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tianyizheng02 merged 12 commits into from
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added smith waterman algorithm #9001

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added smith waterman algorithm
BAW2501 Aug 20, 2023
44314e4
[pre-commit.ci] auto fixes from pre-commit.com hooks
pre-commit-ci[bot] Aug 20, 2023
65b95a6
descriptive names for the parameters a and b
BAW2501 Aug 22, 2023
8e56b7e
Merge branch 'master' of https://github.com/BAW2501/Python
BAW2501 Aug 22, 2023
d8a6bcb
doctesting lowercase upcase empty string cases
BAW2501 Aug 22, 2023
fc58801
updated block quot,fixed traceback and doctests
BAW2501 Sep 24, 2023
0662f69
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BAW2501 Sep 25, 2023
892858a
global vars to func params,more doctests
BAW2501 Sep 25, 2023
37d7fed
Merge branch 'master' of https://github.com/BAW2501/Python
BAW2501 Sep 25, 2023
0e199f7
updated doctests
BAW2501 Sep 25, 2023
2729a57
user access to SW params
BAW2501 Sep 27, 2023
2a3e20a
formating
BAW2501 Sep 27, 2023
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193 changes: 193 additions & 0 deletions dynamic_programming/smith_waterman.py
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"""
https://en.wikipedia.org/wiki/Smith%E2%80%93Waterman_algorithm
The Smith-Waterman algorithm is a dynamic programming algorithm used for sequence
alignment. It is particularly useful for finding similarities between two sequences,
such as DNA or protein sequences. In this implementation, gaps are penalized
linearly, meaning that the score is reduced by a fixed amount for each gap introduced
in the alignment. However, it's important to note that the Smith-Waterman algorithm
supports other gap penalty methods as well.
"""


def score_function(
source_char: str,
target_char: str,
match: int = 1,
mismatch: int = -1,
gap: int = -2,
) -> int:
"""
Calculate the score for a character pair based on whether they match or mismatch.
Returns 1 if the characters match, -1 if they mismatch, and -2 if either of the
characters is a gap.
>>> score_function('A', 'A')
1
>>> score_function('A', 'C')
-1
>>> score_function('-', 'A')
-2
>>> score_function('A', '-')
-2
>>> score_function('-', '-')
-2
"""
if "-" in (source_char, target_char):
return gap
return match if source_char == target_char else mismatch


def smith_waterman(
query: str,
subject: str,
match: int = 1,
mismatch: int = -1,
gap: int = -2,
) -> list[list[int]]:
"""
Perform the Smith-Waterman local sequence alignment algorithm.
Returns a 2D list representing the score matrix. Each value in the matrix
corresponds to the score of the best local alignment ending at that point.
>>> smith_waterman('ACAC', 'CA')
[[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]]
Comment thread
BAW2501 marked this conversation as resolved.
>>> smith_waterman('acac', 'ca')
[[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]]
>>> smith_waterman('ACAC', 'ca')
[[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]]
>>> smith_waterman('acac', 'CA')
[[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]]
>>> smith_waterman('ACAC', '')
[[0], [0], [0], [0], [0]]
>>> smith_waterman('', 'CA')
[[0, 0, 0]]
>>> smith_waterman('ACAC', 'CA')
[[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]]

>>> smith_waterman('acac', 'ca')
[[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]]

>>> smith_waterman('ACAC', 'ca')
[[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]]

>>> smith_waterman('acac', 'CA')
[[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]]

>>> smith_waterman('ACAC', '')
[[0], [0], [0], [0], [0]]

>>> smith_waterman('', 'CA')
[[0, 0, 0]]

>>> smith_waterman('AGT', 'AGT')
[[0, 0, 0, 0], [0, 1, 0, 0], [0, 0, 2, 0], [0, 0, 0, 3]]

>>> smith_waterman('AGT', 'GTA')
[[0, 0, 0, 0], [0, 0, 0, 1], [0, 1, 0, 0], [0, 0, 2, 0]]

>>> smith_waterman('AGT', 'GTC')
[[0, 0, 0, 0], [0, 0, 0, 0], [0, 1, 0, 0], [0, 0, 2, 0]]

>>> smith_waterman('AGT', 'G')
[[0, 0], [0, 0], [0, 1], [0, 0]]

>>> smith_waterman('G', 'AGT')
[[0, 0, 0, 0], [0, 0, 1, 0]]

>>> smith_waterman('AGT', 'AGTCT')
[[0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 0, 0, 3, 1, 1]]

>>> smith_waterman('AGTCT', 'AGT')
[[0, 0, 0, 0], [0, 1, 0, 0], [0, 0, 2, 0], [0, 0, 0, 3], [0, 0, 0, 1], [0, 0, 0, 1]]

>>> smith_waterman('AGTCT', 'GTC')
[[0, 0, 0, 0], [0, 0, 0, 0], [0, 1, 0, 0], [0, 0, 2, 0], [0, 0, 0, 3], [0, 0, 1, 1]]
"""
# make both query and subject uppercase
query = query.upper()
subject = subject.upper()

# Initialize score matrix
m = len(query)
n = len(subject)
score = [[0] * (n + 1) for _ in range(m + 1)]
kwargs = {"match": match, "mismatch": mismatch, "gap": gap}

for i in range(1, m + 1):
for j in range(1, n + 1):
# Calculate scores for each cell
match = score[i - 1][j - 1] + score_function(
query[i - 1], subject[j - 1], **kwargs
)
delete = score[i - 1][j] + gap
insert = score[i][j - 1] + gap

# Take maximum score
score[i][j] = max(0, match, delete, insert)

return score


def traceback(score: list[list[int]], query: str, subject: str) -> str:
r"""
Perform traceback to find the optimal local alignment.
Starts from the highest scoring cell in the matrix and traces back recursively
until a 0 score is found. Returns the alignment strings.
>>> traceback([[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]], 'ACAC', 'CA')
'CA\nCA'
>>> traceback([[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]], 'acac', 'ca')
'CA\nCA'
>>> traceback([[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]], 'ACAC', 'ca')
'CA\nCA'
>>> traceback([[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]], 'acac', 'CA')
'CA\nCA'
>>> traceback([[0, 0, 0]], 'ACAC', '')
''
"""
# make both query and subject uppercase
query = query.upper()
subject = subject.upper()
# find the indices of the maximum value in the score matrix
max_value = float("-inf")
i_max = j_max = 0
for i, row in enumerate(score):
for j, value in enumerate(row):
if value > max_value:
max_value = value
i_max, j_max = i, j
# Traceback logic to find optimal alignment
i = i_max
j = j_max
align1 = ""
align2 = ""
gap = score_function("-", "-")
# guard against empty query or subject
if i == 0 or j == 0:
return ""
while i > 0 and j > 0:
if score[i][j] == score[i - 1][j - 1] + score_function(
query[i - 1], subject[j - 1]
):
# optimal path is a diagonal take both letters
align1 = query[i - 1] + align1
align2 = subject[j - 1] + align2
i -= 1
j -= 1
elif score[i][j] == score[i - 1][j] + gap:
# optimal path is a vertical
align1 = query[i - 1] + align1
align2 = f"-{align2}"
i -= 1
else:
# optimal path is a horizontal
align1 = f"-{align1}"
align2 = subject[j - 1] + align2
j -= 1

