Someone devises the following algorithm to solve the spectrum convolution proble

Question

Someone devises the following algorithm to solve the spectrum convolution problem. Is the algorithm correct? What is the run time of the algorithm? Can you revise the algorithm to make its run time only dependent on the size of spectrum and independent on MaxMass?

Input: A collection of integers Spectrum NovelSpectrumConvolution(Spectrum) Max Mass maximum integer in Spectrum Initialize an array Count of size MaxMass with all values 0 Sort Spectrum in increasing order for each MI in Spectrum for each M2 Mi in Spectrum Diff M2-M1 Count Diff] € Count Diff1 1 ConvolutionSpectrum empty set for i 1 to MaxMass if Count Diff] 0 add Diff, Count DiffD into ConvolutionSpectrum il(mass, multiplicity) Sort ConvolutionSpectrum in decreasing order of the multiplic output ConvolutionSpectrum

Explanation / Answer

Yes, the given algorithm is correct for spectrum convolution because the code perforems auto-correlation and convolution which are key aspects of the algorithm.

Time complexity: Since we are sorting Spectrum element, therefore O (n log n) where n is the number of elements in Spectrum

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