diff --git a/solution/0800-0899/0825.Friends Of Appropriate Ages/README.md b/solution/0800-0899/0825.Friends Of Appropriate Ages/README.md
index 456c7e99695a7..4e00b92accac7 100644
--- a/solution/0800-0899/0825.Friends Of Appropriate Ages/README.md	
+++ b/solution/0800-0899/0825.Friends Of Appropriate Ages/README.md	
@@ -77,7 +77,15 @@ tags:
 
 <!-- solution:start -->
 
-### 方法一
+### 方法一：计数 + 枚举
+
+我们可以用一个长度为 $121$ 的数组 $\textit{cnt}$ 记录每个年龄的人数。
+
+接下来，枚举所有可能的年龄对 $(\textit{ax}, \textit{ay})$，如果 $\textit{ax}$ 和 $\textit{ay}$ 不满足题目中的任意一个条件，这些年龄对 $(\textit{ax}, \textit{ay})$ 就可以互发好友请求。
+
+此时，如果 $\textit{ax} = \textit{ay}$，年龄相同，那么 $\textit{ax}$ 和 $\textit{ay}$ 之间的好友请求数为 $\textit{cnt}[\textit{ax}] \times (\textit{cnt}[\textit{ax}] - 1)$；否则，年龄不同，那么 $\textit{ax}$ 和 $\textit{ay}$ 之间的好友请求数为 $\textit{cnt}[\textit{ax}] \times \textit{cnt}[\textit{ay}]$。我们将这些好友请求数累加到答案中即可。
+
+时间复杂度 $O(n + m^2)$，其中 $n$ 是数组 $\textit{ages}$ 的长度，而 $m$ 是年龄的最大值，本题中 $m = 121$。
 
 <!-- tabs:start -->
 
@@ -86,16 +94,14 @@ tags:
 ```python
 class Solution:
     def numFriendRequests(self, ages: List[int]) -> int:
-        counter = Counter(ages)
+        cnt = [0] * 121
+        for x in ages:
+            cnt[x] += 1
         ans = 0
-        for i in range(1, 121):
-            n1 = counter[i]
-            for j in range(1, 121):
-                n2 = counter[j]
-                if not (j <= 0.5 * i + 7 or j > i or (j > 100 and i < 100)):
-                    ans += n1 * n2
-                    if i == j:
-                        ans -= n2
+        for ax, x in enumerate(cnt):
+            for ay, y in enumerate(cnt):
+                if not (ay <= 0.5 * ax + 7 or ay > ax or (ay > 100 and ax < 100)):
+                    ans += x * (y - int(ax == ay))
         return ans
 ```
 
@@ -104,20 +110,16 @@ class Solution:
 ```java
 class Solution {
     public int numFriendRequests(int[] ages) {
-        int[] counter = new int[121];
-        for (int age : ages) {
-            ++counter[age];
+        final int m = 121;
+        int[] cnt = new int[m];
+        for (int x : ages) {
+            ++cnt[x];
         }
         int ans = 0;
-        for (int i = 1; i < 121; ++i) {
-            int n1 = counter[i];
-            for (int j = 1; j < 121; ++j) {
-                int n2 = counter[j];
-                if (!(j <= 0.5 * i + 7 || j > i || (j > 100 && i < 100))) {
-                    ans += n1 * n2;
-                    if (i == j) {
-                        ans -= n2;
-                    }
+        for (int ax = 1; ax < m; ++ax) {
+            for (int ay = 1; ay < m; ++ay) {
+                if (!(ay <= 0.5 * ax + 7 || ay > ax || (ay > 100 && ax < 100))) {
+                    ans += cnt[ax] * (cnt[ay] - (ax == ay ? 1 : 0));
                 }
             }
         }
@@ -132,16 +134,16 @@ class Solution {
 class Solution {
 public:
     int numFriendRequests(vector<int>& ages) {
-        vector<int> counter(121);
-        for (int age : ages) ++counter[age];
+        const int m = 121;
+        vector<int> cnt(m);
+        for (int x : ages) {
+            ++cnt[x];
+        }
         int ans = 0;
