**Problem Statement:**2. For each function \( f(n) \) and time \( t \) in the following table, determine the largest size \( n \) of a problem that can be solved in time \( t \), assuming that the algorithm to solve the problem takes \( f(n) \) microseconds.**Conversions:**- \( 1 \text{s} = 10^6 \) microseconds- \( 1 \text{m} = 60 \times 1 \text{s} \)- \( 1 \text{hr} = 60 \times 1 \text{m} \)- \( 1 \text{day} = 24 \times 1 \text{hr} \)- \( 1 \text{month} = 28 \times 1 \text{day} \)- \( 1 \text{year} = 12 \times 1 \text{month} \)- \( 1 \text{century} = 100 \times 1 \text{year} \)**Table: Time Complexity Analysis**| Function | 1 second | 1 minute | 1 hour | 1 day | 1 month | 1 year | 1 century ||----------|----------|----------|--------|-------|---------|--------|-----------|| \( \log n \) | | | | | | | || \( \sqrt{n} \) | | | | | | | || \( n \log n \) | | | | | | | || \( n^2 \) | | | | | | | || \( n^3 \) | | | | | | | || \( 2^n \) | | | | | | | || \( n! \) | | | | | | | |Each row in the table corresponds to a common complexity function, and each column corresponds to a time duration, with the goal of determining the maximum size \( n \) that can be handled. **Analysis Strategy:**To complete the table, calculate the largest possible \( n

1s=10^6 μs 1m = 60 x 1s log n Vn nlogn n² 2. For each function f(n) and time t in the following table, determine the largest size n of a problem that can be solved in time t, assuming that the algorithm to solve the problem takes f(n) microseconds. n³ 2n n! 1hr 60 x 1m 1 day = 24 x 1hr 1 second 1 minute 1 hour 1 month= 28 x 1 day 1 day 1 month 1 year = 12 x 1 month 1 year 1 century = 100 x 1 year 1 century

1s=10^6 μs 1m = 60 x 1s log n Vn nlogn n² 2. For each function f(n) and time t in the following table, determine the largest size n of a problem that can be solved in time t, assuming that the algorithm to solve the problem takes f(n) microseconds. n³ 2n n! 1hr 60 x 1m 1 day = 24 x 1hr 1 second 1 minute 1 hour 1 month= 28 x 1 day 1 day 1 month 1 year = 12 x 1 month 1 year 1 century = 100 x 1 year 1 century

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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**Problem Statement:**

2. For each function \( f(n) \) and time \( t \) in the following table, determine the largest size \( n \) of a problem that can be solved in time \( t \), assuming that the algorithm to solve the problem takes \( f(n) \) microseconds.

**Conversions:**

- \( 1 \text{s} = 10^6 \) microseconds
- \( 1 \text{m} = 60 \times 1 \text{s} \)
- \( 1 \text{hr} = 60 \times 1 \text{m} \)
- \( 1 \text{day} = 24 \times 1 \text{hr} \)
- \( 1 \text{month} = 28 \times 1 \text{day} \)
- \( 1 \text{year} = 12 \times 1 \text{month} \)
- \( 1 \text{century} = 100 \times 1 \text{year} \)

**Table: Time Complexity Analysis**

| Function | 1 second | 1 minute | 1 hour | 1 day | 1 month | 1 year | 1 century |
|----------|----------|----------|--------|-------|---------|--------|-----------|
| \( \log n \) | | | | | | | |
| \( \sqrt{n} \) | | | | | | | |
| \( n \log n \) | | | | | | | |
| \( n^2 \) | | | | | | | |
| \( n^3 \) | | | | | | | |
| \( 2^n \) | | | | | | | |
| \( n! \) | | | | | | | |

Each row in the table corresponds to a common complexity function, and each column corresponds to a time duration, with the goal of determining the maximum size \( n \) that can be handled.

**Analysis Strategy:**

To complete the table, calculate the largest possible \( n

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