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How to update a variable in Activity A from Activity B, every time the variable changes?

Image description of the problem
I have a music player app. Activity A is my main menu. You choose a song from a list in Activity A and that takes you to the Activity B with intent(passing data like songTitle, songArtist etc).
When I press the back button when I'm in Activity B, it takes me back to Activity A with intent(passing data like songTitle, songArtist etc). I show the currently playing song title and artist name in Activity A at the bottom.
My problem is that if I'm in Activity A and then the song changes AUTOMATICALLY to the next song in ActivityB, the song title and artist name doesn't change in Activity A because I didn't pass any intent from Activity B to A.
I tried to use SharedPreferences in onStart() but the changes in text doesn't apply unless I press the home button on the device and come back again to the Activity A.
How can I listen the variable changes in another activity and update my TextViews accordingly?

you have two options here. you can transform those activities to fragments and then you will be able to share data with activity scope view model I believe thats good option and you should do it like that, but if for some reason you have huge codebase and it will be very hard to make those activies fragments you could just add onActivityResult in ActivityA and return current music id or something from ActivityB.

You should look into LiveData
LiveData is on observable data class. You can find more about it from here:
LiveData Android

I have solved my problem with SharedPreferences.

keep data retained of listview when switching between activities

i am struggling to keep data or items of list view when i leave one activity to another, for my example i created simple app on click will add number increased to a list view so each click create an item like 1 another click add 2 and so on.
the program works fin for main activity but then i would like to see the result on another activity i call it second activity but the problem is when i hit back button on second activity to go back to main activity, i will lose all of items on the list view.
i was looking on google so many information but could not get my head around it, so please advice and please be little more in detail as i am beginner, i think instance state or shared preference will do the job but i do not know any of them
thanks in advance and here is my app code for main activity and second activity and picture for output
sorry i add code as images becausethe site keep saying the code need indentation thank you
main activity[main out put][2]second activity[second activity out put][4]

You need to save the data of the ListView in some form, either in a file or in a database (local or remote).There is no direct way to store list view, but you can store the data from the list view and then set it in to the ListView later when you switch back to the activity.
You need to keep in mind that switching activity results to invoking of onPause() method in android, and if the data is not saved in the current activity then it will be lost when you move on to another activity.

Add all your values into the array, pass it to the adapter, then after clicking on the list view item, make an intent where you want to switch your activity (means from one activity to second activity), while implemented the intent, pass your array also, using intent.put extra. Then you will get your array in your second activity and coming back to your previous activity, again pass an intent (with your array) and get your array in your previous activity and pass it into the adapter.

Restoring instances of activities in a list?

I was wondering if it is possible to save multiple instances of activities in a list as in when a user selects an item in a listView it opens up its corresponding activity that was activated earlier.
To give you a sense of where I am coming from here is the concept of the app I am making.
In Main Activity there is:
A button that when pressed launches a new activity called Exercise
A fragment WorkoutsFragment that keeps track of a list of prior workouts.
In Exercise Activity (whose parent activity is main activity):
Users can input what exercises they are doing in the activity.
When the user goes back to main activity a new item is added to the list in WorkoutFragment and that item contains a summary of the exercises done in the prior Exercise activity. When this item is pressed I want it to go back to the Exercise activity created earlier with all information retained.
So if a user presses the workout item for June 12 I want to to resume the Exercise Activity that was created on June 12.
Would it make more sense to just start a new exercise activity and populate its contents from a database?

You are thinking right. The right way to do it is to create a new Exercise activity and populate its content from database. Maintaining references to activities is not a good practice.
You can also maintain a cache of recent exercises accessed to avoid the database call.

This seems like a good case for using the Activity onRestoreInstanceState.
See this guide on restoring different states of an Activity:
https://developer.android.com/training/basics/activity-lifecycle/recreating.html
You may pass basic data between your Activities through the Intent extras.

Android: refreshing a listview from a 'grandchild' activity

I have a setup as follows
Activity 1 uses a ListView and ListAdapters to display information
from list of objects of type A (by retrieving from the database the first time its called).
Upon clicking an item in the ListView in Activity 1, the control goes
to Activity 2, which again uses a ListView and ListAdapters to display
information from list of objects of type B.
There is a '+' button in Activity 2, which when tapped switches the
control to Activity 3. Here I can create an object of type B and save it to the database.
Now I use the setResult() in Activity 3 and onActivityResult() in Activity 2 to update the list in Activity 2.
So far so good. I can see the item of type B that I just created in Activity 2.
Now if I press the back button and go back to Activity 1, and tap on
the same item of type A then when I go to the Activity 2, the item that I had just created
does not show. However when I close the app, and open it again, and
follow the same path, I can see that item. (As the list was reloaded from the database)
So how do I update the list in Activity 1?
I hope I explained my question properly (apologize if not!). I don't want to put all the code here, since there is no issue with the code, unless my approach is wrong.

Put your code which loads the list from database in Activity.onResume() method. This way it should execute every time your activity is restored from invisible state (take a look at the docs on activity lifecycle for more info).
Also, you might want to implement loading from database using Loader. It monitors the data source for updates, thus keeping data up to date.

modifying the listview with the result returned bu the another activity in android

i am very confused about how i should implement the following in my android application.
Let me explain the functionality that i want :
-i have a list view in my First Activity , say Activity A
-now , from this activity , i start another activity(activity B) with an intent for a result.
-with the result i get from the B, i want to update the listview in activity A.
-That is add an item in listview with the string returned.
i am thinking of, storing the items in array list and setting the array list to an array adapter to the listview.
now when the Activity B returns with a result i modify the arraylist and again set it to the listview.
i want to know, is it possible??
and also i have a question : when does the activity B returns?
so that in activity A's which methods(such as onResume(), onStart(), onRestart() ) should i write the logic for modifying the listview...?
i am very new to android development

Regarding your first question, I think you are on right track. You can just add the returned string to an ArrayList and then to the ArrayAdapter.
For your second question, you will get a clear understanding how it works, by seeing the activity flow diagram here: http://developer.android.com/reference/android/app/Activity.html