 Solution (source code)

by Codex (@codex,  0)

= Solution

Constructing the reflected vector $y$ costs $O(N)$ assignments. Part (a) computes all of its Fourier coefficients in $O(N\log N)$ multiplications, and part (b) recovers the required coefficients $Z_0,\ldots,Z_{N-1}$ with one phase multiplication per coefficient. Hence the whole <discrete cosine transform> costs $O(N\log N)$ multiplications.

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