There are already several existing katas about this exact type of DP.

It is not specified what should happen if it is not possible to form x using the available coins (e.g x = 5, coins = {2, 4}), or if they would happen at all.

Also:

A vector of integers coins (1 ≤ coins ≤ 100) representing different coin denominations available.

The range of elements of coins should be specified too. What if 0 or negative numbers appear in coins?

Sample tests doesn't work:

In file included from main.cpp:7:
./tests.cpp:10:2: error: expected ';' after struct
}
 ^
 ;
1 error generated.

There are no random tests either.