I have ever use a professional Samsung Data Recovery to solve this trouble. You can not only recover deleted contacts from Samsung Galaxy, but also recover other lost data data from Samsung Galaxy after factory reset, updating Android, rooting, etc.
Below delivers the steps of using the Samsung Data Recovery to recover deleted files from Samsung phones and tablets in details. All steps can be summarized as 3 parts.

http://www.z0download.com/detail/Samsung-Contacts-Recovery

Part1: Connect Samsung phones or tablets with PC
Part2: Start Scanning and Chosse Files to Restore
Part3: Save Recovered Items
Read more: how to recover deleted contacts from rooted Samsung

http://www.z0download.com/useguides/How-to-Recover-Deleted-Contacts-from-Rooted-Galaxy-S5

Take it easy ! There are many ways to recover data from samsung Galaxy phone
1.Do you have Google account? if you have, and made a backup for your data, you can restore data by google account.

2.Samsung KIES, if you have install a KIES to your computer, when you connect the tab to computer,KIES may make a backup for your tab automatically, so, you can try to find whether there is backup on your computer.

3. Maybe you installed some backup apps to your phone, such as Titanium, and have maken a backup, you can restore data from the apps.

4.Finally, if you are so unlucky that there are not any backup in your tab or computer. I am afraid that you should recover your data by recovery software. There are so many recovery software you can choose. Do you know Tenorshare Samsung Data Recovery? I ever used it to get back my lost contacts from my Samsung Galaxy S4.

http://download.cnet.com/Samsung-Data-Recovery/3000-2242_4-76171820.html

You need to get a Samsung Data Recovery for you to recover deleted files on Samsung Galaxy S4/S3/S2/S, here you can turn to Android Data Recovery which is powerful enough to recover deleted contacts, text message, photos and videos from Samsung Galaxy S4 and other Android phones and tablets such as Samsung Captivate, Samsung Infuse, Galaxy Nexus, Samsung Epic 4G Touch, Samsung Galaxy Ace, Samsung Galaxy Note and so on.

Read more: Restore contacts from Samsung Galaxy

http://www.recovery-iphone.com/how-recover-lost-contacts-from-samsung-android.html

Recover SMS messages on Samsung galaxy

http://restore-samsung-contacts.blogspot.com/2014/04/restore-samsung-galaxy-text-messages.html

More Samsung Contact recovery guides:

http://restore-samsung-contacts.blogspot.com

It is possible to directly recover contacts for Samsung Galaxy S3 S4, but you should make sure have backup files somewhere.
1. Google account, if you have a google account for your android phone and open the automaticalli sync, you can try to recover from google account.
2. Offical PC software, generally speaking, an android phone need to upgrade in computer via a official PC software, such as Samsung PC studio, and this applicaiton have a automatically backup function, when you connect the phone to computer and launch the application, it will make a backup for your phone data, thus you can try to find the backup from PC studio.
3. 3rd-party android assistant - Samsung Data Recovery, which is similar with PC studio, and it is more convenient, and the backup is more obvious.
Read more: How to restore contacts from Samsung Galaxy

http://www.datas-recovery.com/static/recover-contacts-from-samsung-galaxy.html

How to Recover Lost SMS from Samsung Galaxy

http://www.datas-recovery.com/static/recover-deleted-sms-from-samsung-galaxy.html

As for me, I used Data Recovery for Android, it is capable of recovering messages, contacts, photos and video from an Android phone or tablet. Due to the ease-to-use interface, it's ideal for everyone, like single users or professionals, even concerned parents who want to protect their kids from negative information. Scan, preview and recover. Simple clicks bring you what you want, this is be your best choice if you need to restore your lost message and contacts:

Resource: Related Articles:
http://iphone-data-recovery-top.blogspot.com
http://www.recover-iphone-android.com/recover-data-from-android-phone.html
Download the free trial version of Android Data Recovery to have a try.
Click here to download:
http://www.recover-iphone-android.com/recover-contacts-from-android.html

You can recover deleted contacts from Samsung Galaxy phones. To do this, connect your Galaxy phone to your laptop and use a Samsung Contact Recovery program to be able to view the deleted files in the task window. After this, click on the ones that you want to recover.
You can get the program here: Samsung Galaxy Q Contacts Recovery.
http://www.android-recovery.net/samsung-data-recovery.html

Hey james. If you saved your contacts to your Google account, once you've added your Google account on an Android phone, the contacts should automatically sync after.