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First Activity not stopped when Second Activity started

As per Android activity life cycle, when activity is no longer visible onStop will get called. But this is not happening, if i exit the second activity quickly.
I have two activities HomeActivity and DetailActivity.
Step 1. Pressing a button on HomeActivity navigates to DetailActivity
Step 2. Back press on DetailActivity navigates to HomeActivity
When navigates to DetailActivity , the onStop of HomeActivity should get called as per activity life cycle, since the DetailActivity gets onStart.
But onStop is not getting called if i back press on DetailActivity quickly.
Activity life cycle if back pressed immediately..
HomeActivity: onPause
DetailActivity: onStart
DetailActivity: onResume
DetailActivity: onPostResume
DetailActivity: onPause
HomeActivity: onResume
HomeActivity: onPostResume
DetailActivity: onStop
Activity life cycle if back pressed after a delay (say few seconds later on DetailActivity)
HomeActivity: onPause
DetailActivity: onStart
DetailActivity: onResume
DetailActivity: onPostResume
HomeActivity: onStop
DetailActivity: onPause
HomeActivity: onStart
HomeActivity: onResume
HomeActivity: onPostResume
DetailActivity: onStop
Doesn't this look like a bug as new Activity is Started, the previous activity is not stopped?

According to Android Docs about stopping and restart of an Activity
The user performs an action in your app that starts a new activity. The current activity is stopped when the second activity is created. If the user then presses the Back button, the first activity is restarted.
They should update it to say If the user the presses the Back button but not to quickly haha, but I think iheanyi is right in the fact that some other process may have been granted cpu time after the DetailsActivity hit onPostResume and the back button was pressed before the OS could continue with the onStop process of the HomeAcitvity

You've described normal behavior. Here's what https://developer.android.com/reference/android/app/Activity.html#ActivityLifecycle says about this:
Called when the activity is no longer visible to the user, because
another activity has been resumed and is covering this one. This may
happen either because a new activity is being started, an existing one
is being brought in front of this one, or this one is being destroyed.
Followed by either onRestart() if this activity is coming back to
interact with the user, or onDestroy() if this activity is going away.
So, you may be wondering, well, if my new activity is visible, doesn't that mean the previous activity is invisible? Not really. Your new activity may not completely overlap the old one (in which case, part of the old is still visible). This could be especially tricky if the old activity has elements that while "invisible" to the user because they look the same as elements from the new activity, are technically still visible (in that they're not completely blocked by the new).
Visibility aside, you could also inadvertently have lifecycle methods timing issues which lead to this. Let's say your onPause() takes a long time to complete. The other activity could completely hide the old, satisfying the conditions for onStop(), but you transition back before onStop() has a chance to run.
Finally, there are many tasks that need to run on the phone and few processors to execute them. Necessarily, some tasks will have higher priority than others. Think about the code that must execute when your new activity is taking over the foreground - there is no way that onStop() has time to run if the phone is busy executing code for your activity. If that code then triggers onResume, onStop would be skipped altogether.
As you can see from the life cycle diagram, you can transition from onPause() back to onResume() without going through onStop(). Perhaps you should think about the scenarios where something like that can happen (and why) to better understand your particular case.

Android Activity life cycle - onPause() and onResume()

In the Android developer diagram, I saw that onResume() is always called before onPause(). Assuming the user starts a new Activity, why should onPause() be preceded by onResume()?
I mean:
OnResume can be called in 2 occassions:
1) when user starting new activity (before OnPause)
2) when activity is in background and if the user brings the activity back to the
foreground
I expect in every case, something else should be done.

You are getting it wrong. Whenever an activity is created, onResume is called just after onStart. Whenever your activity goes back stack onPause is called. Again if your activity comes back to foreground then onResume is called. So, it is not like, onResume is called before onPause. Whenever activity is returning from onPause state, onResume gets called instead of onStart or onCreate. This happens so that Android does not have to create Activity instance again and again though those instances are not properly destroyed. This is quite memory efficient too.
NOTE: If you app is running and the user presses back button or home button, then the Activity goes through onPause() and onStop() state. After this if the user is again coming back to your app then, onRestart(), onStart() and onResume() will be called sequentially.
Then when the activity is only in onPause() state ? When a dialog surfaces on top of your activity or your activity is getting displayed in Split screen but it doesn't have focus (user is not interacting with your app). On these cases, activity goes to onPause() state only.

onResume() is always called before onPause()
This is correct. onResume is always called when the Activity is launched for the first time, before onCreate, and when the Activity is being resumed (user navigates back to your Activity)
Assuming the user starts a new Activity, why should onPause() be
preceded by onResume()
onPause is only called when the Activity is put to background, or before onDestroy if the Application is being destroyed. So onPause is always being called after a call to onResume has been made. Why? Because that's the lifecycle of the Activity as defined by the Android framework.

The life cycle of the activity is as follows
Fresh start via onCreate(), onStart(), onResume .... and close via onPause()->onStop()->onDestroy()
Yellow background: Activity goes into background and thus is no longer visible. The user returns back to the activity.
e.g.
Switch off the phone screen while the activity is running: onPause()->onStop()
Switch on the screen again: onStart() -> onResume()
Green background: The activity stays in the visible screen area but is not active
e.g. Activate multiple windows (split screen) occupying one part of the screen each and tip on your app to make it active
tip on the other app: onPause() is called in your app as it goes into pause but is still visible
tip on your app: onResume() is called
Here is an example of a split screen with two apps:
see android documentation on activity life cycle for details

Life cycle of Android Activity after pressing Back button

I am little confused between the life cycle of two activities.
Suppose I have Activity A and Activity B.
B is called From A i.e A ----> B.
Now currently B is on the screen and I pressed back button. Here I want know:- is there any memory still available for B(Active) or B's memory is flushed(Inactive).