return f"{align1}\n{align2}"


if __name__ == "__main__":
query = "HEAGAWGHEE"
subject = "PAWHEAE"

score = smith_waterman(query, subject, match=1, mismatch=-1, gap=-2)
print(traceback(score, query, subject))
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added smith waterman algorithm by BAW2501 · Pull Request #9001 · TheAlgorithms/Python · GitHub
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 Merged

tianyizheng02
merged 12 commits into

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Sep 30, 2023
 Merged


added smith waterman algorithm
#9001
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4672878

added smith waterman algorithm


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44314e4

[pre-commit.ci] auto fixes from pre-commit.com hooks


pre-commit-ci[bot] Aug 20, 2023
65b95a6

descriptive names for the parameters a and b


BAW2501 Aug 22, 2023
8e56b7e

Merge branch 'master' of https://github.com/BAW2501/Python


BAW2501 Aug 22, 2023
d8a6bcb

doctesting lowercase upcase empty string cases


BAW2501 Aug 22, 2023
fc58801

updated block quot,fixed traceback and doctests


BAW2501 Sep 24, 2023
0662f69

shorter block quote


BAW2501 Sep 25, 2023
892858a

global vars to func params,more doctests


BAW2501 Sep 25, 2023
37d7fed

Merge branch 'master' of https://github.com/BAW2501/Python


BAW2501 Sep 25, 2023
0e199f7

updated doctests


BAW2501 Sep 25, 2023
2729a57

user access to SW params


BAW2501 Sep 27, 2023
2a3e20a

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BAW2501 Sep 27, 2023

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193 changes: 193 additions & 0 deletions
dynamic_programming/smith_waterman.py

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Original file line numberDiff line numberDiff line change
@@ -0,0 +1,193 @@
"""
https://en.wikipedia.org/wiki/Smith%E2%80%93Waterman_algorithm
The Smith-Waterman algorithm is a dynamic programming algorithm used for sequence
alignment. It is particularly useful for finding similarities between two sequences,
such as DNA or protein sequences. In this implementation, gaps are penalized
linearly, meaning that the score is reduced by a fixed amount for each gap introduced
in the alignment. However, it's important to note that the Smith-Waterman algorithm
supports other gap penalty methods as well.
"""


def score_function(
 source_char: str,
 target_char: str,
 match: int = 1,
 mismatch: int = -1,
 gap: int = -2,
) -> int:
 """
 Calculate the score for a character pair based on whether they match or mismatch.
 Returns 1 if the characters match, -1 if they mismatch, and -2 if either of the
 characters is a gap.
 >>> score_function('A', 'A')
 1
 >>> score_function('A', 'C')
 -1
 >>> score_function('-', 'A')
 -2
 >>> score_function('A', '-')
 -2
 >>> score_function('-', '-')
 -2
 """
 if "-" in (source_char, target_char):
 return gap
 return match if source_char == target_char else mismatch


def smith_waterman(
 query: str,
 subject: str,
 match: int = 1,
 mismatch: int = -1,
 gap: int = -2,
) -> list[list[int]]:
 """
 Perform the Smith-Waterman local sequence alignment algorithm.
 Returns a 2D list representing the score matrix. Each value in the matrix
 corresponds to the score of the best local alignment ending at that point.
 >>> smith_waterman('ACAC', 'CA')
 [[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]]
Comment thread
BAW2501 marked this conversation as resolved.

 >>> smith_waterman('acac', 'ca')
 [[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]]
 >>> smith_waterman('ACAC', 'ca')
 [[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]]
 >>> smith_waterman('acac', 'CA')
 [[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]]
 >>> smith_waterman('ACAC', '')
 [[0], [0], [0], [0], [0]]
 >>> smith_waterman('', 'CA')
 [[0, 0, 0]]
 >>> smith_waterman('ACAC', 'CA')
 [[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]]

 >>> smith_waterman('acac', 'ca')
 [[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]]

 >>> smith_waterman('ACAC', 'ca')
 [[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]]

 >>> smith_waterman('acac', 'CA')
 [[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]]

 >>> smith_waterman('ACAC', '')
 [[0], [0], [0], [0], [0]]

 >>> smith_waterman('', 'CA')
 [[0, 0, 0]]

 >>> smith_waterman('AGT', 'AGT')
 [[0, 0, 0, 0], [0, 1, 0, 0], [0, 0, 2, 0], [0, 0, 0, 3]]

 >>> smith_waterman('AGT', 'GTA')
 [[0, 0, 0, 0], [0, 0, 0, 1], [0, 1, 0, 0], [0, 0, 2, 0]]

 >>> smith_waterman('AGT', 'GTC')
 [[0, 0, 0, 0], [0, 0, 0, 0], [0, 1, 0, 0], [0, 0, 2, 0]]

 >>> smith_waterman('AGT', 'G')
 [[0, 0], [0, 0], [0, 1], [0, 0]]

 >>> smith_waterman('G', 'AGT')
 [[0, 0, 0, 0], [0, 0, 1, 0]]

 >>> smith_waterman('AGT', 'AGTCT')
 [[0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 0, 0, 3, 1, 1]]

 >>> smith_waterman('AGTCT', 'AGT')
 [[0, 0, 0, 0], [0, 1, 0, 0], [0, 0, 2, 0], [0, 0, 0, 3], [0, 0, 0, 1], [0, 0, 0, 1]]

 >>> smith_waterman('AGTCT', 'GTC')
 [[0, 0, 0, 0], [0, 0, 0, 0], [0, 1, 0, 0], [0, 0, 2, 0], [0, 0, 0, 3], [0, 0, 1, 1]]
 """
 # make both query and subject uppercase
 query = query.upper()
 subject = subject.upper()

 # Initialize score matrix
 m = len(query)
 n = len(subject)
 score = [[0] * (n + 1) for _ in range(m + 1)]
 kwargs = {"match": match, "mismatch": mismatch, "gap": gap}

 for i in range(1, m + 1):
 for j in range(1, n + 1):
 # Calculate scores for each cell
 match = score[i - 1][j - 1] + score_function(
 query[i - 1], subject[j - 1], **kwargs
 )
 delete = score[i - 1][j] + gap
 insert = score[i][j - 1] + gap

