Database System Concepts
Database System Concepts
7th Edition
ISBN: 9780078022159
Author: Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher: McGraw-Hill Education
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[画像: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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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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