Question: my problem is:

A real sequence $C$, the length is $N$ is multiple of 32, the pattern is as below:

$$C =\left(a\_0,\, a\_1,\, \ldots,\, a\_{\frac N2-1},\,\, b\_0,\, b\_1,\,\ldots,\, b\_{\frac N2 -1}\right)$$

the other two sequence is $A$, $B$, length is also $N$, as below:

$$\begin{align}
A &=(a\_0,& a\_1,& \ldots,& a\_{\frac N2-1},&&0, &&\ldots&0&)\\
B &=(0,&& \ldots,& 0,& b\_0,& b\_1,&\ldots,&& b\_{\frac N2-1}&)
\end{align}$$

you can see, $C= A+B$.

the DFT of sequence $C$ is known, but sequences $A$, $B$ and $C$ are all unknown.

I just want to know the DFT of sequence $A$ and $B$.

I know the ordinary method is

* perform a backward FFT to get sequence $C$, then
* sequence $A$ and $B$ becomes known, then
* perform forward FFT about $A$, the DFT of $B$ can be get by subtract DFT
of $A$ from DFT of $C$;

but the computaton is too complicated,

Is there a faster computation method?

Answer: 
Alas, a multiplication by a rectangular window in the time domain is a convolution in the frequency domain. Thus (assuming no other constraints on or knowledge about A or B), the DFT of A (or B) would have to be the convolution of the DFT of C with a twisty Sinc function, which is computationally far more expensive than 2 FFTs (except by fast convolution, which would require the same number of FFTs as your "ordinary" method).
Continuing from @hotpaw2's analysis, what you need is brickwall zero-phase half-band low-pass filtering of the frequency domain data. Because you have all the data in-place, you can do forward-then-backward infinite impulse response (IIR) lowpass filtering. There is a very efficient half-band IIR filter structure, the two-path polyphase filter. You can calculate the coefficients using Laurent de Soras's [HIIR library](http://ldesoras.free.fr/prod.html). To convert the one-shot filters to periodic-input-output filters, you can wrap the tail of each IIR pass (with zero input) to the beginning of the output data and add it, with some stop condition depending on what numerical accuracy is needed.