Algorithm efficiency basics (fast vs slow) in Intro to Computing - Draw & Compare

Draw This - beginner

Draw a flowchart comparing two simple algorithms that find the largest number in a list of 5 numbers: Algorithm A checks each number one by one (slow), Algorithm B uses a method that compares pairs to reduce steps (faster). Show the steps and decisions clearly.

10 minutes

Hint 1

Hint 2

Hint 3

Hint 4

Hint 5

Grading Criteria

Start and End oval symbols present for both algorithms

Rectangles used for process steps

Diamonds used for decision points

Algorithm A shows checking each number sequentially

Algorithm B shows pairwise comparisons reducing steps

Flowchart paths lead to correct largest number result

Clear labeling of steps and decisions

Solution

Start
  |
  v
+-----------------------------+       +-----------------------------+
| Algorithm A: Check each num  |       | Algorithm B: Compare pairs   |
| 1. Set largest = first num   |       | 1. Compare num1 & num2       |
| 2. For each next number:     |       | 2. Keep larger of pair       |
|    - If number > largest     |       | 3. Compare num3 & num4       |
|      largest = number        |       | 4. Keep larger of pair       |
| 3. Compare largest with num5 |       | 5. Compare winner of pairs & num5 |
| 4. Result: largest           |       | 6. Result: largest number    |
+-----------------------------+       +-----------------------------+
  |                                         |
  v                                         v
 End                                       End

This flowchart shows two ways to find the largest number in a list of 5 numbers.

Algorithm A checks each number one by one. It starts by assuming the first number is the largest. Then it compares each of the other numbers to this largest value, updating it if a bigger number is found. This method requires 4 comparisons.

Algorithm B compares numbers in pairs to reduce the total comparisons. First, it compares the first two numbers and keeps the larger. Then it compares the next two numbers and keeps the larger. Finally, it compares the winner of these pairs with the last number to find the largest. This method uses fewer steps and is faster.

The flowchart uses ovals for start/end, rectangles for steps, and diamonds for decisions, making it easy to follow the logic.

Variations - 2 Challenges

[beginner] Draw a flowchart for finding the smallest number in a list of 7 numbers using a simple linear search (check each number one by one).

[intermediate] Draw a flowchart for finding the largest number in a list of 8 numbers using a divide-and-conquer approach (split list into pairs, find largest in each pair, then find largest among winners).

Practice

1.

What does algorithm efficiency mainly measure?

easy

A. How fast or slow an algorithm solves a problem

B. The color of the computer screen

C. The size of the computer's hard drive

D. The number of users on a website

Solution

1. Step 1: Understand the meaning of algorithm efficiency

   Algorithm efficiency tells us how quickly or slowly an algorithm completes its task.

2. Step 2: Compare options to the definition

   Only How fast or slow an algorithm solves a problem matches the concept of speed or slowness of solving a problem.

3. Final Answer:

   How fast or slow an algorithm solves a problem -> Option A

4. Quick Check:

   Algorithm efficiency = speed of solving [OK]

Hint: Algorithm efficiency = speed of solving problems [OK]

Common Mistakes:

• Confusing efficiency with hardware specs
• Thinking efficiency is about user count
• Mixing efficiency with unrelated computer parts

2.

Which of these is a sign of a faster algorithm?

for i in range(n):
    print(i)

easy

A. The algorithm jumps directly to the middle item

B. The algorithm checks every item one by one

C. The algorithm repeats the same step many times

D. The algorithm uses more memory than needed

Solution

1. Step 1: Analyze the given code

   The code loops through all items from 0 to n-1, checking each one.

2. Step 2: Compare with options describing speed

   Jumping directly to the middle item is faster than checking all items one by one.

3. Final Answer:

   The algorithm jumps directly to the middle item -> Option A

4. Quick Check:

   Jumping steps = faster algorithm [OK]

Hint: Faster algorithms skip steps, not check all [OK]

Common Mistakes:

• Thinking looping over all items is fast
• Confusing memory use with speed
• Ignoring the benefit of skipping steps

3.

What is the output speed difference between these two algorithms when n is very large?

Algorithm 1: Check every item one by one
Algorithm 2: Jump to the middle, then half repeatedly

medium

A. Algorithm 1 is faster because it checks all items

B. Algorithm 2 is faster because it reduces steps quickly

C. Both algorithms take the same time

D. Algorithm 1 uses less memory so it is faster

Solution

1. Step 1: Understand the two algorithms

   Algorithm 1 checks all items one by one (slow for large n). Algorithm 2 jumps to the middle and halves the search repeatedly (fast for large n).

2. Step 2: Compare efficiency for large n

   Algorithm 2 reduces the number of steps quickly, making it faster than Algorithm 1.

3. Final Answer:

   Algorithm 2 is faster because it reduces steps quickly -> Option B

4. Quick Check:

   Halving steps = faster algorithm [OK]

Hint: Halving steps beats checking all [OK]

Common Mistakes:

• Assuming checking all is faster
• Ignoring step reduction benefits
• Confusing memory use with speed

4.

Find the error in this slow algorithm and suggest a faster approach:

def find_item(lst, target):
    for item in lst:
        if item == target:
            return True
    return False

medium

A. The algorithm has a syntax error in the loop

B. The algorithm uses too much memory; reduce list size

C. The algorithm returns the wrong value

D. The algorithm checks all items; use binary search on sorted list instead

Solution

1. Step 1: Identify the algorithm's behavior

   The function checks each item one by one until it finds the target or ends.

2. Step 2: Suggest a faster method

   Using binary search on a sorted list jumps to the middle and halves the search, making it faster.

3. Final Answer:

   The algorithm checks all items; use binary search on sorted list instead -> Option D

4. Quick Check:

   Linear search slow; binary search fast [OK]

Hint: Replace linear search with binary search for speed [OK]

Common Mistakes:

• Thinking syntax error exists
• Confusing memory use with speed
• Believing return value is wrong

5.

You have a list of 1,000,000 numbers sorted in order. You want to find if the number 500,000 is in the list. Which algorithm is best and why?

hard

A. Randomly pick numbers until you find 500,000

B. Check each number from start to end; simple but slow

C. Use binary search to jump and halve the search area repeatedly

D. Sort the list again before searching

Solution

1. Step 1: Understand the problem and data

   The list is sorted with 1,000,000 numbers; searching for 500,000.

2. Step 2: Evaluate algorithm choices

   Checking each number (Check each number from start to end; simple but slow) is slow. Random picking (Randomly pick numbers until you find 500,000) is unreliable. Sorting again (Sort the list again before searching) wastes time. Binary search (Use binary search to jump and halve the search area repeatedly) uses the sorted order to jump and halve search area, making it fastest.

3. Final Answer:

   Use binary search to jump and halve the search area repeatedly -> Option C

4. Quick Check:

   Sorted list + binary search = fastest search [OK]

Hint: Use binary search on sorted lists for fast lookup [OK]

Common Mistakes:

• Choosing linear search for large sorted lists
• Thinking sorting again helps
• Relying on random guessing