Algorithm Design and Problem-solving：練習題

A programmer needs to document an algorithm that calculates the area of a circle. The requirements are:
1. Input the radius (\(r\)).
2. Check if \(r\) is greater than 0.
3. If valid, calculate \(Area = 3.14159 \times r^{2}\).
4. Output the result.

Which tool uses standard geometric symbols such as parallelograms for input/output and diamonds for decisions to represent this logic?

Study the following pseudocode snippet:

Total ← 0
FOR i ← 1 TO 5
  INPUT Value
  IF Value > 10 THEN
    Total ← Total + 1
  ENDIF
NEXT i

If the input values are 5, 12, 10, 15, and 8, what will be the final value of Total?

Consider the following pseudocode intended to find the smallest value in an array List with indices from 1 to 10:

Min ← List[1]
FOR Index ← 2 TO 10
  IF List[Index] < Min THEN
    Min ← List[Index]
  ENDIF
NEXT Index

If List contains the values [40, 30, 50, 20, 20, 10, 60, 5, 80, 100], how many times will the assignment Min ← List[Index] be executed?

An algorithm is being developed using stepwise refinement. Which of the following best describes this process?

A programmer is designing an algorithm to process a list of 500 employee names stored in a 1D array. The names are currently unsorted. The goal is to find the position of a specific name, "Zackary", within the array.

Which search algorithm must be used in this scenario, and what is the maximum number of comparisons required to determine if the name is not in the list?

In the context of Algorithm Design and Problem-solving, identify the computational thinking technique that involves hiding unnecessary details to focus on the essential characteristics required for a specific purpose.

Consider the following pseudocode snippet that performs a linear search on an array Data[1:5] containing the values [12, 7, 25, 14, 9]:

Found ← FALSE
Index ← 1
WHILE Index <= 5 AND NOT Found
  IF Data[Index] = 14 THEN
    Found ← TRUE
  ELSE
    Index ← Index + 1
  ENDIF
ENDWHILE

What is the final value of Index when the loop terminates?

A linked list is implemented using a 1D array of records. The list contains three nodes with StartPointer = 2:
- List[1]: Data = "Cat", NextPointer = -1
- List[2]: Data = "Apple", NextPointer = 3
- List[3]: Data = "Banana", NextPointer = 1

What is the third data value accessed when traversing the linked list from the start pointer?

A software developer is creating a computerized model of a city's public transport system. During the design phase, the developer applies abstraction and decomposition.

(a) Explain the purpose of abstraction when creating this model. (2 points)

(b) Suggest two details that would be essential to include in the model and two details that could be ignored through abstraction. (2 points)

(c) The task "Calculate Journey Time" needs to be broken down. Use decomposition to identify two sub-tasks that would be required to calculate the total travel time between two bus stops. (2 points)

Consider the following pseudocode function:

FUNCTION CalculateScore(Data[1:4] : INTEGER) RETURNS INTEGER
  DECLARE Result : INTEGER
  Result ← 0
  FOR i ← 1 TO 4
    IF Data[i] MOD 2 <> 0 THEN
      Result ← Result + (Data[i] * 2)
    ELSE
      Result ← Result + (Data[i] DIV 2)
    ENDIF
  NEXT i
  RETURN Result
ENDFUNCTION

If the array passed to the function contains the values [3, 8, 5, 4], what is the value returned by the function?