(a) Cônsider the following algorithm segment. for i := 1 to8 for j:= 1 to i [Statements in body of inner loop. None contain branching statements that lead outside the loop.] next j next i How many times will the inner loop be iterated when i = 2? How many times will the inner loop be iterated when i = 3? How many times will the inner loop be iterated when the algorithm is implemented and run? (b) Let n be a positive integer, and consider the following algorithm segment. for i := 1 to n for j := 1 to i [Statements in body of inner loop. None contain branching statements that lead outside the loop.] next j next i How many times will the inner loop be iterated when the algorithm is implemented and run?
(a) Cônsider the following algorithm segment. for i := 1 to8 for j:= 1 to i [Statements in body of inner loop. None contain branching statements that lead outside the loop.] next j next i How many times will the inner loop be iterated when i = 2? How many times will the inner loop be iterated when i = 3? How many times will the inner loop be iterated when the algorithm is implemented and run? (b) Let n be a positive integer, and consider the following algorithm segment. for i := 1 to n for j := 1 to i [Statements in body of inner loop. None contain branching statements that lead outside the loop.] next j next i How many times will the inner loop be iterated when the algorithm is implemented and 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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Question
5
![### Algorithm Analysis Exercise
#### (a) Consider the following algorithm segment:
```
for i := 1 to 8
for j := 1 to i
[Statements in body of inner loop.
None contain branching statements
that lead outside the loop.]
next j
next i
```
1. **How many times will the inner loop be iterated when \( i = 2 \)?**
**Answer:**
2. **How many times will the inner loop be iterated when \( i = 3 \)?**
**Answer:**
3. **How many times will the inner loop be iterated when the algorithm is implemented and run?**
**Answer:**
#### (b) Let \( n \) be a positive integer, and consider the following algorithm segment:
```
for i := 1 to n
for j := 1 to i
[Statements in body of inner loop.
None contain branching statements
that lead outside the loop.]
next j
next i
```
4. **How many times will the inner loop be iterated when the algorithm is implemented and run?**
**Answer:**
---
**Explanation:**
In part (a), the inner loop runs for each value of \( i \) from 1 to 8, iterating \( i \) times. You calculate the total iterations by summing up the series from 1 to 8.
In part (b), the loop runs similarly but for a variable \( n \). The total number of iterations of the inner loop is the sum of the first \( n \) positive integers.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fee2adb54-632e-4297-8ecb-2f461bfae280%2Fb6c0b861-f406-4691-96d4-ddd478e71e2b%2Fkix7eja_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Algorithm Analysis Exercise
#### (a) Consider the following algorithm segment:
```
for i := 1 to 8
for j := 1 to i
[Statements in body of inner loop.
None contain branching statements
that lead outside the loop.]
next j
next i
```
1. **How many times will the inner loop be iterated when \( i = 2 \)?**
**Answer:**
2. **How many times will the inner loop be iterated when \( i = 3 \)?**
**Answer:**
3. **How many times will the inner loop be iterated when the algorithm is implemented and run?**
**Answer:**
#### (b) Let \( n \) be a positive integer, and consider the following algorithm segment:
```
for i := 1 to n
for j := 1 to i
[Statements in body of inner loop.
None contain branching statements
that lead outside the loop.]
next j
next i
```
4. **How many times will the inner loop be iterated when the algorithm is implemented and run?**
**Answer:**
---
**Explanation:**
In part (a), the inner loop runs for each value of \( i \) from 1 to 8, iterating \( i \) times. You calculate the total iterations by summing up the series from 1 to 8.
In part (b), the loop runs similarly but for a variable \( n \). The total number of iterations of the inner loop is the sum of the first \( n \) positive integers.
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