-        for (int i = 1; i < 121; ++i) {
-            int n1 = counter[i];
-            for (int j = 1; j < 121; ++j) {
-                int n2 = counter[j];
-                if (!(j <= 0.5 * i + 7 || j > i || (j > 100 && i < 100))) {
-                    ans += n1 * n2;
-                    if (i == j) ans -= n2;
+        for (int ax = 1; ax < m; ++ax) {
+            for (int ay = 1; ay < m; ++ay) {
+                if (!(ay <= 0.5 * ax + 7 || ay > ax || (ay > 100 && ax < 100))) {
+                    ans += cnt[ax] * (cnt[ay] - (ax == ay ? 1 : 0));
                 }
             }
         }
@@ -153,25 +155,49 @@ public:
 #### Go
 
 ```go
-func numFriendRequests(ages []int) int {
-	counter := make([]int, 121)
-	for _, age := range ages {
-		counter[age]++
+func numFriendRequests(ages []int) (ans int) {
+	cnt := [121]int{}
+	for _, x := range ages {
+		cnt[x]++
 	}
-	ans := 0
-	for i := 1; i < 121; i++ {
-		n1 := counter[i]
-		for j := 1; j < 121; j++ {
-			n2 := counter[j]
-			if !(j <= i/2+7 || j > i || (j > 100 && i < 100)) {
-				ans += n1 * n2
-				if i == j {
-					ans -= n2
-				}
+	for ax, x := range cnt {
+		for ay, y := range cnt {
+			if ay <= ax/2+7 || ay > ax || (ay > 100 && ax < 100) {
+				continue
+			}
+			if ax == ay {
+				ans += x * (x - 1)
+			} else {
+				ans += x * y
 			}
 		}
 	}
-	return ans
+
+	return
+}
+```
+
+#### TypeScript
+
+```ts
+function numFriendRequests(ages: number[]): number {
+    const m = 121;
+    const cnt = Array(m).fill(0);
+    for (const x of ages) {
+        cnt[x]++;
+    }
+
+    let ans = 0;
+    for (let ax = 0; ax < m; ax++) {
+        for (let ay = 0; ay < m; ay++) {
+            if (ay <= 0.5 * ax + 7 || ay > ax || (ay > 100 && ax < 100)) {
+                continue;
+            }
+            ans += cnt[ax] * (cnt[ay] - (ax === ay ? 1 : 0));
+        }
+    }
+
+    return ans;
 }
 ```
 
diff --git a/solution/0800-0899/0825.Friends Of Appropriate Ages/README_EN.md b/solution/0800-0899/0825.Friends Of Appropriate Ages/README_EN.md
index 246df0457f069..c9bdff14438a4 100644
--- a/solution/0800-0899/0825.Friends Of Appropriate Ages/README_EN.md	
+++ b/solution/0800-0899/0825.Friends Of Appropriate Ages/README_EN.md	
@@ -75,7 +75,15 @@ tags:
 
 <!-- solution:start -->
 
-### Solution 1
+### Solution 1: Counting + Enumeration
+
+We can use an array $\textit{cnt}$ of length $121$ to record the number of people of each age.
+
+Next, we enumerate all possible age pairs $(\textit{ax}, \textit{ay})$. If $\textit{ax}$ and $\textit{ay}$ satisfy the conditions given in the problem, these age pairs $(\textit{ax}, \textit{ay})$ can send friend requests to each other.
+
+If $\textit{ax} = \textit{ay}$, meaning the ages are the same, then the number of friend requests between $\textit{ax}$ and $\textit{ay}$ is $\textit{cnt}[\textit{ax}] \times (\textit{cnt}[\textit{ax}] - 1)$. Otherwise, if the ages are different, the number of friend requests between $\textit{ax}$ and $\textit{ay}$ is $\textit{cnt}[\textit{ax}] \times \textit{cnt}[\textit{ay}]$. We accumulate these friend request counts into the answer.