 # Take maximum score
 score[i][j] = max(0, match, delete, insert)

 return score


def traceback(score: list[list[int]], query: str, subject: str) -> str:
 r"""
 Perform traceback to find the optimal local alignment.
 Starts from the highest scoring cell in the matrix and traces back recursively
 until a 0 score is found. Returns the alignment strings.
 >>> traceback([[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]], 'ACAC', 'CA')
 'CA\nCA'
 >>> traceback([[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]], 'acac', 'ca')
 'CA\nCA'
 >>> traceback([[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]], 'ACAC', 'ca')
 'CA\nCA'
 >>> traceback([[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]], 'acac', 'CA')
 'CA\nCA'
 >>> traceback([[0, 0, 0]], 'ACAC', '')
 ''
 """
 # make both query and subject uppercase
 query = query.upper()
 subject = subject.upper()
 # find the indices of the maximum value in the score matrix
 max_value = float("-inf")
 i_max = j_max = 0
 for i, row in enumerate(score):
 for j, value in enumerate(row):
 if value > max_value:
 max_value = value
 i_max, j_max = i, j
 # Traceback logic to find optimal alignment
 i = i_max
 j = j_max
 align1 = ""
 align2 = ""
 gap = score_function("-", "-")
 # guard against empty query or subject
 if i == 0 or j == 0:
 return ""
 while i > 0 and j > 0:
 if score[i][j] == score[i - 1][j - 1] + score_function(
 query[i - 1], subject[j - 1]
 ):
 # optimal path is a diagonal take both letters
 align1 = query[i - 1] + align1
 align2 = subject[j - 1] + align2
 i -= 1
 j -= 1
 elif score[i][j] == score[i - 1][j] + gap:
 # optimal path is a vertical
 align1 = query[i - 1] + align1
 align2 = f"-{align2}"
 i -= 1
 else:
 # optimal path is a horizontal
 align1 = f"-{align1}"
 align2 = subject[j - 1] + align2
 j -= 1

 return f"{align1}\n{align2}"


if __name__ == "__main__":
 query = "HEAGAWGHEE"
 subject = "PAWHEAE"

 score = smith_waterman(query, subject, match=1, mismatch=-1, gap=-2)
 print(traceback(score, query, subject))

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added smith waterman algorithm by BAW2501 · Pull Request #9001 · TheAlgorithms/Python · GitHub
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added smith waterman algorithm#9001

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 Merged

tianyizheng02
merged 12 commits into

from

Sep 30, 2023
 Merged


added smith waterman algorithm
#9001
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4672878

added smith waterman algorithm


BAW2501 Aug 20, 2023
44314e4

[pre-commit.ci] auto fixes from pre-commit.com hooks


pre-commit-ci[bot] Aug 20, 2023
65b95a6

descriptive names for the parameters a and b


BAW2501 Aug 22, 2023
8e56b7e

Merge branch 'master' of https://github.com/BAW2501/Python


BAW2501 Aug 22, 2023
d8a6bcb

doctesting lowercase upcase empty string cases


BAW2501 Aug 22, 2023
fc58801

updated block quot,fixed traceback and doctests


BAW2501 Sep 24, 2023
0662f69

shorter block quote


BAW2501 Sep 25, 2023
892858a

global vars to func params,more doctests


BAW2501 Sep 25, 2023
37d7fed

Merge branch 'master' of https://github.com/BAW2501/Python


BAW2501 Sep 25, 2023
0e199f7

updated doctests


BAW2501 Sep 25, 2023
2729a57

user access to SW params


BAW2501 Sep 27, 2023
2a3e20a

formating


BAW2501 Sep 27, 2023

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193 changes: 193 additions & 0 deletions
dynamic_programming/smith_waterman.py

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Original file line numberDiff line numberDiff line change
@@ -0,0 +1,193 @@
"""
https://en.wikipedia.org/wiki/Smith%E2%80%93Waterman_algorithm
The Smith-Waterman algorithm is a dynamic programming algorithm used for sequence
alignment. It is particularly useful for finding similarities between two sequences,
such as DNA or protein sequences. In this implementation, gaps are penalized
linearly, meaning that the score is reduced by a fixed amount for each gap introduced
in the alignment. However, it's important to note that the Smith-Waterman algorithm
supports other gap penalty methods as well.
"""


def score_function(
 source_char: str,
 target_char: str,
 match: int = 1,
 mismatch: int = -1,
 gap: int = -2,
) -> int:
 """
 Calculate the score for a character pair based on whether they match or mismatch.
 Returns 1 if the characters match, -1 if they mismatch, and -2 if either of the
 characters is a gap.
 >>> score_function('A', 'A')
 1
 >>> score_function('A', 'C')
 -1
 >>> score_function('-', 'A')
 -2
 >>> score_function('A', '-')
 -2
 >>> score_function('-', '-')
 -2
 """
 if "-" in (source_char, target_char):
 return gap
 return match if source_char == target_char else mismatch


def smith_waterman(
 query: str,
 subject: str,
 match: int = 1,
 mismatch: int = -1,
 gap: int = -2,
) -> list[list[int]]:
 """
 Perform the Smith-Waterman local sequence alignment algorithm.
 Returns a 2D list representing the score matrix. Each value in the matrix
 corresponds to the score of the best local alignment ending at that point.
 >>> smith_waterman('ACAC', 'CA')
 [[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]]
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 >>> smith_waterman('acac', 'ca')
 [[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]]
 >>> smith_waterman('ACAC', 'ca')
 [[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]]
 >>> smith_waterman('acac', 'CA')
 [[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]]
 >>> smith_waterman('ACAC', '')
 [[0], [0], [0], [0], [0]]
 >>> smith_waterman('', 'CA')
 [[0, 0, 0]]
 >>> smith_waterman('ACAC', 'CA')
 [[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]]

 >>> smith_waterman('acac', 'ca')
 [[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]]

 >>> smith_waterman('ACAC', 'ca')
 [[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]]

 >>> smith_waterman('acac', 'CA')
 [[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]]

 >>> smith_waterman('ACAC', '')
 [[0], [0], [0], [0], [0]]

 >>> smith_waterman('', 'CA')
 [[0, 0, 0]]

 >>> smith_waterman('AGT', 'AGT')
 [[0, 0, 0, 0], [0, 1, 0, 0], [0, 0, 2, 0], [0, 0, 0, 3]]

 >>> smith_waterman('AGT', 'GTA')
 [[0, 0, 0, 0], [0, 0, 0, 1], [0, 1, 0, 0], [0, 0, 2, 0]]

