Add solution 825

website/content/ChapterFour/0800~0899/0825.Friends-Of-Appropriate-Ages.md

@@ -0,0 +1,148 @@
+# [825. Friends Of Appropriate Ages](https://leetcode.com/problems/friends-of-appropriate-ages/)
+
+
+## 题目
+
+There are `n` persons on a social media website. You are given an integer array `ages` where `ages[i]` is the age of the `ith` person.
+
+A Person `x` will not send a friend request to a person `y` (`x != y`) if any of the following conditions is true:
+
+- `age[y] <= 0.5 * age+ 7`
+- `age[y] > age[x]`
+- `age[y] > 100 && age< 100`
+
+Otherwise, `x` will send a friend request to `y`.
+
+Note that if `x` sends a request to `y`, `y` will not necessarily send a request to `x`. Also, a person will not send a friend request to themself.
+
+Return *the total number of friend requests made*.
+
+**Example 1:**
+
+```
+Input: ages = [16,16]
+Output: 2
+Explanation: 2 people friend request each other.
+
+```
+
+**Example 2:**
+
+```
+Input: ages = [16,17,18]
+Output: 2
+Explanation: Friend requests are made 17 -> 16, 18 -> 17.
+
+```
+
+**Example 3:**
+
+```
+Input: ages = [20,30,100,110,120]
+Output: 3
+Explanation: Friend requests are made 110 -> 100, 120 -> 110, 120 -> 100.
+
+```
+
+**Constraints:**
+
+- `n == ages.length`
+- `1 <= n <= 2 * 10^4`
+- `1 <= ages[i] <= 120`
+
+## 题目大意
+
+在社交媒体网站上有 n 个用户。给你一个整数数组 ages ，其中 ages[i] 是第 i 个用户的年龄。
+
+如果下述任意一个条件为真，那么用户 x 将不会向用户 y（x != y）发送好友请求：
+
+- ages[y] <= 0.5 * ages[x] + 7
+- ages[y] > ages[x]
+- ages[y] > 100 && ages[x] < 100
+
+否则，x 将会向 y 发送一条好友请求。注意，如果 x 向 y 发送一条好友请求，y 不必也向 x 发送一条好友请求。另外，用户不会向自己发送好友请求。返回在该社交媒体网站上产生的好友请求总数。
+
+## 解题思路
+
+- 解法三，暴力解法。先统计 [1,120] 范围内每个年龄的人数。然后利用题目中的三个判断条件，筛选符合条件的用户对。需要注意的是，相同年龄的人可以相互发送好友请求。不同年龄的人发送好友请求是单向的，即年龄老的向年龄轻的发送好友请求，年龄轻的不会对年龄老的发送好友请求。
+- 解法二，排序 + 双指针。题目给定的 3 个条件其实是 2 个。条件 3 包含在条件 2 中。条件 1 和条件 2 组合起来是 `0.5 × ages[x]+7 < ages[y] ≤ ages[x]`。当 ages[x] 小于 15 时，这个等式无解。考虑到年龄是单调递增的，`(0.5 × ages[x]+7,ages[x]]` 这个区间左右边界也是单调递增的。于是可以用双指针维护两个边界。在区间 [left, right] 内，这些下标对应的的 y 值都满足条件。当 `ages[left] > 0.5 × ages[x]+7` 时，左指针停止右移。当 `ages[right+1] > ages[x]` 时， 右指针停止右移。在 `[left, right]` 区间内，满足条件的 y 有 `right-left+1` 个，即使得 `ages[y]` 取值在 `(0.5 × ages[x]+7,ages[x]]` 之间。依照题意，`x≠y`，即该区间右边界取不到。y 的取值个数需要再减一，减去的是取到和 x 相同的值的下标。那么每个区间能取 `right-left` 个值。累加所有满足条件的值即为好友请求总数。
+- 解法一。在解法二中，计算满足不等式 y 下标所在区间的时候，区间和区间存在重叠的情况，这些重叠情况导致了重复计算。所以这里可以优化。可以用 prefix sum 前缀和数组优化。代码见下方。
+
+## 代码
+
+```go
+package leetcocde
+
+import "sort"
+
+// 解法一 前缀和，时间复杂度 O(n)
+func numFriendRequests(ages []int) int {
+	count, prefixSum, res := make([]int, 121), make([]int, 121), 0
+	for _, age := range ages {
+		count[age]++
+	}
+	for i := 1; i < 121; i++ {
+		prefixSum[i] = prefixSum[i-1] + count[i]
+	}
+	for i := 15; i < 121; i++ {
+		if count[i] > 0 {
+			bound := i/2 + 8
+			res += count[i] * (prefixSum[i] - prefixSum[bound-1] - 1)
+		}
+	}
+	return res
+}
+
+// 解法二 双指针 + 排序，时间复杂度 O(n logn)
+func numFriendRequests1(ages []int) int {
+	sort.Ints(ages)
+	left, right, res := 0, 0, 0
+	for _, age := range ages {
+		if age < 15 {
+			continue
+		}
+		for ages[left]*2 <= age+14 {
+			left++
+		}
+		for right+1 < len(ages) && ages[right+1] <= age {
+			right++
+		}
+		res += right - left
+	}
+	return res
+}
+
+// 解法三 暴力解法 O(n^2)
+func numFriendRequests2(ages []int) int {
+	res, count := 0, [125]int{}
+	for _, x := range ages {
+		count[x]++
+	}
+	for i := 1; i <= 120; i++ {
+		for j := 1; j <= 120; j++ {
+			if j > i {
+				continue
+			}
+			if (j-7)*2 <= i {
+				continue
+			}
+			if j > 100 && i < 100 {
+				continue
+			}
+			if i != j {
+				res += count[i] * count[j]
+			} else {
+				res += count[i] * (count[j] - 1)
+			}
+		}
+	}
+	return res
+}
+```
+
+
+----------------------------------------------
+<div style="display: flex;justify-content: space-between;align-items: center;">
+<p><a href="https://books.halfrost.com/leetcode/ChapterFour/0800~0899/0823.Binary-Trees-With-Factors/">⬅️上一页</a></p>
+<p><a href="https://books.halfrost.com/leetcode/ChapterFour/0800~0899/0826.Most-Profit-Assigning-Work/">下一页➡️</a></p>
+</div>