+
+The time complexity is $O(n + m^2)$, where $n$ is the length of the array $\textit{ages}$, and $m$ is the maximum age, which is $121$ in this problem.
 
 <!-- tabs:start -->
 
@@ -84,16 +92,14 @@ tags:
 ```python
 class Solution:
     def numFriendRequests(self, ages: List[int]) -> int:
-        counter = Counter(ages)
+        cnt = [0] * 121
+        for x in ages:
+            cnt[x] += 1
         ans = 0
-        for i in range(1, 121):
-            n1 = counter[i]
-            for j in range(1, 121):
-                n2 = counter[j]
-                if not (j <= 0.5 * i + 7 or j > i or (j > 100 and i < 100)):
-                    ans += n1 * n2
-                    if i == j:
-                        ans -= n2
+        for ax, x in enumerate(cnt):
+            for ay, y in enumerate(cnt):
+                if not (ay <= 0.5 * ax + 7 or ay > ax or (ay > 100 and ax < 100)):
+                    ans += x * (y - int(ax == ay))
         return ans
 ```
 
@@ -102,20 +108,16 @@ class Solution:
 ```java
 class Solution {
     public int numFriendRequests(int[] ages) {
-        int[] counter = new int[121];
-        for (int age : ages) {
-            ++counter[age];
+        final int m = 121;
+        int[] cnt = new int[m];
+        for (int x : ages) {
+            ++cnt[x];
         }
         int ans = 0;
-        for (int i = 1; i < 121; ++i) {
-            int n1 = counter[i];
-            for (int j = 1; j < 121; ++j) {
-                int n2 = counter[j];
-                if (!(j <= 0.5 * i + 7 || j > i || (j > 100 && i < 100))) {
-                    ans += n1 * n2;
-                    if (i == j) {
-                        ans -= n2;
-                    }
+        for (int ax = 1; ax < m; ++ax) {
+            for (int ay = 1; ay < m; ++ay) {
+                if (!(ay <= 0.5 * ax + 7 || ay > ax || (ay > 100 && ax < 100))) {
+                    ans += cnt[ax] * (cnt[ay] - (ax == ay ? 1 : 0));
                 }
             }
         }
@@ -130,16 +132,16 @@ class Solution {
 class Solution {
 public:
     int numFriendRequests(vector<int>& ages) {
-        vector<int> counter(121);
-        for (int age : ages) ++counter[age];
+        const int m = 121;
+        vector<int> cnt(m);
+        for (int x : ages) {
+            ++cnt[x];
+        }
         int ans = 0;
-        for (int i = 1; i < 121; ++i) {
-            int n1 = counter[i];
-            for (int j = 1; j < 121; ++j) {
-                int n2 = counter[j];
-                if (!(j <= 0.5 * i + 7 || j > i || (j > 100 && i < 100))) {
-                    ans += n1 * n2;
-                    if (i == j) ans -= n2;
+        for (int ax = 1; ax < m; ++ax) {
+            for (int ay = 1; ay < m; ++ay) {
+                if (!(ay <= 0.5 * ax + 7 || ay > ax || (ay > 100 && ax < 100))) {
+                    ans += cnt[ax] * (cnt[ay] - (ax == ay ? 1 : 0));
                 }
             }
         }
@@ -151,25 +153,49 @@ public:
 #### Go
 
 ```go
-func numFriendRequests(ages []int) int {
-	counter := make([]int, 121)
-	for _, age := range ages {
-		counter[age]++
+func numFriendRequests(ages []int) (ans int) {
+	cnt := [121]int{}
+	for _, x := range ages {
+		cnt[x]++
 	}
-	ans := 0
-	for i := 1; i < 121; i++ {
-		n1 := counter[i]
-		for j := 1; j < 121; j++ {
