```First, we can exclude all the spaces around the 0s:
<pre>-----------------------------------------
| 2 |   | 1 | . | 1 |   | 3 |   |   |   |
-----------------------------------------
|   |   | . | 0 | . |   |   |   | 2 | 1 |
-----------------------------------------
| 2 |   | . | . | 1 | . | . |   |   |   |
-----------------------------------------
|   |   | 1 |   | . | 0 | . |   | 3 | . |
-----------------------------------------
|   |   |   |   | . | . | . |   | . | 0 |
-----------------------------------------
|   |   | 3 |   | 3 |   |   |   | . | . |
-----------------------------------------
|   |   |   |   | 2 |   |   | 1 |   |   |
-----------------------------------------
| . | . |   | 4 |   |   | 1 | . | . | 2 |
-----------------------------------------
| 0 | . |   |   |   |   | . | 0 | . |   |
-----------------------------------------
| . | . |   | 3 |   | 2 | . | . | 2 |   |
-----------------------------------------</pre>

The 2 in the bottom right only has two open spaces next to it, so we can fill those in. We also have some squares in the top left with only one possibility.

<pre>-----------------------------------------
| 2 | . | 1 | . | 1 |   | 3 |   |   |   |
-----------------------------------------
| &lt; | &gt; | . | 0 | . |   |   |   | 2 | 1 |
-----------------------------------------
| 2 | . | . | . | 1 | . | . |   |   |   |
-----------------------------------------
| . | . | 1 |   | . | 0 | . |   | 3 | . |
-----------------------------------------
|   |   |   |   | . | . | . |   | . | 0 |
-----------------------------------------
|   |   | 3 |   | 3 |   |   |   | . | . |
-----------------------------------------
|   |   |   |   | 2 |   |   | 1 |   |   |
-----------------------------------------
| . | . |   | 4 |   |   | 1 | . | . | 2 |
-----------------------------------------
| 0 | . |   |   |   |   | . | 0 | . | ^ |
-----------------------------------------
| . | . |   | 3 |   | 2 | . | . | 2 | v |
-----------------------------------------</pre>
The 3 above the 2 in the center requires that there is some part of a ship in the space above and to the left of it:

<pre>-----------------------------------------
| 2 | . | 1 | . | 1 | . | 3 |   |   |   |
-----------------------------------------
| &lt; | &gt; | . | 0 | . | ? |   |   | 2 | 1 |
-----------------------------------------
| 2 | . | . | . | 1 | . | . |   |   |   |
-----------------------------------------
| . | . | 1 | . | . | 0 | . |   | 3 | . |
-----------------------------------------
|   | . | . | ? | . | . | . |   | . | 0 |
-----------------------------------------
|   |   | 3 |   | 3 |   |   |   | . | . |
-----------------------------------------
|   |   |   |   | 2 |   |   | 1 |   |   |
-----------------------------------------
| . | . |   | 4 |   |   | 1 | . | . | 2 |
-----------------------------------------
| 0 | . |   |   |   |   | . | 0 | . | ^ |
-----------------------------------------
| . | . |   | 3 |   | 2 | . | . | 2 | v |
-----------------------------------------</pre>

Now the 3 in the top row has only one possibility that works with the 2-1 to its right, and the 3 below those is left with only 3 spaces around it:

<pre>-----------------------------------------
| 2 | . | 1 | . | 1 | . | 3 | . | . |   |
-----------------------------------------
| &lt; | &gt; | . | 0 | . | &lt; | x | &gt; | 2 | 1 |
-----------------------------------------
| 2 | . | . | . | 1 | . | . | . | . | o |
-----------------------------------------
| . | . | 1 | . | . | 0 | . | ^ | 3 | . |
-----------------------------------------
|   | . | . | ? | . | . | . | ? | . | 0 |
-----------------------------------------
|   |   | 3 |   | 3 |   |   |   | . | . |
-----------------------------------------
|   |   |   |   | 2 |   |   | 1 |   |   |
-----------------------------------------
| . | . |   | 4 |   |   | 1 | . | . | 2 |
-----------------------------------------
| 0 | . |   |   |   |   | . | 0 | . | ^ |
-----------------------------------------
| . | . |   | 3 |   | 2 | . | . | 2 | v |
-----------------------------------------</pre>

At this point, there is only one possible location for the flagship:
<pre>-----------------------------------------
| 2 | . | 1 | . | 1 | . | 3 | . | . |   |
-----------------------------------------
| &lt; | &gt; | . | 0 | . | &lt; | x | &gt; | 2 | 1 |
-----------------------------------------
| 2 | . | . | . | 1 | . | . | . | . | o |
-----------------------------------------
| . | . | 1 | . | . | 0 | . | ^ | 3 | . |
-----------------------------------------
|   | . | . | ? | . | . | . | ? | . | 0 |
-----------------------------------------
|   |   | 3 |   | 3 |   |   |   | . | . |
-----------------------------------------
|   |   |   |   | 2 | . | . | 1 |   |   |
-----------------------------------------
| . | . | . | 4 | . | . | 1 | . | . | 2 |
-----------------------------------------
| 0 | . | &lt; | x | x | &gt; | . | 0 | . | ^ |
-----------------------------------------
| . | . | . | 3 | . | 2 | . | . | 2 | v |
-----------------------------------------</pre>

The space between the two 3s and the 4 must have a ship part, otherwise it becomes impossible to place enough parts in that area.
