How to handle bottom navigation perfectly with back pressed

According to the guidelines for Material Design

On Android, the Back button does not navigate between bottom navigation bar views.

EDIT: Material Design link no longer mentions back button behavior.

Pressing the back button you can quit the application, which is the default behavior, such as in Google Photo...

FragmentManager fragmentManager = getFragmentManager();
FragmentTransaction fragmentTransaction = fragmentManager.beginTransaction();
fragmentTransaction.replace(R.id.content, fragment);
// note: there is NOT a addToBackStack call
fragmentTransaction.commit();

...or lead the user to the home section and then, if pushed again, at the exit.

Personally I find this last pattern much better.

To get it without override onBackPressed you need to identify the home fragment and differentiate it from all the others

navigation = (BottomNavigationView) findViewById(R.id.navigation);
navigation.setOnNavigationItemSelectedListener(new BottomNavigationView.OnNavigationItemSelectedListener() {
    @Override
    public boolean onNavigationItemSelected(@NonNull MenuItem item) {
        switch (item.getItemId()) {
            case R.id.navigation_home:
                viewFragment(new HomeFragment(), FRAGMENT_HOME);
                return true;
            case R.id.navigation_page_1:
                viewFragment(new OneFragment(), FRAGMENT_OTHER);
                return true;
            case R.id.navigation_page_2:
                viewFragment(new TwoFragment(), FRAGMENT_OTHER);
                return true;
        }
        return false;
    }
});

What you have to do now is write the viewfragment method that have to:

1. Know how many fragments there are in the stack before the commit

2. If the fragment is not "home type", save it to the stack before the commit

3. Add an OnBackStackChangedListener that when the stack decreases, (i.e. when I pressed back ), delete all the fragments that are not "home type" (POP_BACK_STACK_INCLUSIVE) , bringing us to the home fragment

Below the full method with comments

private void viewFragment(Fragment fragment, String name){
    final FragmentManager fragmentManager = getFragmentManager();
    FragmentTransaction fragmentTransaction = fragmentManager.beginTransaction();
    fragmentTransaction.replace(R.id.content, fragment);
    // 1. Know how many fragments there are in the stack
    final int count = fragmentManager.getBackStackEntryCount();
    // 2. If the fragment is **not** "home type", save it to the stack
    if( name.equals( FRAGMENT_OTHER) ) {
        fragmentTransaction.addToBackStack(name);
    }
    // Commit !
    fragmentTransaction.commit();
    // 3. After the commit, if the fragment is not an "home type" the back stack is changed, triggering the
    // OnBackStackChanged callback
    fragmentManager.addOnBackStackChangedListener(new FragmentManager.OnBackStackChangedListener() {
        @Override
        public void onBackStackChanged() {
            // If the stack decreases it means I clicked the back button
            if( fragmentManager.getBackStackEntryCount() <= count){
                // pop all the fragment and remove the listener
                fragmentManager.popBackStack(FRAGMENT_OTHER, POP_BACK_STACK_INCLUSIVE);
                fragmentManager.removeOnBackStackChangedListener(this);
                // set the home button selected
                navigation.getMenu().getItem(0).setChecked(true);
            }
        }
    });
}

Try this

@Override
    public void onBackPressed() {
        BottomNavigationView bottomNavigationView = (BottomNavigationView) findViewById(R.id.navigation);
        int seletedItemId = bottomNavigationView.getSelectedItemId();
        if (R.id.home != seletedItemId) {
            setHomeItem(MainActivity.this);
        } else {
            super.onBackPressed();
        }
    }

public static void setHomeItem(Activity activity) {
    BottomNavigationView bottomNavigationView = (BottomNavigationView)
            activity.findViewById(R.id.navigation);
    bottomNavigationView.setSelectedItemId(R.id.home);
}