From a8dac4007e911f6914d209720a24d541d482adeb Mon Sep 17 00:00:00 2001 From: halfrost Date: Tue, 25 Jan 2022 22:22:22 +0800 Subject: [PATCH] Add solution 825 --- .../0825.Friends-Of-Appropriate-Ages.md | 148 ++++++++++++++++++ .../0826.Most-Profit-Assigning-Work.md | 2 +- .../0845.Longest-Mountain-in-Array.md | 2 +- 3 files changed, 150 insertions(+), 2 deletions(-) create mode 100644 website/content/ChapterFour/0800~0899/0825.Friends-Of-Appropriate-Ages.md diff --git a/website/content/ChapterFour/0800~0899/0825.Friends-Of-Appropriate-Ages.md b/website/content/ChapterFour/0800~0899/0825.Friends-Of-Appropriate-Ages.md new file mode 100644 index 00000000..4f278efa --- /dev/null +++ b/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 +} +``` + + +---------------------------------------------- +
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diff --git a/website/content/ChapterFour/0800~0899/0826.Most-Profit-Assigning-Work.md b/website/content/ChapterFour/0800~0899/0826.Most-Profit-Assigning-Work.md index e2893738..fa7464db 100644 --- a/website/content/ChapterFour/0800~0899/0826.Most-Profit-Assigning-Work.md +++ b/website/content/ChapterFour/0800~0899/0826.Most-Profit-Assigning-Work.md @@ -109,6 +109,6 @@ func maxProfitAssignment(difficulty []int, profit []int, worker []int) int { ----------------------------------------------
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diff --git a/website/content/ChapterFour/0800~0899/0845.Longest-Mountain-in-Array.md b/website/content/ChapterFour/0800~0899/0845.Longest-Mountain-in-Array.md index d0270ed5..8854bef4 100644 --- a/website/content/ChapterFour/0800~0899/0845.Longest-Mountain-in-Array.md +++ b/website/content/ChapterFour/0800~0899/0845.Longest-Mountain-in-Array.md @@ -94,5 +94,5 @@ func longestMountain(A []int) int { ----------------------------------------------

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