website/content/ChapterFour/0800~0899/0826.Most-Profit-Assigning-Work.md

@@ -109,6 +109,6 @@ func maxProfitAssignment(difficulty []int, profit []int, worker []int) int {
 
 ----------------------------------------------
 <div style="display: flex;justify-content: space-between;align-items: center;">
-<p><a href="https://books.halfrost.com/leetcode/ChapterFour/0800~0899/0823.Binary-Trees-With-Factors/">⬅️上一页</a></p>
+<p><a href="https://books.halfrost.com/leetcode/ChapterFour/0800~0899/0825.Friends-Of-Appropriate-Ages/">⬅️上一页</a></p>
 <p><a href="https://books.halfrost.com/leetcode/ChapterFour/0800~0899/0828.Count-Unique-Characters-of-All-Substrings-of-a-Given-String/">下一页➡️</a></p>
 </div>

website/content/ChapterFour/0800~0899/0845.Longest-Mountain-in-Array.md

@@ -94,5 +94,5 @@ func longestMountain(A []int) int {
 ----------------------------------------------
 <div style="display: flex;justify-content: space-between;align-items: center;">
 <p><a href="https://books.halfrost.com/leetcode/ChapterFour/0800~0899/0844.Backspace-String-Compare/">⬅️上一页</a></p>
-<p><a href="https://books.halfrost.com/leetcode/ChapterFour/0800~0899/0850.Rectangle-Area-II/">下一页➡️</a></p>
+<p><a href="https://books.halfrost.com/leetcode/ChapterFour/0800~0899/0846.Hand-of-Straights/">下一页➡️</a></p>
 </div>