreasing.
- **Outputs**: A logical true if the condition is satisfied, otherwise false. Indicates false if the input is not a vector.
3. **Function - `hw4_problem3`**:
- **Inputs**: A positive integer scalar `k`.
- **Objective**: Find the smallest prime number `p` less than 1000 such that `p+k` is also a prime. Return 0 if no such `p` exists.
- **Hints**: Utilize built-in functions like `primes` and/or `isprime`.
4. **Function - `hw4_problem4`**:
- **Calculation**:
\[
s = \sum_{k=1}^{n} \frac{1}{k} = 1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \ldots
\]
- **Objective**: Calculate the smallest `n` such that `s` exceeds `limit`. Return `n` and corresponding `s`.
- **Restriction**: Do not use for loops.
- **Examples**:
```plaintext
>> [n s] = hw4_problem4(1)
n = 2
s = 1.50000000000000
>> [n s] = hw4_problem4(2
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