ACTIVITY 3.3 1. Answer questions based on the following algorithm segment. step 1 sum $$

Question

ACTIVITY 3.3 1. Answer questions based on the following algorithm segment. step 1 sum $$ <0 $$ Step 2 Input number Step 3 while number not equal to -99 do start loop Step 4 sum $$ \leftarrow $$ sum + number end loop Step 5 Output sum 1.1 Draw a tracetable for an input value of 6. (up until the sum is 24) 12 Write in your own words what the problem is with this segment. 1.3 Will step 5 ever get executed? Substantiate your answer 1.4 How can we solve this problem? You may use step numbers in your answer if you wish th delete or insert steps.

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### **1.1 Trace Table for Input Value of 6 (Up Until Sum is 24)**

Assuming the user enters the number **6** repeatedly until the sum reaches **24**, the trace table would look like this:

| **Step** | **sum** | **number** | **Description**                            |
|----------|---------|------------|--------------------------------------------|
| 1        | 0       | -          | Initialize `sum` to 0                      |
| 2        | 0       | 6          | Input `number` = 6                         |
| 3        | 0       | 6          | Check if `number` ≠ -99 (True) → Enter loop |
| 4        | 6       | 6          | `sum` ← `sum` + `number` = 0 + 6 = 6       |
| 3        | 6       | 6          | Check if `number` ≠ -99 (True) → Enter loop |
| 4        | 12      | 6          | `sum` ← `sum` + `number` = 6 + 6 = 12      |
| 3        | 12      | 6          | Check if `number` ≠ -99 (True) → Enter loop |
| 4        | 18      | 6          | `sum` ← `sum` + `number` = 12 + 6 = 18     |
| 3        | 18      | 6          | Check if `number` ≠ -99 (True) → Enter loop |
| 4        | 24      | 6          | `sum` ← `sum` + `number` = 18 + 6 = 24     |

*Note:* Without additional input steps inside the loop, the `number` remains **6**, and the loop continues indefinitely. However, for the purpose of this trace table, we've stopped once the sum reaches **24**.

---

### **1.2 Problem with the Algorithm Segment**

The primary issue with the algorithm is that **there is no mechanism to update the `number` within the loop**. After the initial input in Step 2, the `number` remains unchanged inside the `while` loop. This results in an **infinite loop** because the condition `number ≠ -99` will always be true unless the initial `number` is **-99**. Consequently, the program never exits the loop to execute Step 5 (`Output sum`).

---

### **1.3 Execution of Step 5**

**Will Step 5 Ever Get Executed?**

**No, Step 5 will never get executed** under the current algorithm structure **if the initial `number` is not -99**. Since the `while` loop continuously checks if `number` is not equal to **-99** and there is no additional input to potentially change `number` within the loop, the loop becomes infinite. This means the program is stuck in the loop and never reaches the `Output sum` step.

---

### **1.4 Solution to the Problem**

To resolve the issue of the infinite loop and ensure that Step 5 (`Output sum`) is executed, **we need to allow the user to input a new `number` within the loop**. This way, the user can eventually input **-99** to terminate the loop. Here's how you can modify the algorithm:

1. **Initialize `sum` to 0.**
   ```plaintext
   Step 1: sum ← 0
   ```

2. **Input the first `number`.**
   ```plaintext
   Step 2: Input number
   ```

3. **Start the loop that continues until `number` is -99.**
   ```plaintext
   Step 3: while number ≠ -99 do
   ```

4. **Add the current `number` to `sum`.**
   ```plaintext
   Step 4: sum ← sum + number
   ```

5. **Input the next `number` inside the loop.**
   ```plaintext
   Step 5: Input number
   ```
   
6. **End of the loop.**

7. **Output the final `sum`.**
   ```plaintext
   Step 6: Output sum
   ```

**Revised Algorithm:**
```plaintext
Step 1: sum ← 0
Step 2: Input number
Step 3: while number ≠ -99 do
    Step 4: sum ← sum + number
    Step 5: Input number
Step 6: Output sum
```

**Explanation of Changes:**

- **Inserted Step 5 (`Input number`) within the loop:** This allows the user to provide a new input each time the loop iterates, which can eventually be **-99** to terminate the loop.
  
- **Adjusted Step Numbers accordingly:** After inserting the new input step, ensure that the subsequent steps are renumbered to maintain clarity.

**Benefits of the Revised Algorithm:**

- **Prevents Infinite Loop:** By allowing `number` to be updated within the loop, the condition `number ≠ -99` can eventually become false, allowing the loop to terminate.
  
- **Enables Proper Sum Calculation:** The `sum` is accurately updated with each new input until the termination condition is met.

---

By implementing these changes, the algorithm will function as intended, allowing users to input multiple numbers, accumulate their sum, and terminate the input sequence by entering **-99**, after which the final sum will be correctly outputted.
**1.1 Trace Table for Input Value of 6 (Up Until Sum is 24):** | **Step** | **sum** | **number** | **Description** | |----------|---------|------------|--------------------------------------------| | 1 | 0 | - | Initialize `sum` to 0 | | 2 | 0 | 6 | Input `number` = 6 | | 3 | 0 | 6 | Check if `number` ≠ -99 (True) → Enter loop | | 4 | 6 | 6 | `sum` ← `sum` + `number` = 0 + 6 = 6 | | 3 | 6 | 6 | Check if `number` ≠ -99 (True) → Enter loop | | 4 | 12 | 6 | `sum` ← `sum` + `number` = 6 + 6 = 12 | | 3 | 12 | 6 | Check if `number` ≠ -99 (True) → Enter loop | | 4 | 18 | 6 | `sum` ← `sum` + `number` = 12 + 6 = 18 | | 3 | 18 | 6 | Check if `number` ≠ -99 (True) → Enter loop | | 4 | 24 | 6 | `sum` ← `sum` + `number` = 18 + 6 = 24 | *Note:* The loop continues until the sum reaches **24**. --- **1.2 Problem with the Algorithm Segment:** The algorithm has an infinite loop because there's no way to change the `number` inside the loop, so it never becomes **-99** to exit. --- **1.3 Will Step 5 Ever Get Executed?** No, Step 5 (`Output sum`) will never execute because the loop never ends. --- **1.4 Solution to the Problem:** Add an input step inside the loop to allow `number` to be updated: 1. **Initialize `sum` to 0.** 2. **Input the first `number`.** 3. **Start the loop that continues until `number` is -99.** 4. **Add the current `number` to `sum`.** 5. **Input the next `number` inside the loop.** 6. **End of the loop.** 7. **Output the final `sum`.** This ensures the loop can terminate and Step 5 is executed.

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