# Find a Cyclic Peptide with Theoretical Spectrum Matching an Ideal Spectrum solved by 546

July 29, 2015, 1:04 a.m. by Rosalind Team

In “Compute the Number of Peptides of Given Total Mass”, we first encountered the problem of reconstructing a cyclic peptide from its theoretical spectrum; this problem is called the Cyclopeptide Sequencing Problem and is given below. It is solved by the following algorithm.

    CYCLOPEPTIDESEQUENCING(Spectrum)        Peptides ← a set containing only the empty peptide        while Peptides is nonempty            Peptides ← Expand(Peptides)            for each peptide Peptide in Peptides                if Mass(Peptide) = ParentMass(Spectrum)                    if Cyclospectrum(Peptide) = Spectrum                        output Peptide                    remove Peptide from Peptides                else if Peptide is not consistent with Spectrum                    remove Peptide from Peptides

## Cyclopeptide Sequencing Problem

Given an ideal experimental spectrum, find a cyclic peptide whose theoretical spectrum matches the experimental spectrum.

Given: A collection of (possibly repeated) integers Spectrum corresponding to an ideal experimental spectrum.

Return: Every amino acid string Peptide such that Cyclospectrum(Peptide) = Spectrum (if such a string exists).

## Sample Dataset

0 113 128 186 241 299 314 427


## Sample Output

186-128-113 186-113-128 128-186-113 128-113-186 113-186-128 113-128-186