feat: update lc problems

solution/2500-2599/2505.Bitwise OR of All Subsequence Sums/README_EN.md

@@ -55,7 +55,11 @@ And we have 0 OR 1 OR 2 OR 3 OR 4 OR 5 OR 6 = 7, so we return 7.
 
 <!-- solution:start -->
 
-### Solution 1
+### Solution 1: Bit Manipulation
+
+We first use an array $cnt$ to count the number of 1s in each bit position. Then, from the lowest bit to the highest bit, if the number of 1s in that bit position is greater than 0, we add the value represented by that bit to the answer. Then, we check if there can be a carry-over, and if so, we add it to the next bit.
+
+The time complexity is $O(n \times \log M)$, where $n$ is the length of the array and $M$ is the maximum value in the array.
 
 <!-- tabs:start -->
 

solution/2500-2599/2507.Smallest Value After Replacing With Sum of Prime Factors/README_EN.md

@@ -65,7 +65,11 @@ tags:
 
 <!-- solution:start -->
 
-### Solution 1
+### Solution 1: Brute Force Simulation
+
+According to the problem statement, we can perform a process of prime factorization, i.e., continuously decompose a number into its prime factors until it can no longer be decomposed. During the process, add the prime factors each time they are decomposed, and perform this recursively or iteratively.
+
+The time complexity is $O(\sqrt{n})$.
 
 <!-- tabs:start -->
 

solution/2500-2599/2508.Add Edges to Make Degrees of All Nodes Even/README_EN.md

@@ -69,7 +69,19 @@ Every node in the resulting graph is connected to an even number of edges.
 
 <!-- solution:start -->
 
-### Solution 1
+### Solution 1: Case Analysis
+
+We first build the graph $g$ using `edges`, and then find all nodes with odd degrees, denoted as $vs$.
+
+If the length of $vs$ is $0$, it means all nodes in the graph $g$ have even degrees, so we return `true`.
+
+If the length of $vs$ is $2$, it means there are two nodes with odd degrees in the graph $g$. If we can directly connect these two nodes with an edge, making all nodes in the graph $g$ have even degrees, we return `true`. Otherwise, if we can find a third node $c$ such that we can connect $a$ and $c$, and $b$ and $c$, making all nodes in the graph $g$ have even degrees, we return `true`. Otherwise, we return `false`.
+
+If the length of $vs$ is $4$, we enumerate all possible pairs and check if any combination meets the conditions. If so, we return `true`; otherwise, we return `false`.
+
+In other cases, we return `false`.
+
+The time complexity is $O(n + m)$, and the space complexity is $O(n + m)$. Where $n$ and $m$ are the number of nodes and edges, respectively.
 
 <!-- tabs:start -->
 

solution/2500-2599/2509.Cycle Length Queries in a Tree/README_EN.md

@@ -84,7 +84,13 @@ tags:
 
 <!-- solution:start -->
 
-### Solution 1
+### Solution 1: Finding the Lowest Common Ancestor
+
+For each query, we find the lowest common ancestor of the two nodes $a$ and $b$, and record the number of steps taken upwards. The answer to the query is the number of steps plus one.
+
+To find the lowest common ancestor, if $a > b$, we move $a$ to its parent node; if $a < b$, we move $b$ to its parent node. We accumulate the number of steps until $a = b$.
+
+The time complexity is $O(n \times m)$, where $m$ is the length of the `queries` array.
 
 <!-- tabs:start -->
 

solution/2500-2599/2511.Maximum Enemy Forts That Can Be Captured/README.md

@@ -221,41 +221,4 @@ impl Solution {
 
 <!-- solution:end -->
 
-<!-- solution:start -->
-
-### 方法二
-
-<!-- tabs:start -->
-
-#### Rust
-
-```rust
-impl Solution {
-    pub fn capture_forts(forts: Vec<i32>) -> i32 {
-        let mut ans = 0;
-        let mut i = 0;
-
-        while let Some((idx, &value)) = forts.iter().enumerate().skip(i).find(|&(_, &x)| x != 0) {
-            if let Some((jdx, _)) = forts
-                .iter()
-                .enumerate()
-                .skip(idx + 1)
-                .find(|&(_, &x)| x != 0)
-            {
-                if value + forts[jdx] == 0 {
-                    ans = ans.max(jdx - idx - 1);
-                }
-            }
-            i = idx + 1;
-        }
-
-        ans as i32
-    }
-}
-```
-
-<!-- tabs:end -->
-
-<!-- solution:end -->
-
 <!-- problem:end -->

solution/2500-2599/2511.Maximum Enemy Forts That Can Be Captured/README_EN.md

@@ -72,7 +72,11 @@ Since 4 is the maximum number of enemy forts that can be captured, we return 4.
 
 <!-- solution:start -->
 
-### Solution 1
+### Solution 1: Two Pointers
+
+We use a pointer $i$ to traverse the array $forts$, and a pointer $j$ to start traversing from the next position of $i$ until it encounters the first non-zero position, i.e., $forts[j] \neq 0$. If $forts[i] + forts[j] = 0$, then we can move the army between $i$ and $j$, destroying $j - i - 1$ enemy forts. We use the variable $ans$ to record the maximum number of enemy forts that can be destroyed.
+
+The time complexity is $O(n)$, and the space complexity is $O(1)$. Where $n$ is the length of the array `forts`.
 