The following activity call back methods are called, after pressing back button.
onPause()
onStop()
onDestroy()
The activity is destroyed.
And it recreates when launched again. These are the callback methods when it launches again.
onCreate()
onStart()
onResume()

I know the answer is been accepcted, still if this helps someone I am putting it.
When app is opening for the first time, by clicking the Icon
onCreate()
onStart()
onResume()
When home button is pressed
onPause()
onStop()
when app is again opened by clicking the app icon or launched from recent
onRestart()
onStart()
onResume()
when app is opened and then back button is pressed
onPause()
onStop()
onDestroy()

The onDestroy method is called after back press. Then activity will be popped from the Activity back stack.
From docs:
If an activity is paused or stopped, the system can drop the activity from memory by either asking it to finish, or simply killing its process. When it is displayed again to the user, it must be completely restarted and restored to its previous state.
onDestroy() from docs:
The final call you receive before your activity is destroyed. This can happen either because the activity is finishing (someone called finish() on it, or because the system is temporarily destroying this instance of the activity to save space. You can distinguish between these two scenarios with the isFinishing() method.

Activity B will be destroyed and will no longer remain in memory.
For more information please visit the official documentation for android and have a look at the activity life cycle figure.
Once you press the back key the activity's onDestroy() method will be called and the activity will be flushed out of the memory. You will then be required to restart the activity by calling the startActivity() method which will in turn call its onCreate() Method.

I would suggest to refer following link for activity lifecycle
http://stackoverflow.com/a/8516056/3110609
and following link for launch mode of activity.
www.intridea.com/blog/2011/6/16/android-understanding-activity-launchmode

After pressing the back button, Activity B will b destroyed. You see, Android Manages Activities like a Stack(an explanation of a stack). Everytime you start an activity, it pushes into the Activity Stack. So when Activity A calls Activity B, Activity B is now on top of Activity B, and when you press the back button, it also does a pop in the Activity Stack. So in concept, Activity B is gone. Pressing a Home Button is different from pressing back, it pauses the Activity, therefore it still eats a little of the phone's memory.
Here is a good explanation of how Android Manages Activities.

Android Activity-Lifecycle... how to avoid onDestroy()?

I have an App, which uses an ActicityGroup to have a stack of Activitys. If I start a new Activity, I do this as Child of my ActivityGroup. Lets assume I'm in my starting Activity (1), and I start a new one(2), so here is what's getting called:
(1): onPause()
(2): onCreate(), onStart(), onResume()
until here, everything as aspected. if I press my BackButton the stack is as following:
(2): onPause(), onStop(), onDestroy()
(1): onStop(), onDestroy() [sic]
(1): onCreate(), onStart(), onResume()
I see no reason,first why (1) should perform onStop, and onDestroy(), to reCreate again, and second why onRestart never gets called on (1).
Has anyone a Reason for this behavior? Can I 'cancel' calls to onStop() or onDestroy() somehow?
any idea apreciated

Try using FLAG_ACTIVITY_SINGLE_TOP when starting child activity, like:
Window window = getLocalActivityManager().startActivity(id,
intent.addFlags(Intent.FLAG_ACTIVITY_SINGLE_TOP));
More info here:
http://developer.android.com/reference/android/content/Intent.html#FLAG_ACTIVITY_SINGLE_TOP

You can avoid Activity onDestroy method when back button pressed in a very simple way,
Just mention
android:persistent="true"
for your activity, that should prevent your activity getting destroyed, To know more in detail you can visit the below SO post
Prevent activity from being destroyed as long as possible

when you press back button it's default behavior is stop or destroy the current activity you can override the back button. If you press home button then it will use the onPause() that means os will consider that you want to continue with current activity when you again launch same activity but if you press back button it means that you finish your current activity and back to the last activity

Onstop() and onDestroy() will not call untill you did not finish activity. Ondestory() called for releasing of resource that occupied by Activity. IF activity use has been over then it is better to destroy this activity.
Second it will be good for memory management scheme. and if you do not call destroy then it will automatically call when you exit from app
and finally
if you doesnot want to call destroy when you press back button then you can use override method onBackpressed()

Did back key destroy an activity?

I have an activity defined as below:
<activity android:name="com.example.ui.HomeActivity"
android:alwaysRetainTaskState="true"/>
A strange thing is that, when running on emulator, and the back key is pressed, the activity was destroyed (I saw onDestroy() called in log). But when running on my Nexus One phone, and the back key is pressed, the activity is not destroyed (I didn't see onDestroy() called in log).
Could someone tell me why?
Thanks.

When activity is in the background (after pressing Back key) it is always stopped but System can also decide to destroy it (eg. when system resources are low). You can't determine when it will be destroyed.
Activity can also be destroyed by calling finish(). You can determine that by checking isFinishing() status in onPause or onStop callback.
Do not count on onDestroy callback. If system will kill activity it wont be called.

By default, pressing the BACK key finishes (destroys) the current activity and displays the previous activity to the user.
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