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Retranslate the complete English edition from Simplified Chinese (#2010)

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* Retranslate the complete English edition from Simplified Chinese

* Polish three English explanations after reader-focused review
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Yudong Jin
2026-10-31 03:35:51 +08:00
committed by GitHub
parent ef46e2ed95
commit 14c314c08c
1502 changed files with 29459 additions and 23517 deletions
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68
en/codes/python/chapter_dynamic_programming/edit_distance.py
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@@ -6,100 +6,100 @@ Author: krahets (krahets@163.com)
def edit_distance_dfs(s: str, t: str, i: int, j: int) -> int:
"""Edit distance: Brute-force search"""
# If both s and t are empty, return 0
"""Edit distance: brute-force search"""
# If both prefixes s[:i] and t[:j] are empty, return 0
if i == 0 and j == 0:
return 0
# If s is empty, return length of t
# If prefix s[:i] is empty, return the length j of prefix t[:j]
if i == 0:
return j
# If t is empty, return length of s
# If prefix t[:j] is empty, return the length i of prefix s[:i]
if j == 0:
return i
# If two characters are equal, skip both characters
# If the two characters are equal, skip both of them
if s[i - 1] == t[j - 1]:
return edit_distance_dfs(s, t, i - 1, j - 1)
# Minimum edit steps = minimum edit steps of insert, delete, replace + 1
# Minimum edits = the minimum among the insertion, deletion, and replacement subproblems + 1
insert = edit_distance_dfs(s, t, i, j - 1)
delete = edit_distance_dfs(s, t, i - 1, j)
replace = edit_distance_dfs(s, t, i - 1, j - 1)
# Return minimum edit steps
# Return the minimum number of edits
return min(insert, delete, replace) + 1
def edit_distance_dfs_mem(s: str, t: str, mem: list[list[int]], i: int, j: int) -> int:
"""Edit distance: Memoization search"""
# If both s and t are empty, return 0
"""Edit distance: memoized search"""
# If both prefixes s[:i] and t[:j] are empty, return 0
if i == 0 and j == 0:
return 0
# If s is empty, return length of t
# If prefix s[:i] is empty, return the length j of prefix t[:j]
if i == 0:
return j
# If t is empty, return length of s
# If prefix t[:j] is empty, return the length i of prefix s[:i]
if j == 0:
return i
# If there's a record, return it directly
# If a result has already been recorded, return it directly
if mem[i][j] != -1:
return mem[i][j]
# If two characters are equal, skip both characters
# If the two characters are equal, skip both of them
if s[i - 1] == t[j - 1]:
return edit_distance_dfs_mem(s, t, mem, i - 1, j - 1)
# Minimum edit steps = minimum edit steps of insert, delete, replace + 1
# Minimum edits = the minimum among the insertion, deletion, and replacement subproblems + 1
insert = edit_distance_dfs_mem(s, t, mem, i, j - 1)
delete = edit_distance_dfs_mem(s, t, mem, i - 1, j)
replace = edit_distance_dfs_mem(s, t, mem, i - 1, j - 1)
# Record and return minimum edit steps
# Record and return the minimum number of edits
mem[i][j] = min(insert, delete, replace) + 1
return mem[i][j]
def edit_distance_dp(s: str, t: str) -> int:
"""Edit distance: Dynamic programming"""
"""Edit distance: dynamic programming"""
n, m = len(s), len(t)
dp = [[0] * (m + 1) for _ in range(n + 1)]
# State transition: first row and first column
# State transitions: first row and first column
for i in range(1, n + 1):
dp[i][0] = i
for j in range(1, m + 1):
dp[0][j] = j
# State transition: rest of the rows and columns
# State transitions: remaining rows and columns
for i in range(1, n + 1):
for j in range(1, m + 1):
if s[i - 1] == t[j - 1]:
# If two characters are equal, skip both characters
# If the two characters are equal, skip both of them
dp[i][j] = dp[i - 1][j - 1]
else:
# Minimum edit steps = minimum edit steps of insert, delete, replace + 1
# Minimum edits = the minimum among the insertion, deletion, and replacement subproblems + 1
dp[i][j] = min(dp[i][j - 1], dp[i - 1][j], dp[i - 1][j - 1]) + 1
return dp[n][m]
def edit_distance_dp_comp(s: str, t: str) -> int:
"""Edit distance: Space-optimized dynamic programming"""
"""Edit distance: space-optimized dynamic programming"""
n, m = len(s), len(t)
dp = [0] * (m + 1)
# State transition: first row
# State transitions: first row
for j in range(1, m + 1):
dp[j] = j
# State transition: rest of the rows
# State transitions: remaining rows
for i in range(1, n + 1):
# State transition: first column
# State transitions: first column
leftup = dp[0] # Temporarily store dp[i-1, j-1]
dp[0] += 1
# State transition: rest of the columns
# State transitions: remaining columns
for j in range(1, m + 1):
temp = dp[j]
if s[i - 1] == t[j - 1]:
# If two characters are equal, skip both characters
# If the two characters are equal, skip both of them
dp[j] = leftup
else:
# Minimum edit steps = minimum edit steps of insert, delete, replace + 1
# Minimum edits = the minimum among the insertion, deletion, and replacement subproblems + 1
dp[j] = min(dp[j - 1], dp[j], leftup) + 1
leftup = temp # Update for next round's dp[i-1, j-1]
leftup = temp # Update to dp[i-1, j-1] for the next iteration
return dp[m]
"""Driver Code"""
"""Driver code"""
if __name__ == "__main__":
s = "bag"
t = "pack"
@@ -107,17 +107,17 @@ if __name__ == "__main__":
# Brute-force search
res = edit_distance_dfs(s, t, n, m)
print(f"Changing {s} to {t} requires a minimum of {res} edits")
print(f"Changing {s} to {t} requires at least {res} edits")
# Memoization search
# Memoized search
mem = [[-1] * (m + 1) for _ in range(n + 1)]
res = edit_distance_dfs_mem(s, t, mem, n, m)
print(f"Changing {s} to {t} requires a minimum of {res} edits")
print(f"Changing {s} to {t} requires at least {res} edits")
# Dynamic programming
res = edit_distance_dp(s, t)
print(f"Changing {s} to {t} requires a minimum of {res} edits")
print(f"Changing {s} to {t} requires at least {res} edits")
# Space-optimized dynamic programming
res = edit_distance_dp_comp(s, t)
print(f"Changing {s} to {t} requires a minimum of {res} edits")
print(f"Changing {s} to {t} requires at least {res} edits")