 >>> smith_waterman('AGT', 'GTC')
 [[0, 0, 0, 0], [0, 0, 0, 0], [0, 1, 0, 0], [0, 0, 2, 0]]

 >>> smith_waterman('AGT', 'G')
 [[0, 0], [0, 0], [0, 1], [0, 0]]

 >>> smith_waterman('G', 'AGT')
 [[0, 0, 0, 0], [0, 0, 1, 0]]

 >>> smith_waterman('AGT', 'AGTCT')
 [[0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 0, 0, 3, 1, 1]]

 >>> smith_waterman('AGTCT', 'AGT')
 [[0, 0, 0, 0], [0, 1, 0, 0], [0, 0, 2, 0], [0, 0, 0, 3], [0, 0, 0, 1], [0, 0, 0, 1]]

 >>> smith_waterman('AGTCT', 'GTC')
 [[0, 0, 0, 0], [0, 0, 0, 0], [0, 1, 0, 0], [0, 0, 2, 0], [0, 0, 0, 3], [0, 0, 1, 1]]
 """
 # make both query and subject uppercase
 query = query.upper()
 subject = subject.upper()

 # Initialize score matrix
 m = len(query)
 n = len(subject)
 score = [[0] * (n + 1) for _ in range(m + 1)]
 kwargs = {"match": match, "mismatch": mismatch, "gap": gap}

 for i in range(1, m + 1):
 for j in range(1, n + 1):
 # Calculate scores for each cell
 match = score[i - 1][j - 1] + score_function(
 query[i - 1], subject[j - 1], **kwargs
 )
 delete = score[i - 1][j] + gap
 insert = score[i][j - 1] + gap

 # Take maximum score
 score[i][j] = max(0, match, delete, insert)

 return score


def traceback(score: list[list[int]], query: str, subject: str) -> str:
 r"""
 Perform traceback to find the optimal local alignment.
 Starts from the highest scoring cell in the matrix and traces back recursively
 until a 0 score is found. Returns the alignment strings.
 >>> traceback([[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]], 'ACAC', 'CA')
 'CA\nCA'
 >>> traceback([[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]], 'acac', 'ca')
 'CA\nCA'
 >>> traceback([[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]], 'ACAC', 'ca')
 'CA\nCA'
 >>> traceback([[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]], 'acac', 'CA')
 'CA\nCA'
 >>> traceback([[0, 0, 0]], 'ACAC', '')
 ''
 """
 # make both query and subject uppercase
 query = query.upper()
 subject = subject.upper()
 # find the indices of the maximum value in the score matrix
 max_value = float("-inf")
 i_max = j_max = 0
 for i, row in enumerate(score):
 for j, value in enumerate(row):
 if value > max_value:
 max_value = value
 i_max, j_max = i, j
 # Traceback logic to find optimal alignment
 i = i_max
 j = j_max
 align1 = ""
 align2 = ""
 gap = score_function("-", "-")
 # guard against empty query or subject
 if i == 0 or j == 0:
 return ""
 while i > 0 and j > 0:
 if score[i][j] == score[i - 1][j - 1] + score_function(
 query[i - 1], subject[j - 1]
 ):
 # optimal path is a diagonal take both letters
 align1 = query[i - 1] + align1
 align2 = subject[j - 1] + align2
 i -= 1
 j -= 1
 elif score[i][j] == score[i - 1][j] + gap:
 # optimal path is a vertical
 align1 = query[i - 1] + align1
 align2 = f"-{align2}"
 i -= 1
 else:
 # optimal path is a horizontal
 align1 = f"-{align1}"
 align2 = subject[j - 1] + align2
 j -= 1

 return f"{align1}\n{align2}"


if __name__ == "__main__":
 query = "HEAGAWGHEE"
 subject = "PAWHEAE"

 score = smith_waterman(query, subject, match=1, mismatch=-1, gap=-2)
 print(traceback(score, query, subject))

, 'i');
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var ref = document.referrer;
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}
} catch(__e) { console.warn('[Userscript:Highlight Search Terms]', __e); }
})();
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try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '
added smith waterman algorithm by BAW2501 · Pull Request #9001 · TheAlgorithms/Python · GitHub
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Merge branch 'master' of https://github.com/BAW2501/Python


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dynamic_programming/smith_waterman.py

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Original file line numberDiff line numberDiff line change
@@ -0,0 +1,193 @@
"""
https://en.wikipedia.org/wiki/Smith%E2%80%93Waterman_algorithm
The Smith-Waterman algorithm is a dynamic programming algorithm used for sequence
alignment. It is particularly useful for finding similarities between two sequences,
such as DNA or protein sequences. In this implementation, gaps are penalized
linearly, meaning that the score is reduced by a fixed amount for each gap introduced
in the alignment. However, it's important to note that the Smith-Waterman algorithm
supports other gap penalty methods as well.
"""


def score_function(
 source_char: str,
 target_char: str,
 match: int = 1,
 mismatch: int = -1,
 gap: int = -2,
) -> int:
 """
 Calculate the score for a character pair based on whether they match or mismatch.
 Returns 1 if the characters match, -1 if they mismatch, and -2 if either of the
 characters is a gap.
 >>> score_function('A', 'A')
 1
 >>> score_function('A', 'C')
 -1
 >>> score_function('-', 'A')
 -2
 >>> score_function('A', '-')
 -2
 >>> score_function('-', '-')
 -2
 """
 if "-" in (source_char, target_char):
 return gap
 return match if source_char == target_char else mismatch


def smith_waterman(
 query: str,
 subject: str,
 match: int = 1,
 mismatch: int = -1,
 gap: int = -2,
) -> list[list[int]]:
 """
 Perform the Smith-Waterman local sequence alignment algorithm.
 Returns a 2D list representing the score matrix. Each value in the matrix
 corresponds to the score of the best local alignment ending at that point.
 >>> smith_waterman('ACAC', 'CA')
 [[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]]
Comment thread
BAW2501 marked this conversation as resolved.

