2076. Process Restricted Friend Requests
Description
You are given an integer n
indicating the number of people in a network. Each person is labeled from 0
to n - 1
.
You are also given a 0-indexed 2D integer array restrictions
, where restrictions[i] = [xi, yi]
means that person xi
and person yi
cannot become friends, either directly or indirectly through other people.
Initially, no one is friends with each other. You are given a list of friend requests as a 0-indexed 2D integer array requests
, where requests[j] = [uj, vj]
is a friend request between person uj
and person vj
.
A friend request is successful if uj
and vj
can be friends. Each friend request is processed in the given order (i.e., requests[j]
occurs before requests[j + 1]
), and upon a successful request, uj
and vj
become direct friends for all future friend requests.
Return a boolean array result
, where each result[j]
is true
if the jth
friend request is successful or false
if it is not.
Note: If uj
and vj
are already direct friends, the request is still successful.
Example 1:
Input: n = 3, restrictions = [[0,1]], requests = [[0,2],[2,1]] Output: [true,false] Explanation: Request 0: Person 0 and person 2 can be friends, so they become direct friends. Request 1: Person 2 and person 1 cannot be friends since person 0 and person 1 would be indirect friends (1--2--0).
Example 2:
Input: n = 3, restrictions = [[0,1]], requests = [[1,2],[0,2]] Output: [true,false] Explanation: Request 0: Person 1 and person 2 can be friends, so they become direct friends. Request 1: Person 0 and person 2 cannot be friends since person 0 and person 1 would be indirect friends (0--2--1).
Example 3:
Input: n = 5, restrictions = [[0,1],[1,2],[2,3]], requests = [[0,4],[1,2],[3,1],[3,4]] Output: [true,false,true,false] Explanation: Request 0: Person 0 and person 4 can be friends, so they become direct friends. Request 1: Person 1 and person 2 cannot be friends since they are directly restricted. Request 2: Person 3 and person 1 can be friends, so they become direct friends. Request 3: Person 3 and person 4 cannot be friends since person 0 and person 1 would be indirect friends (0--4--3--1).
Constraints:
2 <= n <= 1000
0 <= restrictions.length <= 1000
restrictions[i].length == 2
0 <= xi, yi <= n - 1
xi != yi
1 <= requests.length <= 1000
requests[j].length == 2
0 <= uj, vj <= n - 1
uj != vj
Solutions
Solution 1: Union-Find
We can use a union-find set to maintain the friend relationships, and then for each request, we determine whether it meets the restriction conditions.
For the two people $(u, v)$ in the current request, if they are already friends, then the request can be directly accepted; otherwise, we traverse the restriction conditions. If there exists a restriction condition $(x, y)$ such that $u$ and $x$ are friends and $v$ and $y$ are friends, or $u$ and $y$ are friends and $v$ and $x$ are friends, then the request cannot be accepted.
The time complexity is $O(q \times m \times \log(n))$, and the space complexity is $O(n)$. Where $q$ and $m$ are the number of requests and the number of restriction conditions respectively.
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