Fix multilingual content typos (#1958)

en/docs/chapter_dynamic_programming/edit_distance_problem.md

@@ -35,7 +35,7 @@ In other words, each round of decision (edit operation) we make on string $s$ wi
 
 State $[i, j]$ corresponds to the subproblem: **the minimum number of edits required to change the first $i$ characters of $s$ into the first $j$ characters of $t$**.
 
-From this, we obtain a two-dimensional $dp$ table of size $(i+1) \times (j+1)$.
+From this, we obtain a two-dimensional $dp$ table of size $(n+1) \times (m+1)$.
 
 **Step 2: Identify the optimal substructure, and then derive the state transition equation**
 

en/docs/chapter_dynamic_programming/knapsack_problem.md

@@ -134,7 +134,7 @@ As shown in the figure below, both time complexity and space complexity are dete
 
 ### Space Optimization
 
-Since each state is only related to the state in the row above it, we can use two arrays rolling forward to reduce the space complexity from $O(n^2)$ to $O(n)$.
+Since each state is only related to the state in the row above it, we can use two arrays rolling forward to reduce the space complexity from $O(n \times cap)$ to $O(cap)$.
 
 Further thinking, can we achieve space optimization using just one array? Observing, we can see that each state is transferred from the cell directly above or the cell in the upper-left. If there is only one array, when we start traversing row $i$, that array still stores the state of row $i-1$.
 

en/docs/chapter_dynamic_programming/summary.md

@@ -21,5 +21,5 @@
 **Edit distance problem**
 
 - Edit distance (Levenshtein distance) is used to measure the similarity between two strings, defined as the minimum number of edit steps from one string to another, with edit operations including insert, delete, and replace.
-- The state definition for the edit distance problem is the minimum number of edit steps required to change the first $i$ characters of $s$ into the first $j$ characters of $t$. When $s[i] \ne t[j]$, there are three decisions: insert, delete, replace, each with corresponding remaining subproblems. From this, the optimal substructure can be identified and the state transition equation constructed. When $s[i] = t[j]$, no edit is required for the current character.
+- The state definition for the edit distance problem is the minimum number of edit steps required to change the first $i$ characters of $s$ into the first $j$ characters of $t$. When $s[i-1] \ne t[j-1]$, there are three decisions: insert, delete, replace, each with corresponding remaining subproblems. From this, the optimal substructure can be identified and the state transition equation constructed. When $s[i-1] = t[j-1]$, no edit is required for the current character.
 - In edit distance, the state depends on the state directly above, directly to the left, and to the upper-left, so after space optimization, neither forward nor reverse traversal can correctly perform state transitions. For this reason, we use a variable to temporarily store the upper-left state, thus transforming to a situation equivalent to the unbounded knapsack problem, allowing for forward traversal after space optimization.