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LESSON 142 OF 410 · LOOPS & GLOBAL VARIABLES

Student Grades - Python Solution with O(n) Time Complexity

Practice Read the full explanation

Given the grades of a student as a list, determine if the student has passed the class.

A Student has passed the class if the average of grades is 5 or more.

The average is defined as (grades[0] + grades[1] + ... + grades[n - 1]) / n

Example 1:

Input: grades = [4, 7, 5, 9, 8, 2]
Output: True
Explanation:
average = (4 + 7 + 5 + 9 + 8 + 2) / 6 =
= 35 / 6 = 5.833333333... >= 5

Example 2:

Input: grades = [4, 7, 5, 3, 8, 2]
Output: False
Explanation:
average = (4 + 7 + 5 + 3 + 8 + 2) / 6 =
= 29 / 6 = 4.83333.. < 5

Hints:

The problem can be broken in 3 steps:
1. Compute the sum of the array
2. Compute the average by dividing the sum by the length of the array
3. Decide the result based on the average being greater than or equal to 5
Let's start with step 1: How can we compute the sum of the array?

First of all, we should store this sum somewhere as we compute it. That 'somewhere' is a variable, let's name it sum. We have to iterate through every element of grades and add its value to sum. How can we achieve this?

With a loop! Let's use a for loop and a variable grade to iterate through the elements: 
sum = 0
for each grade in grades:
	sum += grade
When the loop terminates, we know the sum. What should we do next?

We should compute average = sum / length and return average >= 5: 
sum = 0
for each grade in grades:
	sum += grade
average = sum / length
return average >= 5


We have a for loop that performs exactly n iterations (n is the length of grades), thus the Time Complexity is O(n).
The only extra space we use are the variables sum, average and the iterator variable grade inside the loop, thus the Extra Space used is O(1).
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    PYTHON · LOOPS & GLOBAL VARIABLES

    Student Grades in Python, explained

    Understanding the Problem

    The core challenge of this problem is to determine if the average of a list of grades meets a certain threshold. This is a common problem in educational software where determining pass/fail status based on grades is essential.

    Potential pitfalls include not correctly calculating the sum or average, or misunderstanding the threshold condition.

    Approach

    To solve this problem, we can break it down into three main steps:

    1. Compute the sum of the grades.
    2. Compute the average by dividing the sum by the number of grades.
    3. Check if the average is greater than or equal to 5.

    Let's start with a naive solution and then discuss why it is optimal for this problem.

    Naive Solution

    The naive solution involves iterating through the list of grades to compute the sum, then dividing by the number of grades to get the average. This approach is straightforward and efficient for this problem.

    Optimized Solution

    Given the simplicity of the problem, the naive solution is already optimal. The time complexity is O(n) because we need to iterate through all n grades to compute the sum. The space complexity is O(1) because we only use a few extra variables.

    Algorithm

    Here is a step-by-step breakdown of the algorithm:

    1. Initialize a variable sum to 0.
    2. Iterate through each grade in the list and add it to sum.
    3. Compute the average by dividing sum by the length of the list.
    4. Return True if the average is greater than or equal to 5, otherwise return False.

    Code Implementation

    def has_passed(grades):
    # Step 1: Compute the sum of the grades
    total_sum = 0
    for grade in grades:
        total_sum += grade
    
    # Step 2: Compute the average
    average = total_sum / len(grades)
    
    # Step 3: Check if the average is >= 5
    return average >= 5

# Example usage:
grades1 = [4, 7, 5, 9, 8, 2]
print(has_passed(grades1))  # Output: True

grades2 = [4, 7, 5, 3, 8, 2]
print(has_passed(grades2))  # Output: False

    Complexity Analysis

    The time complexity of this solution is O(n) because we iterate through the list of grades once. The space complexity is O(1) because we only use a few extra variables.

    Edge Cases

    Potential edge cases include:

    • An empty list of grades. This should be handled by checking if the list is empty before computing the average.
    • All grades being the same. The algorithm will still correctly compute the average.

    Testing

    To test the solution comprehensively, consider the following test cases:

    • Grades with all values above 5.
    • Grades with all values below 5.
    • Grades with a mix of values above and below 5.
    • An empty list of grades.

    Thinking and Problem-Solving Tips

    When approaching such problems, it is helpful to break down the problem into smaller steps and solve each step methodically. Practice similar problems to improve problem-solving skills.

    Conclusion

    In this blog post, we discussed how to determine if a student has passed based on their grades. We covered the problem definition, approach, algorithm, code implementation, complexity analysis, edge cases, and testing. Understanding and solving such problems is crucial for developing strong problem-solving skills.

    Additional Resources

    For further reading and practice problems, consider the following resources:

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