-			n2 := counter[j]
-			if !(j <= i/2+7 || j > i || (j > 100 && i < 100)) {
-				ans += n1 * n2
-				if i == j {
-					ans -= n2
-				}
+	for ax, x := range cnt {
+		for ay, y := range cnt {
+			if ay <= ax/2+7 || ay > ax || (ay > 100 && ax < 100) {
+				continue
+			}
+			if ax == ay {
+				ans += x * (x - 1)
+			} else {
+				ans += x * y
 			}
 		}
 	}
-	return ans
+
+	return
+}
+```
+
+#### TypeScript
+
+```ts
+function numFriendRequests(ages: number[]): number {
+    const m = 121;
+    const cnt = Array(m).fill(0);
+    for (const x of ages) {
+        cnt[x]++;
+    }
+
+    let ans = 0;
+    for (let ax = 0; ax < m; ax++) {
+        for (let ay = 0; ay < m; ay++) {
+            if (ay <= 0.5 * ax + 7 || ay > ax || (ay > 100 && ax < 100)) {
+                continue;
+            }
+            ans += cnt[ax] * (cnt[ay] - (ax === ay ? 1 : 0));
+        }
+    }
+
+    return ans;
 }
 ```
 
diff --git a/solution/0800-0899/0825.Friends Of Appropriate Ages/Solution.cpp b/solution/0800-0899/0825.Friends Of Appropriate Ages/Solution.cpp
index 2391a481bb7ce..eb65048457aab 100644
--- a/solution/0800-0899/0825.Friends Of Appropriate Ages/Solution.cpp	
+++ b/solution/0800-0899/0825.Friends Of Appropriate Ages/Solution.cpp	
@@ -1,19 +1,19 @@
 class Solution {
 public:
     int numFriendRequests(vector<int>& ages) {
-        vector<int> counter(121);
-        for (int age : ages) ++counter[age];
+        const int m = 121;
+        vector<int> cnt(m);
+        for (int x : ages) {
+            ++cnt[x];
+        }
         int ans = 0;
-        for (int i = 1; i < 121; ++i) {
-            int n1 = counter[i];
-            for (int j = 1; j < 121; ++j) {
-                int n2 = counter[j];
-                if (!(j <= 0.5 * i + 7 || j > i || (j > 100 && i < 100))) {
-                    ans += n1 * n2;
-                    if (i == j) ans -= n2;
+        for (int ax = 1; ax < m; ++ax) {
+            for (int ay = 1; ay < m; ++ay) {
+                if (!(ay <= 0.5 * ax + 7 || ay > ax || (ay > 100 && ax < 100))) {
+                    ans += cnt[ax] * (cnt[ay] - (ax == ay ? 1 : 0));
                 }
             }
         }
         return ans;
     }
-};
\ No newline at end of file
+};
diff --git a/solution/0800-0899/0825.Friends Of Appropriate Ages/Solution.go b/solution/0800-0899/0825.Friends Of Appropriate Ages/Solution.go
index 63c581630b7be..7185f8d6acbb2 100644
--- a/solution/0800-0899/0825.Friends Of Appropriate Ages/Solution.go	
+++ b/solution/0800-0899/0825.Friends Of Appropriate Ages/Solution.go	
@@ -1,20 +1,20 @@
-func numFriendRequests(ages []int) int {
-	counter := make([]int, 121)
-	for _, age := range ages {
-		counter[age]++
+func numFriendRequests(ages []int) (ans int) {
+	cnt := [121]int{}
+	for _, x := range ages {
+		cnt[x]++
 	}
-	ans := 0
-	for i := 1; i < 121; i++ {
-		n1 := counter[i]
-		for j := 1; j < 121; j++ {
-			n2 := counter[j]
-			if !(j <= i/2+7 || j > i || (j > 100 && i < 100)) {
-				ans += n1 * n2
-				if i == j {
-					ans -= n2
-				}
+	for ax, x := range cnt {
+		for ay, y := range cnt {
+			if ay <= ax/2+7 || ay > ax || (ay > 100 && ax < 100) {
+				continue
+			}
+			if ax == ay {
+				ans += x * (x - 1)
+			} else {
+				ans += x * y
 			}
 		}
 	}
-	return ans
-}
\ No newline at end of file
