Calculating the Sum of Numbers

Welcome back to our journey into the world of algorithms! In this section, we'll tackle a fundamental problem that's surprisingly common in programming: calculating the sum of a series of numbers. This might seem simple, but it's a fantastic stepping stone to understanding how computers can perform repetitive tasks efficiently.

Imagine you have a list of numbers, say 5, 10, and 3. Your goal is to find their total. In human terms, you'd just add them up: 5 + 10 + 3 = 18. An algorithm essentially automates this process for a computer, especially when the list of numbers might be very long or change frequently.

To solve this problem algorithmically, we need a way to keep track of the running total as we go through the numbers. We'll introduce a variable, let's call it sum, and initialize it to zero. This sum variable will act as our accumulator.

graph TD;
    A[Start]
    B[Initialize sum = 0]
    C{Are there more numbers to add?}
    D[Get the next number]
    E[Add the number to sum]
    F{Are there more numbers to add?}
    G[Output sum]
    H[End]

    A --> B
    B --> C
    C -- Yes --> D
    D --> E
    E --> F
    F -- Yes --> D
    C -- No --> G
    F -- No --> G
    G --> H

Here's how the process works, step-by-step, using our example list of 5, 10, and 3:

1. Initialization: We start by setting sum to 0.

2. First Number: We take the first number, which is 5, and add it to our sum. So, sum becomes 0 + 5 = 5.

3. Second Number: Next, we take the second number, 10, and add it to the current sum. sum becomes 5 + 10 = 15.