 >>> smith_waterman('acac', 'ca')
 [[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]]
 >>> smith_waterman('ACAC', 'ca')
 [[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]]
 >>> smith_waterman('acac', 'CA')
 [[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]]
 >>> smith_waterman('ACAC', '')
 [[0], [0], [0], [0], [0]]
 >>> smith_waterman('', 'CA')
 [[0, 0, 0]]
 >>> smith_waterman('ACAC', 'CA')
 [[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]]

 >>> smith_waterman('acac', 'ca')
 [[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]]

 >>> smith_waterman('ACAC', 'ca')
 [[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]]

 >>> smith_waterman('acac', 'CA')
 [[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]]

 >>> smith_waterman('ACAC', '')
 [[0], [0], [0], [0], [0]]

 >>> smith_waterman('', 'CA')
 [[0, 0, 0]]

 >>> smith_waterman('AGT', 'AGT')
 [[0, 0, 0, 0], [0, 1, 0, 0], [0, 0, 2, 0], [0, 0, 0, 3]]

 >>> smith_waterman('AGT', 'GTA')
 [[0, 0, 0, 0], [0, 0, 0, 1], [0, 1, 0, 0], [0, 0, 2, 0]]

 >>> smith_waterman('AGT', 'GTC')
 [[0, 0, 0, 0], [0, 0, 0, 0], [0, 1, 0, 0], [0, 0, 2, 0]]

 >>> smith_waterman('AGT', 'G')
 [[0, 0], [0, 0], [0, 1], [0, 0]]

 >>> smith_waterman('G', 'AGT')
 [[0, 0, 0, 0], [0, 0, 1, 0]]

 >>> smith_waterman('AGT', 'AGTCT')
 [[0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 0, 0, 3, 1, 1]]

 >>> smith_waterman('AGTCT', 'AGT')
 [[0, 0, 0, 0], [0, 1, 0, 0], [0, 0, 2, 0], [0, 0, 0, 3], [0, 0, 0, 1], [0, 0, 0, 1]]

 >>> smith_waterman('AGTCT', 'GTC')
 [[0, 0, 0, 0], [0, 0, 0, 0], [0, 1, 0, 0], [0, 0, 2, 0], [0, 0, 0, 3], [0, 0, 1, 1]]
 """
 # make both query and subject uppercase
 query = query.upper()
 subject = subject.upper()

 # Initialize score matrix
 m = len(query)
 n = len(subject)
 score = [[0] * (n + 1) for _ in range(m + 1)]
 kwargs = {"match": match, "mismatch": mismatch, "gap": gap}

 for i in range(1, m + 1):
 for j in range(1, n + 1):
 # Calculate scores for each cell
 match = score[i - 1][j - 1] + score_function(
 query[i - 1], subject[j - 1], **kwargs
 )
 delete = score[i - 1][j] + gap
 insert = score[i][j - 1] + gap

 # Take maximum score
 score[i][j] = max(0, match, delete, insert)

 return score


def traceback(score: list[list[int]], query: str, subject: str) -> str:
 r"""
 Perform traceback to find the optimal local alignment.
 Starts from the highest scoring cell in the matrix and traces back recursively
 until a 0 score is found. Returns the alignment strings.
 >>> traceback([[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]], 'ACAC', 'CA')
 'CA\nCA'
 >>> traceback([[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]], 'acac', 'ca')
 'CA\nCA'
 >>> traceback([[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]], 'ACAC', 'ca')
 'CA\nCA'
 >>> traceback([[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]], 'acac', 'CA')
 'CA\nCA'
 >>> traceback([[0, 0, 0]], 'ACAC', '')
 ''
 """
 # make both query and subject uppercase
 query = query.upper()
 subject = subject.upper()
 # find the indices of the maximum value in the score matrix
 max_value = float("-inf")
 i_max = j_max = 0
 for i, row in enumerate(score):
 for j, value in enumerate(row):
 if value > max_value:
 max_value = value
 i_max, j_max = i, j
 # Traceback logic to find optimal alignment
 i = i_max
 j = j_max
 align1 = ""
 align2 = ""
 gap = score_function("-", "-")
 # guard against empty query or subject
 if i == 0 or j == 0:
 return ""
 while i > 0 and j > 0:
 if score[i][j] == score[i - 1][j - 1] + score_function(
 query[i - 1], subject[j - 1]
 ):
 # optimal path is a diagonal take both letters
 align1 = query[i - 1] + align1
 align2 = subject[j - 1] + align2
 i -= 1
 j -= 1
 elif score[i][j] == score[i - 1][j] + gap:
 # optimal path is a vertical
 align1 = query[i - 1] + align1
 align2 = f"-{align2}"
 i -= 1
 else:
 # optimal path is a horizontal
 align1 = f"-{align1}"
 align2 = subject[j - 1] + align2
 j -= 1

 return f"{align1}\n{align2}"


if __name__ == "__main__":
 query = "HEAGAWGHEE"
 subject = "PAWHEAE"

 score = smith_waterman(query, subject, match=1, mismatch=-1, gap=-2)
 print(traceback(score, query, subject))

, 'i');
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'fbclid', 'gclid', 'dclid', 'msclkid', 'yclid',
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added smith waterman algorithm by BAW2501 · Pull Request #9001 · TheAlgorithms/Python · GitHub
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added smith waterman algorithm#9001

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 Merged

tianyizheng02
merged 12 commits into

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Sep 30, 2023
 Merged


added smith waterman algorithm
#9001
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4672878

added smith waterman algorithm


BAW2501 Aug 20, 2023
44314e4

[pre-commit.ci] auto fixes from pre-commit.com hooks


pre-commit-ci[bot] Aug 20, 2023
65b95a6

descriptive names for the parameters a and b


BAW2501 Aug 22, 2023
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Merge branch 'master' of https://github.com/BAW2501/Python


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doctesting lowercase upcase empty string cases


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fc58801

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0662f69

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global vars to func params,more doctests


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37d7fed

Merge branch 'master' of https://github.com/BAW2501/Python


BAW2501 Sep 25, 2023
0e199f7

updated doctests


BAW2501 Sep 25, 2023
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BAW2501 Sep 27, 2023
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dynamic_programming/smith_waterman.py

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Original file line numberDiff line numberDiff line change
@@ -0,0 +1,193 @@
"""
https://en.wikipedia.org/wiki/Smith%E2%80%93Waterman_algorithm
The Smith-Waterman algorithm is a dynamic programming algorithm used for sequence
alignment. It is particularly useful for finding similarities between two sequences,
such as DNA or protein sequences. In this implementation, gaps are penalized
linearly, meaning that the score is reduced by a fixed amount for each gap introduced
in the alignment. However, it's important to note that the Smith-Waterman algorithm
supports other gap penalty methods as well.
"""


def score_function(
 source_char: str,
 target_char: str,
 match: int = 1,
 mismatch: int = -1,
 gap: int = -2,
) -> int:
 """
 Calculate the score for a character pair based on whether they match or mismatch.
 Returns 1 if the characters match, -1 if they mismatch, and -2 if either of the
 characters is a gap.
 >>> score_function('A', 'A')
 1
 >>> score_function('A', 'C')
 -1
 >>> score_function('-', 'A')
 -2
 >>> score_function('A', '-')
 -2
 >>> score_function('-', '-')
 -2
 """
 if "-" in (source_char, target_char):
 return gap
 return match if source_char == target_char else mismatch


def smith_waterman(
 query: str,
 subject: str,
 match: int = 1,
 mismatch: int = -1,
 gap: int = -2,
) -> list[list[int]]:
 """
 Perform the Smith-Waterman local sequence alignment algorithm.
 Returns a 2D list representing the score matrix. Each value in the matrix
 corresponds to the score of the best local alignment ending at that point.
 >>> smith_waterman('ACAC', 'CA')
 [[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]]
Comment thread
BAW2501 marked this conversation as resolved.

