Space complexity of adding Java Strings char by char

Question

When building a Java String char by char through a loop through "addition", it can be observed that the time complexity of performing this operation is poor: it is of quadratic O(n^2) time. However, I am wondering if the space complexity of "adding" a String char-by-char through a loop is also poor.

Here is a minimal example of a program which performs building a String via char-by-char addition with stopwatch timing. The results I got shown below clearly show a quadratic curve:

/**Create a String of n 'A's char-by-char.
 * @param n Number of 'A's to be appended
 * @return The finished string
 */
public static String appendString(int n) {
    String str = "";
    // Timed run starts here
    long t = System.currentTimeMillis();
    // String concatenation occurs here
    for (int k = 0; k < n; k++)
        str += "A";
    t = System.currentTimeMillis() - t;
    // Timed run ends
    System.out.printf("%d\t%d\n", n, t);
    return str;
}

Although I can get the time complexity of the program, I am wondering what is the space complexity of building a String char-by-char?

A detailed answer that addresses memory management is preferred. (I suspect it is also quadratic because Strings are immutable, and each time you have to allocate new memory for ever-increasing Strings)

Note: This is not a duplicate of String concatenation complexity in C++ and Java because it does not address space complexity. I am specifically asking for a detailed space complexity analysis.

Answer 1

It uses quadratic space. Or, rather, a quadratic amount of space is allocated, because each iteration of the loop will (at least in code which the JIT doesn't do something clever with) allocate a new char array:

new char[1]
new char[2]
new char[3]
// Etc.

The reason for the quadratic time performance is copying the strings into these ever-larger arrays.