java.lang.StringBuilder uses a resizing array to represent a string of length n, with the first character in the string at array index 0 and the last character in the string at array index n - 1. Assume the array length is doubled when full and halved when one-quarter full. For reference, here is a partial API public class StringBuilder StringBuilder() create an empty string void append(char c) add character c to the end of the string void prepend(char c) add character c to the beginning of the string char charAt(int i) return the character at index i and a diagram of the underlying representation for reference. first character last character a[] M. D R M. 1. 2. 3 7. Mark all properties that apply. O e(1) time in the worst case for charAt(). O e(1) time in the worst case for append. Starting from an empty StringBuilder, any sequence of n append operations takes O(n) time in the worst case. Starting from an empty stringBuilder, any sequence of n append and prepend operations takes (n) time in the worst case. OUses (n) memory in the worst case.

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### Java StringBuilder Overview

The `java.lang.StringBuilder` class uses a resizing array to represent a string of length \( n \). The first character in the string is placed at array index 0, and the last character is at array index \( n - 1 \). The array length is doubled when full and halved when one-quarter full to efficiently manage memory.

#### Partial API Reference

```java
public class StringBuilder {
    StringBuilder()              // create an empty string
    void append(char c)          // add character c to the end of the string
    void prepend(char c)         // add character c to the beginning of the string
    char charAt(int i)           // return the character at index i
}
```

#### Diagram of Underlying Representation

A diagram is provided to illustrate how the `StringBuilder` manages its character array:

- **Array Indexing:**
  - The array is indexed from 0 to \( n \).
  - Characters are stored sequentially in the array with unused space illustrated after the last character.

- **Example:**
  - First character: Index 0 ('M')
  - Last character: Index 6 ('M')
  - Array contents: ['M', 'I', 'D', 'T', 'E', 'R', 'M', '-']
  - Unused space (indicated by '-') follows the last character.

```plaintext
  first character                  last character
  a[] ->  M  I  D  T  E  R  M  -
         0  1  2  3  4  5  6  7
```

#### Performance Properties

Please mark any properties that apply:

- [ ] \( \Theta(1) \) time in the worst case for `charAt()`.
- [ ] \( \Theta(1) \) time in the worst case for `append`.
- [ ] Starting from an empty `StringBuilder`, any sequence of \( n \) `append` operations takes \( \Theta(n) \) time in the worst case.
- [ ] Starting from an empty `StringBuilder`, any sequence of \( n \) `append` and `prepend` operations takes \( \Theta(n) \) time in the worst case.
- [ ] Uses \( \Theta(n) \) memory in the worst case.

This overview is designed to assist students in
Transcribed Image Text:### Java StringBuilder Overview The `java.lang.StringBuilder` class uses a resizing array to represent a string of length \( n \). The first character in the string is placed at array index 0, and the last character is at array index \( n - 1 \). The array length is doubled when full and halved when one-quarter full to efficiently manage memory. #### Partial API Reference ```java public class StringBuilder { StringBuilder() // create an empty string void append(char c) // add character c to the end of the string void prepend(char c) // add character c to the beginning of the string char charAt(int i) // return the character at index i } ``` #### Diagram of Underlying Representation A diagram is provided to illustrate how the `StringBuilder` manages its character array: - **Array Indexing:** - The array is indexed from 0 to \( n \). - Characters are stored sequentially in the array with unused space illustrated after the last character. - **Example:** - First character: Index 0 ('M') - Last character: Index 6 ('M') - Array contents: ['M', 'I', 'D', 'T', 'E', 'R', 'M', '-'] - Unused space (indicated by '-') follows the last character. ```plaintext first character last character a[] -> M I D T E R M - 0 1 2 3 4 5 6 7 ``` #### Performance Properties Please mark any properties that apply: - [ ] \( \Theta(1) \) time in the worst case for `charAt()`. - [ ] \( \Theta(1) \) time in the worst case for `append`. - [ ] Starting from an empty `StringBuilder`, any sequence of \( n \) `append` operations takes \( \Theta(n) \) time in the worst case. - [ ] Starting from an empty `StringBuilder`, any sequence of \( n \) `append` and `prepend` operations takes \( \Theta(n) \) time in the worst case. - [ ] Uses \( \Theta(n) \) memory in the worst case. This overview is designed to assist students in
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