 >>> smith_waterman('acac', 'ca')
 [[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]]
 >>> smith_waterman('ACAC', 'ca')
 [[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]]
 >>> smith_waterman('acac', 'CA')
 [[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]]
 >>> smith_waterman('ACAC', '')
 [[0], [0], [0], [0], [0]]
 >>> smith_waterman('', 'CA')
 [[0, 0, 0]]
 >>> smith_waterman('ACAC', 'CA')
 [[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]]

 >>> smith_waterman('acac', 'ca')
 [[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]]

 >>> smith_waterman('ACAC', 'ca')
 [[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]]

 >>> smith_waterman('acac', 'CA')
 [[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]]

 >>> smith_waterman('ACAC', '')
 [[0], [0], [0], [0], [0]]

 >>> smith_waterman('', 'CA')
 [[0, 0, 0]]

 >>> smith_waterman('AGT', 'AGT')
 [[0, 0, 0, 0], [0, 1, 0, 0], [0, 0, 2, 0], [0, 0, 0, 3]]

 >>> smith_waterman('AGT', 'GTA')
 [[0, 0, 0, 0], [0, 0, 0, 1], [0, 1, 0, 0], [0, 0, 2, 0]]

 >>> smith_waterman('AGT', 'GTC')
 [[0, 0, 0, 0], [0, 0, 0, 0], [0, 1, 0, 0], [0, 0, 2, 0]]

 >>> smith_waterman('AGT', 'G')
 [[0, 0], [0, 0], [0, 1], [0, 0]]

 >>> smith_waterman('G', 'AGT')
 [[0, 0, 0, 0], [0, 0, 1, 0]]

 >>> smith_waterman('AGT', 'AGTCT')
 [[0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 0, 0, 3, 1, 1]]

 >>> smith_waterman('AGTCT', 'AGT')
 [[0, 0, 0, 0], [0, 1, 0, 0], [0, 0, 2, 0], [0, 0, 0, 3], [0, 0, 0, 1], [0, 0, 0, 1]]

 >>> smith_waterman('AGTCT', 'GTC')
 [[0, 0, 0, 0], [0, 0, 0, 0], [0, 1, 0, 0], [0, 0, 2, 0], [0, 0, 0, 3], [0, 0, 1, 1]]
 """
 # make both query and subject uppercase
 query = query.upper()
 subject = subject.upper()

 # Initialize score matrix
 m = len(query)
 n = len(subject)
 score = [[0] * (n + 1) for _ in range(m + 1)]
 kwargs = {"match": match, "mismatch": mismatch, "gap": gap}

 for i in range(1, m + 1):
 for j in range(1, n + 1):
 # Calculate scores for each cell
 match = score[i - 1][j - 1] + score_function(
 query[i - 1], subject[j - 1], **kwargs
 )
 delete = score[i - 1][j] + gap
 insert = score[i][j - 1] + gap

 # Take maximum score
 score[i][j] = max(0, match, delete, insert)

 return score


def traceback(score: list[list[int]], query: str, subject: str) -> str:
 r"""
 Perform traceback to find the optimal local alignment.
 Starts from the highest scoring cell in the matrix and traces back recursively
 until a 0 score is found. Returns the alignment strings.
 >>> traceback([[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]], 'ACAC', 'CA')
 'CA\nCA'
 >>> traceback([[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]], 'acac', 'ca')
 'CA\nCA'
 >>> traceback([[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]], 'ACAC', 'ca')
 'CA\nCA'
 >>> traceback([[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]], 'acac', 'CA')
 'CA\nCA'
 >>> traceback([[0, 0, 0]], 'ACAC', '')
 ''
 """
 # make both query and subject uppercase
 query = query.upper()
 subject = subject.upper()
 # find the indices of the maximum value in the score matrix
 max_value = float("-inf")
 i_max = j_max = 0
 for i, row in enumerate(score):
 for j, value in enumerate(row):
 if value > max_value:
 max_value = value
 i_max, j_max = i, j
 # Traceback logic to find optimal alignment
 i = i_max
 j = j_max
 align1 = ""
 align2 = ""
 gap = score_function("-", "-")
 # guard against empty query or subject
 if i == 0 or j == 0:
 return ""
 while i > 0 and j > 0:
 if score[i][j] == score[i - 1][j - 1] + score_function(
 query[i - 1], subject[j - 1]
 ):
 # optimal path is a diagonal take both letters
 align1 = query[i - 1] + align1
 align2 = subject[j - 1] + align2
 i -= 1
 j -= 1
 elif score[i][j] == score[i - 1][j] + gap:
 # optimal path is a vertical
 align1 = query[i - 1] + align1
 align2 = f"-{align2}"
 i -= 1
 else:
 # optimal path is a horizontal
 align1 = f"-{align1}"
 align2 = subject[j - 1] + align2
 j -= 1

 return f"{align1}\n{align2}"


if __name__ == "__main__":
 query = "HEAGAWGHEE"
 subject = "PAWHEAE"

 score = smith_waterman(query, subject, match=1, mismatch=-1, gap=-2)
 print(traceback(score, query, subject))

, 'i');
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added smith waterman algorithm by BAW2501 · Pull Request #9001 · TheAlgorithms/Python · GitHub
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dynamic_programming/smith_waterman.py

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"""
https://en.wikipedia.org/wiki/Smith%E2%80%93Waterman_algorithm
The Smith-Waterman algorithm is a dynamic programming algorithm used for sequence
alignment. It is particularly useful for finding similarities between two sequences,
such as DNA or protein sequences. In this implementation, gaps are penalized
linearly, meaning that the score is reduced by a fixed amount for each gap introduced
in the alignment. However, it's important to note that the Smith-Waterman algorithm
supports other gap penalty methods as well.
"""


def score_function(
 source_char: str,
 target_char: str,
 match: int = 1,
 mismatch: int = -1,
 gap: int = -2,
) -> int:
 """
 Calculate the score for a character pair based on whether they match or mismatch.
 Returns 1 if the characters match, -1 if they mismatch, and -2 if either of the
 characters is a gap.
 >>> score_function('A', 'A')
 1
 >>> score_function('A', 'C')
 -1
 >>> score_function('-', 'A')
 -2
 >>> score_function('A', '-')
 -2
 >>> score_function('-', '-')
 -2
 """
 if "-" in (source_char, target_char):
 return gap
 return match if source_char == target_char else mismatch


def smith_waterman(
 query: str,
 subject: str,
 match: int = 1,
 mismatch: int = -1,
 gap: int = -2,
) -> list[list[int]]:
 """
 Perform the Smith-Waterman local sequence alignment algorithm.
 Returns a 2D list representing the score matrix. Each value in the matrix
 corresponds to the score of the best local alignment ending at that point.
 >>> smith_waterman('ACAC', 'CA')
 [[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]]
Comment thread
BAW2501 marked this conversation as resolved.

