Database System Concepts
Database System Concepts
7th Edition
ISBN: 9780078022159
Author: Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher: McGraw-Hill Education
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How many squares are drawn if foo(0,0,5,2) is called?

The provided text describes a function in an educational context regarding computer programming and graphics.

---

**Explanation of the Function:**

The text defines a recursive function `foo` that uses an auxiliary function called `drawSquare`. The `drawSquare(double x, double y, double halfLen)` function is responsible for drawing a square centered at coordinates `(x, y)` with a side length that is double the given `halfLen`. For instance, `drawSquare(0,0,5)` would draw a square centered at the origin `(0,0)` with a side length of `10`.

**Detailed Breakdown of the Code:**

```java
public static void foo(double x, double y, double len, int n) {
    if (n < 1) return;
    drawSquare(x, y, len);
    foo(x - len/2, y - len/2, len/2, n - 1);
    foo(x - len/2, y + len/2, len/2, n - 1);
    foo(x + len/2, y + len/2, len/2, n - 1);
    foo(x + len/2, y - len/2, len/2, n - 1);
}
```

**Function Behavior:**

- **Base Case:** The recursion stops when `n < 1`. In this case, the function simply returns without doing anything.
  
- **Recursive Case:** 
  - First, it draws a square centered at `(x, y)` with side length `len`.
  - Then, it makes four recursive calls to itself, each time subdividing the current square into four smaller squares and recentering. 
    - The square's center for the recursive calls is adjusted by half of the current length (`len/2`) to cover all four quadrants:
      - Bottom-left
      - Top-left
      - Top-right
      - Bottom-right

This method is often used to create fractal patterns or divide graphical space efficiently.

--- 

This explanation provides a detailed view of the recursive structure and graphical operations performed by the `foo` function, essential for understanding recursion and graphical transformations in programming.
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Transcribed Image Text:The provided text describes a function in an educational context regarding computer programming and graphics. --- **Explanation of the Function:** The text defines a recursive function `foo` that uses an auxiliary function called `drawSquare`. The `drawSquare(double x, double y, double halfLen)` function is responsible for drawing a square centered at coordinates `(x, y)` with a side length that is double the given `halfLen`. For instance, `drawSquare(0,0,5)` would draw a square centered at the origin `(0,0)` with a side length of `10`. **Detailed Breakdown of the Code:** ```java public static void foo(double x, double y, double len, int n) { if (n < 1) return; drawSquare(x, y, len); foo(x - len/2, y - len/2, len/2, n - 1); foo(x - len/2, y + len/2, len/2, n - 1); foo(x + len/2, y + len/2, len/2, n - 1); foo(x + len/2, y - len/2, len/2, n - 1); } ``` **Function Behavior:** - **Base Case:** The recursion stops when `n < 1`. In this case, the function simply returns without doing anything. - **Recursive Case:** - First, it draws a square centered at `(x, y)` with side length `len`. - Then, it makes four recursive calls to itself, each time subdividing the current square into four smaller squares and recentering. - The square's center for the recursive calls is adjusted by half of the current length (`len/2`) to cover all four quadrants: - Bottom-left - Top-left - Top-right - Bottom-right This method is often used to create fractal patterns or divide graphical space efficiently. --- This explanation provides a detailed view of the recursive structure and graphical operations performed by the `foo` function, essential for understanding recursion and graphical transformations in programming.
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