 <!-- tabs:start -->
 
@@ -217,41 +221,4 @@ impl Solution {
 
 <!-- solution:end -->
 
-<!-- solution:start -->
-
-### Solution 2
-
-<!-- tabs:start -->
-
-#### Rust
-
-```rust
-impl Solution {
-    pub fn capture_forts(forts: Vec<i32>) -> i32 {
-        let mut ans = 0;
-        let mut i = 0;
-
-        while let Some((idx, &value)) = forts.iter().enumerate().skip(i).find(|&(_, &x)| x != 0) {
-            if let Some((jdx, _)) = forts
-                .iter()
-                .enumerate()
-                .skip(idx + 1)
-                .find(|&(_, &x)| x != 0)
-            {
-                if value + forts[jdx] == 0 {
-                    ans = ans.max(jdx - idx - 1);
-                }
-            }
-            i = idx + 1;
-        }
-
-        ans as i32
-    }
-}
-```
-
-<!-- tabs:end -->
-
-<!-- solution:end -->
-
 <!-- problem:end -->

solution/2500-2599/2514.Count Anagrams/README.md

@@ -70,23 +70,17 @@ tags:
 #### Python3
 
 ```python
-mod = 10**9 + 7
-f = [1]
-for i in range(1, 10**5 + 1):
-    f.append(f[-1] * i % mod)
-
-
 class Solution:
     def countAnagrams(self, s: str) -> int:
-        ans = 1
+        mod = 10**9 + 7
+        ans = mul = 1
         for w in s.split():
-            cnt = Counter(w)
-            ans *= f[len(w)]
-            ans %= mod
-            for v in cnt.values():
-                ans *= pow(f[v], -1, mod)
-                ans %= mod
-        return ans
+            cnt = Counter()
+            for i, c in enumerate(w, 1):
+                cnt[c] += 1
+                mul = mul * cnt[c] % mod
+                ans = ans * i % mod
+        return ans * pow(mul, -1, mod) % mod
 ```
 
 #### Java
@@ -190,30 +184,4 @@ func pow(x, n int) int {
 
 <!-- solution:end -->
 
-<!-- solution:start -->
-
-### 方法二
-
-<!-- tabs:start -->
-
-#### Python3
-
-```python
-class Solution:
-    def countAnagrams(self, s: str) -> int:
-        mod = 10**9 + 7
-        ans = mul = 1
-        for w in s.split():
-            cnt = Counter()
-            for i, c in enumerate(w, 1):
-                cnt[c] += 1
-                mul = mul * cnt[c] % mod
-                ans = ans * i % mod
-        return ans * pow(mul, -1, mod) % mod
-```
-
-<!-- tabs:end -->
-
-<!-- solution:end -->
-
 <!-- problem:end -->

solution/2500-2599/2514.Count Anagrams/README_EN.md

@@ -70,23 +70,17 @@ tags:
 #### Python3
 
 ```python
-mod = 10**9 + 7
-f = [1]
-for i in range(1, 10**5 + 1):
-    f.append(f[-1] * i % mod)
-
-
 class Solution:
     def countAnagrams(self, s: str) -> int:
-        ans = 1
+        mod = 10**9 + 7
+        ans = mul = 1
         for w in s.split():
-            cnt = Counter(w)
-            ans *= f[len(w)]
-            ans %= mod
-            for v in cnt.values():
-                ans *= pow(f[v], -1, mod)
-                ans %= mod
-        return ans
+            cnt = Counter()
+            for i, c in enumerate(w, 1):
+                cnt[c] += 1
+                mul = mul * cnt[c] % mod
+                ans = ans * i % mod
+        return ans * pow(mul, -1, mod) % mod
 ```
 
 #### Java
@@ -190,30 +184,4 @@ func pow(x, n int) int {
 
 <!-- solution:end -->
 
-<!-- solution:start -->
-
-### Solution 2
-
-<!-- tabs:start -->
-
-#### Python3
-
-```python
-class Solution:
-    def countAnagrams(self, s: str) -> int:
-        mod = 10**9 + 7
-        ans = mul = 1
-        for w in s.split():
-            cnt = Counter()
-            for i, c in enumerate(w, 1):
-                cnt[c] += 1
-                mul = mul * cnt[c] % mod
-                ans = ans * i % mod
-        return ans * pow(mul, -1, mod) % mod
-```
-
-<!-- tabs:end -->
-
-<!-- solution:end -->
-
 <!-- problem:end -->

solution/2500-2599/2514.Count Anagrams/Solution.py

@@ -1,17 +1,11 @@
-mod = 10**9 + 7
-f = [1]
-for i in range(1, 10**5 + 1):
-    f.append(f[-1] * i % mod)
-
-
 class Solution:
     def countAnagrams(self, s: str) -> int:
-        ans = 1
+        mod = 10**9 + 7
+        ans = mul = 1
         for w in s.split():
-            cnt = Counter(w)
-            ans *= f[len(w)]
-            ans %= mod
-            for v in cnt.values():
-                ans *= pow(f[v], -1, mod)
-                ans %= mod
-        return ans
+            cnt = Counter()
+            for i, c in enumerate(w, 1):
+                cnt[c] += 1
+                mul = mul * cnt[c] % mod
+                ans = ans * i % mod
+        return ans * pow(mul, -1, mod) % mod