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Nov 17, 2024
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feat: add solutions to lc problem: No.0825 #3767

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118 changes: 72 additions & 46 deletions solution/0800-0899/0825.Friends Of Appropriate Ages/README.md
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Original file line number Diff line number Diff line change
Expand Up @@ -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 -->

Expand All @@ -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
```

Expand All @@ -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));
}
}
}
Expand All @@ -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));
}
}
}
Expand All @@ -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;
}
```

Expand Down
118 changes: 72 additions & 46 deletions solution/0800-0899/0825.Friends Of Appropriate Ages/README_EN.md
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Original file line number Diff line number Diff line change
Expand Up @@ -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 -->

Expand All @@ -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
```

Expand All @@ -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));
}
}
}
Expand All @@ -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));
}
}
}
Expand All @@ -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;
}
```

Expand Down
20 changes: 10 additions & 10 deletions solution/0800-0899/0825.Friends Of Appropriate Ages/Solution.cpp
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Original file line number Diff line number Diff line change
@@ -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;
}
};
};
32 changes: 16 additions & 16 deletions solution/0800-0899/0825.Friends Of Appropriate Ages/Solution.go
View file
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Original file line number Diff line number Diff line change
@@ -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
}

return
}
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