Recursive String Building and Summation

Recursion on Strings shrinks the input by removing or processing one character per call. The recursive case typically uses substring to peel off a piece; the base case returns an empty String "" or a final character.

Summation works the same way: process one element, then add to the result of the recursive call on the rest.

On the AP exam, String recursion appears in reverse, repeat, and palindrome FRQs; summation appears in digit-sum and array-sum problems.

Reverse a String

public String reverseString(String s) {
    if (s.length() <= 1) return s;
    return reverseString(s.substring(1)) + s.charAt(0);
}

Peels off the first char; recurses on the rest; appends the peeled char at the end. The last char of the result is the first char of the input.

Repeat a String n times

public String repeat(String s, int n) {
    if (n <= 0) return "";
    return s + repeat(s, n - 1);
}

Each call concatenates one copy of s; n counts down. repeat("ab", 3) returns "ababab".

Sum the digits of a number

public int sumDigits(int n) {
    if (n == 0) return 0;
    return (n % 10) + sumDigits(n / 10);
}

Peels off the last digit; recurses on the rest of the number; adds the digit to the smaller sum.

The shared pattern

• Base case: empty or zero — returns the additive identity ("" or 0).
• Recursive case: isolate one piece (first char, last digit) and combine with the recursive call.
• Direction: input shrinks by one piece each call.