finding the shortest word in an array of strings java

compareTo doesn't compare length of Strings, but their alphabetic order.

You should change your condition to if (SA[i].length()<first.length()).

In Java 8, you create a Comparator that will check the length of string which would make the array ascending, convert that list in a stream, and use sorted to sort the array, eventually, use findFirst to return the first element and get() to convert it into a String.

String[] words = new String[]{"Hello", "aadsads", "adssadsadads", "aaa"};
String shortest = Arrays.asList(words).stream()
        .sorted((e2, e1) -> e1.length() > e2.length() ? -1 : 1)
        .findFirst().get();

Shortest algorithm with Java 8+ using elegant Comparator.comparing method.

final String shortest = List.of("hello", "yes", "no")
                          .stream()
                          .min(Comparator.comparing(String::length))
                          .get();

Your method is close, but your variable names are a bit difficult to read to start you only need to call your method once to print the shortest name (calling it twice searches twice, and discards the first result),

public static void main(String[] args) {
    String[] SA = { "hello", "goodbye", "jack", "bye", "yes", "no", "yoo" };
    System.out.println("The shortest word is " + smallest(SA));
}

Next, it's usually a good idea to test that your input is valid (not null and at least one element). You should also decide how you want to handle those cases, I chose to return ""; below. Finally, you need to check length() the String(s) to get the shortest word. Something like,

public static String smallest(String words[]) {
    if (words == null || words.length < 1) {
        return "";
    }
    String smallest = words[0];
    for (int i = 1; i < words.length; i++) {
        if (words[i].length() < smallest.length()) {
            smallest = words[i];
        }
    }
    return smallest;
}// smallest

import java.util.Comparator;
import java.util.function.Function;

import static java.util.Arrays.asList;

public class Foo {

    public static void main(String[] args) {
        String[] words =
            {"hello", "goodbye", "jack", "bye", "yes", "no", "yoo"};
        System.out.println(shortestWord(words));
    }

    static String shortestWord(String[] words) {
        return asList(words).stream().min(compareBy(String::length)).get();
    }

    static <A, B extends Comparable<B>> Comparator<A> compareBy(
            Function<A, B> f) {
        return (A x, A y) -> f.apply(x).compareTo(f.apply(y));
    }
}

Im not sure what you are trying to do with the method compareTo(), but if you want to keep find the length of a string you use the length() method.

public class function 2
{

    public static void main(String[] args) {
        String [] SA = {"hello" , "goodbye"  , "jack" , "bye" , "yes" , "no" , "yoo"};

        System.out.println("The shortest word is " + smallest(SA));
    }

    public static String smallest(String SA[]) {
        //Keep track of the shortest word by index and length
        int index = 0, minLength = SA[0].length();
        for (int i = 1; i < SA.length; i++){
            //if the next string is smaller in length then we save that index and length in our variables
            if(SA[i].length() < minLength){
                index = i;
                minLength = SA[i].length();  
            }           
        }
        //returns the smallest word
        return SA[index];
    }

}