Algorithm design (planning solutions) in Intro to Computing - Draw & Build Visually

Draw This - beginner

Draw a flowchart to plan an algorithm that finds the largest of three numbers: A=15, B=23, C=8.

10 minutes

Hint 1

Hint 2

Hint 3

Hint 4

Grading Criteria

Start and End symbols present

Input step clearly shown

Decision diamonds used for comparisons

Correct comparison order (A vs B, then C vs Max)

Max variable updated correctly

Output step to display largest number

Flow lines correctly connect all steps

Solution

  +-------+
  | Start |
  +-------+
      |
      v
  +---------------------+
  | Input A=15, B=23, C=8 |
  +---------------------+
      |
      v
  +-----------------+
  | Is A > B?       |<-------------------+
  +-----------------+                    |
     /       \                          |
   Yes       No                         |
   /          \                        |
  v            v                       |
+---------+  +---------+               |
| Max=A   |  | Max=B   |               |
+---------+  +---------+               |
      |          |                     |
      +----------+---------------------+
                 |
                 v
         +-----------------+
         | Is C > Max?     |<----------------+
         +-----------------+                 |
            /        \                       |
          Yes        No                      |
           /          \                      |
          v            v                     |
     +---------+  +---------+                |
     | Max=C   |  | Max=Max |                |
     +---------+  +---------+                |
           |          |                      |
           +----------+----------------------+ 
                      |
                      v
               +--------------+
               | Display Max  |
               +--------------+
                      |
                      v
                 +-------+
                 | End   |
                 +-------+

This flowchart starts by taking three numbers A=15, B=23, and C=8 as input.

First, it compares A and B using a decision diamond. If A is greater than B, it sets Max to A; otherwise, Max is set to B.

Next, it compares C with the current Max. If C is greater, Max is updated to C; otherwise, Max remains the same.

Finally, the flowchart displays the largest number stored in Max and ends.

This step-by-step comparison ensures the largest of the three numbers is found correctly.

Variations - 2 Challenges

[beginner] Draw a flowchart to find the smallest of three numbers: A=12, B=7, C=19.

[intermediate] Draw a flowchart to find the largest of four numbers: A=10, B=25, C=17, D=22.

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