Here is the explanation from the API of the LinkedList equals method.
http://java.sun.com/j2se/1.4.2/docs/api/java/util/AbstractList.html#equals(java.lang.Object)
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public boolean equals(Object o)
Compares the specified object with this list for equality. Returns true if and only if the specified object is also a list, both lists have the same size, and all corresponding pairs of elements in the two lists are equal. (Two elements e1 and e2 are equal if (e1==null ? e2==null : e1.equals(e2)).) In other words, two lists are defined to be equal if they contain the same elements in the same order.
This implementation first checks if the specified object is this list. If so, it returns true; if not, it checks if the specified object is a list. If not, it returns false; if so, it iterates over both lists, comparing corresponding pairs of elements. If any comparison returns false, this method returns false. If either iterator runs out of elements before the other it returns false (as the lists are of unequal length); otherwise it returns true when the iterations complete.
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If your linked lists contain objects that implement the equals method such that the equals method compares values (Example Strings) then calling linkedList.equals(otherList) will work fine.
However, if you are putting custom objects into your linked lists you need to make sure that objects of those type implement the equals() method. By default, equals() (which is inherited from Object) just checks to see if that object is the same object.
Example:
CustomObject o1 = new CustomObject(1, 2);
CustomObject o2 = new CustomObject(1, 2);
CustomObject o3 = o1;
o1.equals(o2) //FALSE
o1.equals(o3) //TRUE
If your CustomObject implements the equals method such that it compares certain values (like the constructor args, in this example). Then you can make it so that
o1.equals(o2) //TRUE
And then those objects would work just fine if you called the equals() method on the LinkedList.