我使用递归按字母顺序获取第一个字符串的java代码给出了不正确的输出。我需要添加一个辅助方法吗？

public class StringSort {
    public static String sortString(String str) {
        return sortStringRec(str, "");
    }

    private static String sortStringRec(String str, String sortedStr) {
        if (str.length() == 0) {
            return sortedStr;
        }

        char smallestChar = getSmallestChar(str);
        String remainingStr = removeChar(str, smallestChar);
        sortedStr += smallestChar;

        return sortStringRec(remainingStr, sortedStr);
    }

    private static char getSmallestChar(String str) {
        char smallestChar = str.charAt(0);
        for (int i = 1; i < str.length(); i++) {
            if (str.charAt(i) < smallestChar) {
                smallestChar = str.charAt(i);
            }
        }
        return smallestChar;
    }

    private static String removeChar(String str, char c) {
        StringBuilder sb = new StringBuilder();
        for (int i = 0; i < str.length(); i++) {
            if (str.charAt(i) != c) {
                sb.append(str.charAt(i));
            }
        }
        return sb.toString();
    }

    public static void main(String[] args) {
        String input = "recursion";
        String sortedString = sortString(input);
        System.out.println(sortedString);  // 输出：ceinorrsu
    }
}