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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
This commit is contained in:
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/cpp/chapter_dynamic_programming/edit_distance.cpp
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@@ -6,73 +6,73 @@
#include "../utils/common.hpp"
/* Edit distance: Brute-force search */
/* Edit distance: brute-force search */
int editDistanceDFS(string s, string t, int i, int j) {
// If both s and t are empty, return 0
// If both prefixes s[0:i] and t[0:j] are empty, return 0
if (i == 0 && j == 0)
return 0;
// If s is empty, return length of t
// If the prefix s[0:i] is empty, return j, the length of t[0:j]
if (i == 0)
return j;
// If t is empty, return length of s
// If the prefix t[0:j] is empty, return i, the length of s[0: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 editDistanceDFS(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
int insert = editDistanceDFS(s, t, i, j - 1);
int del = editDistanceDFS(s, t, i - 1, j);
int replace = editDistanceDFS(s, t, i - 1, j - 1);
// Return minimum edit steps
// Return the minimum number of edits
return min(min(insert, del), replace) + 1;
}
/* Edit distance: Memoization search */
/* Edit distance: memoized search */
int editDistanceDFSMem(string s, string t, vector<vector<int>> &mem, int i, int j) {
// If both s and t are empty, return 0
// If both prefixes s[0:i] and t[0:j] are empty, return 0
if (i == 0 && j == 0)
return 0;
// If s is empty, return length of t
// If the prefix s[0:i] is empty, return j, the length of t[0:j]
if (i == 0)
return j;
// If t is empty, return length of s
// If the prefix t[0:j] is empty, return i, the length of s[0: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 editDistanceDFSMem(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
int insert = editDistanceDFSMem(s, t, mem, i, j - 1);
int del = editDistanceDFSMem(s, t, mem, i - 1, j);
int replace = editDistanceDFSMem(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(min(insert, del), replace) + 1;
return mem[i][j];
}
/* Edit distance: Dynamic programming */
/* Edit distance: dynamic programming */
int editDistanceDP(string s, string t) {
int n = s.length(), m = t.length();
vector<vector<int>> dp(n + 1, vector<int>(m + 1, 0));
// State transition: first row and first column
// State transitions: first row and first column
for (int i = 1; i <= n; i++) {
dp[i][0] = i;
}
for (int j = 1; j <= m; j++) {
dp[0][j] = j;
}
// State transition: rest of the rows and columns
// State transitions: remaining rows and columns
for (int i = 1; i <= n; i++) {
for (int j = 1; j <= m; 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[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(min(dp[i][j - 1], dp[i - 1][j]), dp[i - 1][j - 1]) + 1;
}
}
@@ -80,36 +80,36 @@ int editDistanceDP(string s, string t) {
return dp[n][m];
}
/* Edit distance: Space-optimized dynamic programming */
/* Edit distance: space-optimized dynamic programming */
int editDistanceDPComp(string s, string t) {
int n = s.length(), m = t.length();
vector<int> dp(m + 1, 0);
// State transition: first row
// State transitions: first row
for (int j = 1; j <= m; j++) {
dp[j] = j;
}
// State transition: rest of the rows
// State transitions: remaining rows
for (int i = 1; i <= n; i++) {
// State transition: first column
// State transitions: first column
int leftup = dp[0]; // Temporarily store dp[i-1, j-1]
dp[0] = i;
// State transition: rest of the columns
// State transitions: remaining columns
for (int j = 1; j <= m; j++) {
int 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(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 */
int main() {
string s = "bag";
string t = "pack";
@@ -117,20 +117,20 @@ int main() {
// Brute-force search
int res = editDistanceDFS(s, t, n, m);
cout << "Changing " << s << " to " << t << " requires a minimum of " << res << " edits";
cout << "Changing " << s << " to " << t << " requires at least " << res << " edits\n";
// Memoization search
// Memoized search
vector<vector<int>> mem(n + 1, vector<int>(m + 1, -1));
res = editDistanceDFSMem(s, t, mem, n, m);
cout << "Changing " << s << " to " << t << " requires a minimum of " << res << " edits";
cout << "Changing " << s << " to " << t << " requires at least " << res << " edits\n";
// Dynamic programming
res = editDistanceDP(s, t);
cout << "Changing " << s << " to " << t << " requires a minimum of " << res << " edits";
cout << "Changing " << s << " to " << t << " requires at least " << res << " edits\n";
// Space-optimized dynamic programming
res = editDistanceDPComp(s, t);
cout << "Changing " << s << " to " << t << " requires a minimum of " << res << " edits";
cout << "Changing " << s << " to " << t << " requires at least " << res << " edits\n";
return 0;
}