Here's the grading scheme for assignment 3. The average was 47.4 out of 54, or something near 87.5%.

- algorithm: 4 marks

uniqueness: 2 marks - big O estimate: 3 marks
- computing a sample
*U*: 3 marks

- algorithm: 4 marks
- solving recurrences: 4 marks

upper and lower bounds: 2 marks

conclusion: 1 mark - space requirement, including big O in terms of
*n*: 3 marks

- solving recurrences: 4 marks
- two complex numbers: 3 marks
- three complex numbers: 1 mark
- n complex numbers, including number of Real multiplies: 3 marks

- evaluate FFT for A and B: 4 marks
- point-wise product and reconstruction of C: 3 marks
- implementation and check of example: 5 marks

- decomposition: 2 marks
- symmetry condition and proof of sufficiency: 3 marks
- proof that a primitive root of unity satisifies the symmetry condition: 3 marks
- runtime estimate: 2 marks
- the 3-way FFT algorithm in Maple-like detail: 3 marks

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