Algorithm design (planning solutions) in Intro to Computing - Practice Problems & Coding Challenges

Challenge - 5 Problems

🧠 Conceptual

intermediate

Understanding Algorithm Steps

Which of the following best describes the first step in designing an algorithm to sort a list of numbers?

A Identify the input and output clearly

B Write the code directly without planning

C Ignore edge cases to save time

D Test the algorithm with random data first

💡 Hint

Think about what you need to know before starting to solve a problem.

The first step in algorithm design is to clearly understand what input you have and what output you want. This helps in planning the solution effectively.

❓ trace

intermediate

Tracing Algorithm Execution

Given the flowchart below for finding the maximum number in a list, what is the value of the maximum after processing the list [3, 7, 2, 9, 5]?

Intro to Computing

Start -> Set max to first element -> For each element in list: If element > max, set max = element -> End

A 5

B 7

C 9

D 3

💡 Hint

Compare each number with the current max and update if larger.

The algorithm compares each number to the current max and updates it if the number is larger. The largest number in the list is 9.

❓ Comparison

advanced

Comparing Algorithm Efficiency

Which algorithm design approach is generally more efficient for sorting large datasets?

A Randomly swapping elements until sorted

B Bubble sort with nested loops

C Checking each element one by one without sorting

D Divide and conquer approach like merge sort

💡 Hint

Think about how breaking problems into smaller parts helps.

Divide and conquer algorithms like merge sort break the problem into smaller parts and combine results, making them efficient for large datasets.

❓ identification

advanced

Identifying Algorithm Components

In the algorithm design process, which component is responsible for deciding the next step based on a condition?

A Decision or conditional statement

B Input

C Loop

D Output

💡 Hint

This component helps the algorithm choose between different paths.

Decision or conditional statements allow the algorithm to choose the next step based on a condition, guiding the flow.

🚀 Application

expert

Designing an Algorithm for a Real-World Problem

You need to design an algorithm to help a librarian find a book by its title in a large unsorted collection. Which approach is best to plan the solution?

A Ask the librarian to remember the position of each book

B Scan each book one by one until the title is found

C Sort the books by title first, then use binary search

D Randomly pick books until the correct title is found

💡 Hint

Consider the collection is unsorted and you want to find a specific item.

Since the collection is unsorted, scanning each book one by one is the straightforward approach. Sorting first would take extra time and is not part of the problem.

Practice

1. What is the main purpose of designing an algorithm before coding?

easy

A. To plan clear steps to solve a problem

B. To write the final program code

C. To test the program output

D. To choose the programming language

Solution

1. Step 1: Understand the role of an algorithm

   An algorithm is a step-by-step plan to solve a problem before coding.

2. Step 2: Differentiate algorithm from coding and testing

   Coding is writing the program, testing checks output, but algorithm is planning steps.

3. Final Answer:

   To plan clear steps to solve a problem -> Option A

4. Quick Check:

   Algorithm = plan steps [OK]

Hint: Algorithms are plans, not code or tests [OK]

Common Mistakes:

• Confusing algorithm with coding
• Thinking algorithm is testing output
• Believing algorithm chooses language

2. Which of the following is the correct way to start an algorithm for finding the largest number in a list?

easy

A. Set largest to 0

B. Set largest to the first number in the list

C. Print the list

D. Sort the list alphabetically

Solution

1. Step 1: Understand initialization in algorithms

   To find the largest number, start by assuming the first number is the largest.

2. Step 2: Evaluate other options

   Setting largest to 0 may fail if all numbers are negative; printing or sorting alphabetically is unrelated.

3. Final Answer:

   Set largest to the first number in the list -> Option B

4. Quick Check:

   Initialize largest with first list item [OK]

Hint: Initialize with first list item, not zero [OK]

Common Mistakes:

• Starting largest at 0 without checking list values
• Sorting list alphabetically instead of numerically
• Printing list instead of initializing variable

3. Consider this algorithm to sum numbers from 1 to 4:

sum = 0
for i in range(1, 5):
  sum = sum + i
print(sum)

What will be the output?

medium

A. 10

B. 15

C. 0

D. Error

Solution

1. Step 1: Understand the loop range

   The loop runs with i = 1, 2, 3, 4 (range(1,5) excludes 5).

2. Step 2: Calculate sum step-by-step

   sum = 0+1=1, 1+2=3, 3+3=6, 6+4=10.

3. Final Answer:

   10 -> Option A

4. Quick Check:

   1+2+3+4 = 10 [OK]

Hint: Sum numbers 1 to 4 = 10 quickly [OK]

Common Mistakes:

• Including 5 in the sum
• Confusing range end as inclusive
• Forgetting to add all numbers

4. This algorithm is meant to find the smallest number in a list:

numbers = [3, 1, 4]
smallest = 0
for num in numbers:
  if num < smallest:
    smallest = num
print(smallest)

What is the error in this algorithm?

medium

A. The print statement is missing parentheses

B. The loop should use 'while' instead of 'for'

C. The comparison should be 'num > smallest'

D. smallest should start as the first list number, not 0

Solution

1. Step 1: Check initialization of smallest

   Starting smallest at 0 fails if all numbers are positive and greater than 0.

2. Step 2: Correct initialization

   Set smallest to the first number in the list (3) to compare properly.

3. Final Answer:

   smallest should start as the first list number, not 0 -> Option D

4. Quick Check:

   Initialize smallest with first list item [OK]

Hint: Initialize smallest with first list item, not zero [OK]

Common Mistakes:

• Using wrong comparison operator
• Confusing for and while loops
• Ignoring initialization importance

5. You want to design an algorithm to count how many words in a sentence start with the letter 'a'. Which step should you include in your algorithm?

hard

A. Sort the words alphabetically before counting

B. Count all letters 'a' in the sentence regardless of position

C. Split the sentence into words and check each word's first letter

D. Replace all 'a's with 'b's before counting

Solution

1. Step 1: Break sentence into words

   Splitting the sentence into words allows checking each word individually.

2. Step 2: Check first letter of each word

   Count only words whose first letter is 'a' to meet the problem requirement.

3. Final Answer:

   Split the sentence into words and check each word's first letter -> Option C

4. Quick Check:

   Check first letter of each word [OK]

Hint: Split sentence, check first letter of each word [OK]

Common Mistakes:

• Counting all 'a's, not just word starts
• Sorting words unnecessarily
• Replacing letters before counting