<pre>-----------------------------------------
| 2 | . | 1 | . | 1 | . | 3 | . | . |   |
-----------------------------------------
| &lt; | &gt; | . | 0 | . | &lt; | x | &gt; | 2 | 1 |
-----------------------------------------
| 2 | . | . | . | 1 | . | . | . | . | o |
-----------------------------------------
| . | . | 1 | . | . | 0 | . | ^ | 3 | . |
-----------------------------------------
|   | . | . | ? | . | . | . | ? | . | 0 |
-----------------------------------------
|   |   | 3 |   | 3 |   |   |   | . | . |
-----------------------------------------
|   |   | . | ? | 2 | . | . | 1 |   |   |
-----------------------------------------
| . | . | . | 4 | . | . | 1 | . | . | 2 |
-----------------------------------------
| 0 | . | &lt; | x | x | &gt; | . | 0 | . | ^ |
-----------------------------------------
| . | . | . | 3 | . | 2 | . | . | 2 | v |
-----------------------------------------</pre>

If the space between the 3s is empty, we find that it is not possible to place all the remaining ships (either we need 5 caravels, or there is nowhere for the other frigate). So the frigate is between the 3s.
<pre>-----------------------------------------
| 2 | . | 1 | . | 1 | . | 3 | . | . |   |
-----------------------------------------
| &lt; | &gt; | . | 0 | . | &lt; | x | &gt; | 2 | 1 |
-----------------------------------------
| 2 | . | . | . | 1 | . | . | . | . | o |
-----------------------------------------
| . | . | 1 | . | . | 0 | . | ^ | 3 | . |
-----------------------------------------
|   | . | . | ^ | . | . | . | v | . | 0 |
-----------------------------------------
|   | . | 3 | x | 3 | . | . | . | . | . |
-----------------------------------------
|   | . | . | v | 2 | . | . | 1 |   |   |
-----------------------------------------
| . | . | . | 4 | . | . | 1 | . | . | 2 |
-----------------------------------------
| 0 | . | &lt; | x | x | &gt; | . | 0 | . | ^ |
-----------------------------------------
| . | . | . | 3 | . | 2 | . | . | 2 | v |
-----------------------------------------</pre>

And all that's left is to place the remaining 3 caravels:

<pre>-----------------------------------------
| 2 |   | 1 |   | 1 |   | 3 |   |   |   |
-----------------------------------------
| &lt; | &gt; |   | 0 |   | &lt; | x | &gt; | 2 | 1 |
-----------------------------------------
| 2 |   |   |   | 1 |   |   |   |   | o |
-----------------------------------------
|   |   | 1 |   |   | 0 |   | ^ | 3 |   |
-----------------------------------------
| o |   |   | ^ |   |   |   | v |   | 0 |
-----------------------------------------
|   |   | 3 | x | 3 |   |   |   |   |   |
-----------------------------------------
| o |   |   | v | 2 |   |   | 1 | o |   |
-----------------------------------------
|   |   |   | 4 |   |   | 1 |   |   | 2 |
-----------------------------------------
| 0 |   | &lt; | x | x | &gt; |   | 0 |   | ^ |
-----------------------------------------
|   |   |   | 3 |   | 2 |   |   | 2 | v |
-----------------------------------------</pre>```