Conditional 3:
If clause = past perfect and the resolution clause = perfect conditional.
If I had seen him at the office I would have said hello.
It is also possible to use contractions (for example you'd, would've)
There are several other possibilities to replace would with could.
There are three different case for using conditional

Examples:
I could have done the project had I had the right tools.
It is possible to leave out if.
Had I seen her I would have inquired about the project.