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I had this issue too and tried all these solutions, but these general solutions will give you clues and not fix the problem. The problem is usually caused by something you've done and you have to follow the clues. Here's what happened

Aptitude does give you more details than apt-get, so run it. i ran it and it said

The following actions will resolve these dependencies:

      Keep the following packages at their current version:
1)      libavcodec-dev [Not Installed]                     
2)      libavdevice-dev [Not Installed]                    
3)      libavfilter-dev [Not Installed]                    
4)      libavformat-dev [Not Installed]                    
5)      libavresample-dev [Not Installed]                  
6)      libgazebo9-dev [Not Installed]

..." up to 25 packages It did not succeed to install, and even when i clicked "Accept this solution Y" it still didnt work. But that list reminded me when I was fooling around with mpeg avcodec a while back . So i tried to install libavcodec-dev

I got:

The following packages have unmet dependencies:
 libavcodec-dev : Depends: libavutil-dev (= 7:3.4.8-0ubuntu0.2) but 7:4.1.3-0york1~18.04 is to be installed
                  Depends: libswresample-dev (= 7:3.4.8-0ubuntu0.2) but it is not going to be installed

So i tried sudo apt-get install libswresample-dev but got

The following packages have unmet dependencies:
 libswresample-dev : Depends: libavutil-dev (= 7:3.4.8-0ubuntu0.2) but 7:4.1.3-0york1~18.04 is to be installed
E: Unable to correct problems, you have held broken packages.

So I tried

sudo apt-get install libavutil-dev
libavutil-dev is already the newest version (7:4.1.3-0york1~18.04).

NOW the issue is clear, when i was messing around with mpeg mp4 codecs I must have installed this york version (7:4.1.3-0york1~18.04) of the libavutil-dev package, which you can see from the errors will not work with libavcodec-dev, which blocks ros-melodic-desktop-full. So i removed that libavutil-dev and reinstalled it, which installed the correct package version (7:3.4.8-0ubuntu0.2) REMOVE BAD VERSION:

sudo apt-get remove libavutil-dev
The following packages will be REMOVED:
  libavutil-dev libswscale-dev
0 upgraded, 0 newly installed, 2 to remove and 103 not upgraded.
After this operation, 2,388 kB disk space will be freed.
Do you want to continue? [Y/n] y
(Reading database ... 288297 files and directories currently installed.)
Removing libswscale-dev:amd64 (7:4.1.3-0york1~18.04) ...
Removing libavutil-dev:amd64 (7:4.1.3-0york1~18.04) ...

NOW REINSTALL THE GOOD VERSION

sudo apt-get install libavutil-dev 
The following NEW packages will be installed:
  libavutil-dev
0 upgraded, 1 newly installed, 0 to remove and 103 not upgraded.
Get:1 http://us.archive.ubuntu.com/ubuntu bionic-updates/universe amd64 libavutil-dev amd64 7:3.4.8-0ubuntu0.2 [294 kB]
Preparing to unpack .../libavutil-dev_7%3a3.4.8-0ubuntu0.2_amd64.deb ...
Unpacking libavutil-dev:amd64 (7:3.4.8-0ubuntu0.2) ...
Setting up libavutil-dev:amd64 (7:3.4.8-0ubuntu0.2) ...

NOW I TRIED INSTALLING THOSE THINGS THAT WERE BLOCKED BY THE BAD PACKAGE AND THEY WORKED:

sudo apt-get install libswresample-dev
sudo apt-get install libavcodec-dev
sudo apt-get install ros-melodic-desktop-full

Success