Nested Sum

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JCSU Unit 2 Problem Set 1 (Click for link to problem statements)

Problem Highlights

• 💡 Difficulty: Easy
• ⏰ Time to complete: 10 mins
• 🛠️ Topics: Nested Loops, Iteration

1: U-nderstand

Understand what the interviewer is asking for by using test cases and questions about the problem.

• Established a set (2-3) of test cases to verify their own solution later.
• Established a set (1-2) of edge cases to verify their solution handles complexities.
• Have fully understood the problem and have no clarifying questions.
• Have you verified any Time/Space Constraints for this problem?

• What is the goal of the problem?
  • The goal is to calculate the sum of all integers in a list of lists.
• Are there constraints on input?
  • The input will always be a list of lists containing integers.

HAPPY CASE Input: nums = [ [1, 2, 3], [4, 5], [6] ] Output: 21 Explanation: The sum is calculated as 1 + 2 + 3 + 4 + 5 + 6 = 21.

EDGE CASE Input: nums = [[]] Output: 0 Explanation: An empty list of lists results in a sum of 0.

2: M-atch

Match what this problem looks like to known categories of problems, e.g. Linked List or Dynamic Programming, and strategies or patterns in those categories.

For nested list summing problems, we want to consider the following approaches:

• Nested Loops: Iterate through each sublist and then through each number in that sublist to calculate the sum.
• Flattening and Summing: Flatten the list of lists into a single list and calculate the sum.

3: P-lan

Plan the solution with appropriate visualizations and pseudocode.

General Idea:
Use nested loops to iterate through each sublist in the main list, then iterate through each element of the sublist and add the values to a running total.

Steps:

1. Initialize a variable total to 0.
2. For each sublist in the input nums:
   • For each number in the sublist:
     • Add the number to total.
3. Return the value of total.

4: I-mplement

Implement the code to solve the algorithm.

def nested_sum(nums):
    total = 0  # Initialize the total sum
    for sublist in nums:  # Iterate through each sublist in the list
        for num in sublist:  # Iterate through each number in the sublist
            total += num  # Add the number to the total sum
    return total  # Return the total sum

5: R-eview

Review the code by running specific example(s) and recording values (watchlist) of your code's variables along the way.

Example 1:

• Input: nums = [ [1, 2, 3], [4, 5], [6] ]
• Expected Output: 21
• Observed Output: 21

Example 2:

• Input: nums = [[]]
• Expected Output: 0
• Observed Output: 0

6: E-valuate

Evaluate the performance of your algorithm and state any strong/weak or future potential work.

Assume n is the total number of integers in the nested lists.

• Time Complexity: O(n) because we iterate through each number exactly once.
• Space Complexity: O(1) because we only use a single variable to store the sum.