Question

DNAs contain genetic and hereditary information of almost every living organism. DNA Sequence Matching is a procedure to compare two DNA sequences and find similarity between them. Given below is the recurrence relation of a dynamic programming algorithm to perform sequence matching of two DNAs. seq(i,j) = max\begin{cases} seq(i,j-1)-1,\\ seq(i-1,j) + p(i,j),\\ seq(i-1,j)-1 \end{cases} where, seq(i,j) = 0, if i = 0 or j = 0 p(i,j) = 1, if DNA1[i] = DNA2[j] p(i,j) = -2, otherwise As you can see, the formula takes two indices, i and j of two DNA sequences given as input. Then it produces a similarity score as output. We want to apply this formula to compare the following DNA sequences. \begin{tabular}{|c|c|c|c|c|c|} \hline index & 1 & 2 & 3 & 4 & 5 \\ \hline DNA1 & G & C & G & T & A \\ \hline DNA2 & C & T & G & A & G \\ \hline \end{tabular} Now answer the following questions: a) [CO1] Put appropriate values to fill the gaps in the line below (answer in your script): seq(\_, \_) represents the final similarity score of the given DNAs. b) [CO1] Apply the formula to calculate a similarity score between the DNA sequences given above. Show your work with either a recursion tree or a memory table. c) [CO2] State the time complexity of this algorithm with proper reasoning. You can assume that, the lengths of the DNA sequences are N and M respectively. d) [CO3] Mriaslun, a talented algorithmist, claims that he can implement the algorithm in an optimized way so that it only takes O(min(N, M)) space. Can you do it too? Explain your idea.

          DNAs contain genetic and hereditary information of almost every living organism. DNA Sequence
Matching is a procedure to compare two DNA sequences and find similarity between them. Given
below is the recurrence relation of a dynamic programming algorithm to perform sequence matching
of two DNAs.
seq(i,j) = max\begin{cases} seq(i,j-1)-1,\\ seq(i-1,j) + p(i,j),\\ seq(i-1,j)-1 \end{cases}
where,
seq(i,j) = 0, if i = 0 or j = 0
p(i,j) = 1, if DNA1[i] = DNA2[j]
p(i,j) = -2, otherwise
As you can see, the formula takes two indices, i and j of two DNA sequences given as input. Then it
produces a similarity score as output. We want to apply this formula to compare the following DNA
sequences.
\begin{tabular}{|c|c|c|c|c|c|}
\hline
index & 1 & 2 & 3 & 4 & 5 \\
\hline
DNA1 & G & C & G & T & A \\
\hline
DNA2 & C & T & G & A & G \\
\hline
\end{tabular}
Now answer the following questions:
a) [CO1] Put appropriate values to fill the gaps in the line below (answer in your script):
seq(\_, \_) represents the final similarity score of the given DNAs.
b) [CO1] Apply the formula to calculate a similarity score between the DNA sequences given
above. Show your work with either a recursion tree or a memory table.
c) [CO2] State the time complexity of this algorithm with proper reasoning.
You can assume that, the lengths of the DNA sequences are N and M respectively.
d) [CO3] Mriaslun, a talented algorithmist, claims that he can implement the algorithm in an
optimized way so that it only takes O(min(N, M)) space. Can you do it too? Explain your idea.

DNAs contain genetic and hereditary information of almost every living organism. DNA Sequence
Matching is a procedure to compare two DNA sequences and find similarity between them. Given
below is the recurrence relation of a dynamic programming algorithm to perform sequence matching
of two DNAs.
seq(i,j) = max seq(i,j-1)-1,
seq(i-1,j) + p(i,j),
seq(i-1,j)-1
where,
seq(i,j) = 0, if i = 0 or j = 0
p(i,j) = 1, if DNA1[i] = DNA2[j]
p(i,j) = -2, otherwise
As you can see, the formula takes two indices, i and j of two DNA sequences given as input. Then it
produces a similarity score as output. We want to apply this formula to compare the following DNA
sequences.

index 1 2 3 4 5

DNA1 G C G T A

DNA2 C T G A G

Now answer the following questions:
a) [CO1] Put appropriate values to fill the gaps in the line below (answer in your script):
seq( represents the final similarity score of the given DNAs.
b) [CO1] Apply the formula to calculate a similarity score between the DNA sequences given
above. Show your work with either a recursion tree or a memory table.
c) [CO2] State the time complexity of this algorithm with proper reasoning.
You can assume that, the lengths of the DNA sequences are N and M respectively.
d) [CO3] Mriaslun, a talented algorithmist, claims that he can implement the algorithm in an
optimized way so that it only takes O(min(N, M)) space. Can you do it too? Explain your idea.

Added by Carmen W.

Question

Please give Ace some feedback