 >>> smith_waterman('acac', 'ca')
 [[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]]
 >>> smith_waterman('ACAC', 'ca')
 [[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]]
 >>> smith_waterman('acac', 'CA')
 [[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]]
 >>> smith_waterman('ACAC', '')
 [[0], [0], [0], [0], [0]]
 >>> smith_waterman('', 'CA')
 [[0, 0, 0]]
 >>> smith_waterman('ACAC', 'CA')
 [[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]]

 >>> smith_waterman('acac', 'ca')
 [[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]]

 >>> smith_waterman('ACAC', 'ca')
 [[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]]

 >>> smith_waterman('acac', 'CA')
 [[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]]

 >>> smith_waterman('ACAC', '')
 [[0], [0], [0], [0], [0]]

 >>> smith_waterman('', 'CA')
 [[0, 0, 0]]

 >>> smith_waterman('AGT', 'AGT')
 [[0, 0, 0, 0], [0, 1, 0, 0], [0, 0, 2, 0], [0, 0, 0, 3]]

 >>> smith_waterman('AGT', 'GTA')
 [[0, 0, 0, 0], [0, 0, 0, 1], [0, 1, 0, 0], [0, 0, 2, 0]]

 >>> smith_waterman('AGT', 'GTC')
 [[0, 0, 0, 0], [0, 0, 0, 0], [0, 1, 0, 0], [0, 0, 2, 0]]

 >>> smith_waterman('AGT', 'G')
 [[0, 0], [0, 0], [0, 1], [0, 0]]

 >>> smith_waterman('G', 'AGT')
 [[0, 0, 0, 0], [0, 0, 1, 0]]

 >>> smith_waterman('AGT', 'AGTCT')
 [[0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 0, 0, 3, 1, 1]]

 >>> smith_waterman('AGTCT', 'AGT')
 [[0, 0, 0, 0], [0, 1, 0, 0], [0, 0, 2, 0], [0, 0, 0, 3], [0, 0, 0, 1], [0, 0, 0, 1]]

 >>> smith_waterman('AGTCT', 'GTC')
 [[0, 0, 0, 0], [0, 0, 0, 0], [0, 1, 0, 0], [0, 0, 2, 0], [0, 0, 0, 3], [0, 0, 1, 1]]
 """
 # make both query and subject uppercase
 query = query.upper()
 subject = subject.upper()

 # Initialize score matrix
 m = len(query)
 n = len(subject)
 score = [[0] * (n + 1) for _ in range(m + 1)]
 kwargs = {"match": match, "mismatch": mismatch, "gap": gap}

 for i in range(1, m + 1):
 for j in range(1, n + 1):
 # Calculate scores for each cell
 match = score[i - 1][j - 1] + score_function(
 query[i - 1], subject[j - 1], **kwargs
 )
 delete = score[i - 1][j] + gap
 insert = score[i][j - 1] + gap

 # Take maximum score
 score[i][j] = max(0, match, delete, insert)

 return score


def traceback(score: list[list[int]], query: str, subject: str) -> str:
 r"""
 Perform traceback to find the optimal local alignment.
 Starts from the highest scoring cell in the matrix and traces back recursively
 until a 0 score is found. Returns the alignment strings.
 >>> traceback([[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]], 'ACAC', 'CA')
 'CA\nCA'
 >>> traceback([[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]], 'acac', 'ca')
 'CA\nCA'
 >>> traceback([[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]], 'ACAC', 'ca')
 'CA\nCA'
 >>> traceback([[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]], 'acac', 'CA')
 'CA\nCA'
 >>> traceback([[0, 0, 0]], 'ACAC', '')
 ''
 """
 # make both query and subject uppercase
 query = query.upper()
 subject = subject.upper()
 # find the indices of the maximum value in the score matrix
 max_value = float("-inf")
 i_max = j_max = 0
 for i, row in enumerate(score):
 for j, value in enumerate(row):
 if value > max_value:
 max_value = value
 i_max, j_max = i, j
 # Traceback logic to find optimal alignment
 i = i_max
 j = j_max
 align1 = ""
 align2 = ""
 gap = score_function("-", "-")
 # guard against empty query or subject
 if i == 0 or j == 0:
 return ""
 while i > 0 and j > 0:
 if score[i][j] == score[i - 1][j - 1] + score_function(
 query[i - 1], subject[j - 1]
 ):
 # optimal path is a diagonal take both letters
 align1 = query[i - 1] + align1
 align2 = subject[j - 1] + align2
 i -= 1
 j -= 1
 elif score[i][j] == score[i - 1][j] + gap:
 # optimal path is a vertical
 align1 = query[i - 1] + align1
 align2 = f"-{align2}"
 i -= 1
 else:
 # optimal path is a horizontal
 align1 = f"-{align1}"
 align2 = subject[j - 1] + align2
 j -= 1

 return f"{align1}\n{align2}"


if __name__ == "__main__":
 query = "HEAGAWGHEE"
 subject = "PAWHEAE"

 score = smith_waterman(query, subject, match=1, mismatch=-1, gap=-2)
 print(traceback(score, query, subject))

, 'i');
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added smith waterman algorithm by BAW2501 · Pull Request #9001 · TheAlgorithms/Python · GitHub
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 Merged

tianyizheng02
merged 12 commits into

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Sep 30, 2023
 Merged


added smith waterman algorithm
#9001
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4672878

added smith waterman algorithm


BAW2501 Aug 20, 2023
44314e4

[pre-commit.ci] auto fixes from pre-commit.com hooks


pre-commit-ci[bot] Aug 20, 2023
65b95a6

descriptive names for the parameters a and b


BAW2501 Aug 22, 2023
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Merge branch 'master' of https://github.com/BAW2501/Python


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Merge branch 'master' of https://github.com/BAW2501/Python


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dynamic_programming/smith_waterman.py

