.ddc consists of the same information as a .db file. ddc is a synopsys encrypted form of your design which can be read by the tools such as Design compiler, IC compiler and prime time. It consists of the netlist(list of components and nets) information of your design along with the constraints which you have specified for implementing the design.
Hope the explanation is good enough..
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Here is some more info:
The .ddc format is backward compatible but not forward compatible.
This format contains back-annotated net delays and constraints. Subsequent topographical mode sessions restore virtual layout data. The .ddc format is
recommended for subsequent topographical mode optimizations and verification. Because when you read the RTL code the unmapped design can be stored in a .ddc format so that when you reread the design the tool can run faster when compared to a verilog or vhdl format.