+
+	return
+}
diff --git a/solution/0800-0899/0825.Friends Of Appropriate Ages/Solution.java b/solution/0800-0899/0825.Friends Of Appropriate Ages/Solution.java
index 6aa39d3d928b0..54ee798628887 100644
--- a/solution/0800-0899/0825.Friends Of Appropriate Ages/Solution.java	
+++ b/solution/0800-0899/0825.Friends Of Appropriate Ages/Solution.java	
@@ -1,22 +1,18 @@
 class Solution {
     public int numFriendRequests(int[] ages) {
-        int[] counter = new int[121];
-        for (int age : ages) {
-            ++counter[age];
+        final int m = 121;
+        int[] cnt = new int[m];
+        for (int x : ages) {
+            ++cnt[x];
         }
         int ans = 0;
-        for (int i = 1; i < 121; ++i) {
-            int n1 = counter[i];
-            for (int j = 1; j < 121; ++j) {
-                int n2 = counter[j];
-                if (!(j <= 0.5 * i + 7 || j > i || (j > 100 && i < 100))) {
-                    ans += n1 * n2;
-                    if (i == j) {
-                        ans -= n2;
-                    }
+        for (int ax = 1; ax < m; ++ax) {
+            for (int ay = 1; ay < m; ++ay) {
+                if (!(ay <= 0.5 * ax + 7 || ay > ax || (ay > 100 && ax < 100))) {
+                    ans += cnt[ax] * (cnt[ay] - (ax == ay ? 1 : 0));
                 }
             }
         }
         return ans;
     }
-}
\ No newline at end of file
+}
diff --git a/solution/0800-0899/0825.Friends Of Appropriate Ages/Solution.py b/solution/0800-0899/0825.Friends Of Appropriate Ages/Solution.py
index 651bc1134b06e..80dbfa08eacdd 100644
--- a/solution/0800-0899/0825.Friends Of Appropriate Ages/Solution.py	
+++ b/solution/0800-0899/0825.Friends Of Appropriate Ages/Solution.py	
@@ -1,13 +1,11 @@
 class Solution:
     def numFriendRequests(self, ages: List[int]) -> int:
-        counter = Counter(ages)
+        cnt = [0] * 121
+        for x in ages:
+            cnt[x] += 1
         ans = 0
-        for i in range(1, 121):
-            n1 = counter[i]
-            for j in range(1, 121):
-                n2 = counter[j]
-                if not (j <= 0.5 * i + 7 or j > i or (j > 100 and i < 100)):
-                    ans += n1 * n2
-                    if i == j:
-                        ans -= n2
+        for ax, x in enumerate(cnt):
+            for ay, y in enumerate(cnt):
+                if not (ay <= 0.5 * ax + 7 or ay > ax or (ay > 100 and ax < 100)):
+                    ans += x * (y - int(ax == ay))
         return ans
diff --git a/solution/0800-0899/0825.Friends Of Appropriate Ages/Solution.ts b/solution/0800-0899/0825.Friends Of Appropriate Ages/Solution.ts
new file mode 100644
index 0000000000000..1ff369f26a76f
--- /dev/null
+++ b/solution/0800-0899/0825.Friends Of Appropriate Ages/Solution.ts	
@@ -0,0 +1,19 @@
+function numFriendRequests(ages: number[]): number {
+    const m = 121;
+    const cnt = Array(m).fill(0);
+    for (const x of ages) {
+        cnt[x]++;
+    }
+
+    let ans = 0;
+    for (let ax = 0; ax < m; ax++) {
+        for (let ay = 0; ay < m; ay++) {
+            if (ay <= 0.5 * ax + 7 || ay > ax || (ay > 100 && ax < 100)) {
+                continue;
+            }
+            ans += cnt[ax] * (cnt[ay] - (ax === ay ? 1 : 0));
+        }
+    }
+
+    return ans;
+}