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Original file line numberDiff line numberDiff line change
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"""
https://en.wikipedia.org/wiki/Smith%E2%80%93Waterman_algorithm
The Smith-Waterman algorithm is a dynamic programming algorithm used for sequence
alignment. It is particularly useful for finding similarities between two sequences,
such as DNA or protein sequences. In this implementation, gaps are penalized
linearly, meaning that the score is reduced by a fixed amount for each gap introduced
in the alignment. However, it's important to note that the Smith-Waterman algorithm
supports other gap penalty methods as well.
"""


def score_function(
 source_char: str,
 target_char: str,
 match: int = 1,
 mismatch: int = -1,
 gap: int = -2,
) -> int:
 """
 Calculate the score for a character pair based on whether they match or mismatch.
 Returns 1 if the characters match, -1 if they mismatch, and -2 if either of the
 characters is a gap.
 >>> score_function('A', 'A')
 1
 >>> score_function('A', 'C')
 -1
 >>> score_function('-', 'A')
 -2
 >>> score_function('A', '-')
 -2
 >>> score_function('-', '-')
 -2
 """
 if "-" in (source_char, target_char):
 return gap
 return match if source_char == target_char else mismatch


def smith_waterman(
 query: str,
 subject: str,
 match: int = 1,
 mismatch: int = -1,
 gap: int = -2,
) -> list[list[int]]:
 """
 Perform the Smith-Waterman local sequence alignment algorithm.
 Returns a 2D list representing the score matrix. Each value in the matrix
 corresponds to the score of the best local alignment ending at that point.
 >>> smith_waterman('ACAC', 'CA')
 [[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]]
Comment thread
BAW2501 marked this conversation as resolved.

 >>> smith_waterman('acac', 'ca')
 [[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]]
 >>> smith_waterman('ACAC', 'ca')
 [[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]]
 >>> smith_waterman('acac', 'CA')
 [[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]]
 >>> smith_waterman('ACAC', '')
 [[0], [0], [0], [0], [0]]
 >>> smith_waterman('', 'CA')
 [[0, 0, 0]]
 >>> smith_waterman('ACAC', 'CA')
 [[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]]

 >>> smith_waterman('acac', 'ca')
 [[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]]

 >>> smith_waterman('ACAC', 'ca')
 [[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]]

 >>> smith_waterman('acac', 'CA')
 [[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]]

 >>> smith_waterman('ACAC', '')
 [[0], [0], [0], [0], [0]]

 >>> smith_waterman('', 'CA')
 [[0, 0, 0]]

 >>> smith_waterman('AGT', 'AGT')
 [[0, 0, 0, 0], [0, 1, 0, 0], [0, 0, 2, 0], [0, 0, 0, 3]]

 >>> smith_waterman('AGT', 'GTA')
 [[0, 0, 0, 0], [0, 0, 0, 1], [0, 1, 0, 0], [0, 0, 2, 0]]

 >>> smith_waterman('AGT', 'GTC')
 [[0, 0, 0, 0], [0, 0, 0, 0], [0, 1, 0, 0], [0, 0, 2, 0]]

 >>> smith_waterman('AGT', 'G')
 [[0, 0], [0, 0], [0, 1], [0, 0]]

 >>> smith_waterman('G', 'AGT')
 [[0, 0, 0, 0], [0, 0, 1, 0]]

 >>> smith_waterman('AGT', 'AGTCT')
 [[0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 2, 0, 0, 0], [0, 0, 0, 3, 1, 1]]

 >>> smith_waterman('AGTCT', 'AGT')
 [[0, 0, 0, 0], [0, 1, 0, 0], [0, 0, 2, 0], [0, 0, 0, 3], [0, 0, 0, 1], [0, 0, 0, 1]]

 >>> smith_waterman('AGTCT', 'GTC')
 [[0, 0, 0, 0], [0, 0, 0, 0], [0, 1, 0, 0], [0, 0, 2, 0], [0, 0, 0, 3], [0, 0, 1, 1]]
 """
 # make both query and subject uppercase
 query = query.upper()
 subject = subject.upper()

 # Initialize score matrix
 m = len(query)
 n = len(subject)
 score = [[0] * (n + 1) for _ in range(m + 1)]
 kwargs = {"match": match, "mismatch": mismatch, "gap": gap}

 for i in range(1, m + 1):
 for j in range(1, n + 1):
 # Calculate scores for each cell
 match = score[i - 1][j - 1] + score_function(
 query[i - 1], subject[j - 1], **kwargs
 )
 delete = score[i - 1][j] + gap
 insert = score[i][j - 1] + gap

 # Take maximum score
 score[i][j] = max(0, match, delete, insert)

 return score


def traceback(score: list[list[int]], query: str, subject: str) -> str:
 r"""
 Perform traceback to find the optimal local alignment.
 Starts from the highest scoring cell in the matrix and traces back recursively
 until a 0 score is found. Returns the alignment strings.
 >>> traceback([[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]], 'ACAC', 'CA')
 'CA\nCA'
 >>> traceback([[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]], 'acac', 'ca')
 'CA\nCA'
 >>> traceback([[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]], 'ACAC', 'ca')
 'CA\nCA'
 >>> traceback([[0, 0, 0], [0, 0, 1], [0, 1, 0], [0, 0, 2], [0, 1, 0]], 'acac', 'CA')
 'CA\nCA'
 >>> traceback([[0, 0, 0]], 'ACAC', '')
 ''
 """
 # make both query and subject uppercase
 query = query.upper()
 subject = subject.upper()
 # find the indices of the maximum value in the score matrix
 max_value = float("-inf")
 i_max = j_max = 0
 for i, row in enumerate(score):
 for j, value in enumerate(row):
 if value > max_value:
 max_value = value
 i_max, j_max = i, j
 # Traceback logic to find optimal alignment
 i = i_max
 j = j_max
 align1 = ""
 align2 = ""
 gap = score_function("-", "-")
 # guard against empty query or subject
 if i == 0 or j == 0:
 return ""
 while i > 0 and j > 0:
 if score[i][j] == score[i - 1][j - 1] + score_function(
 query[i - 1], subject[j - 1]
 ):
 # optimal path is a diagonal take both letters
 align1 = query[i - 1] + align1
 align2 = subject[j - 1] + align2
 i -= 1
 j -= 1
 elif score[i][j] == score[i - 1][j] + gap:
 # optimal path is a vertical
 align1 = query[i - 1] + align1
 align2 = f"-{align2}"
 i -= 1
 else:
 # optimal path is a horizontal
 align1 = f"-{align1}"
 align2 = subject[j - 1] + align2
 j -= 1

 return f"{align1}\n{align2}"


if __name__ == "__main__":
 query = "HEAGAWGHEE"
 subject = "PAWHEAE"

 score = smith_waterman(query, subject, match=1, mismatch=-1, gap=-2)
 print(traceback(score, query, subject))