Trips
题意翻译
**题目大意:**
一共有$n$个人,他们开始互不认识,而每天早上不认识的两个人会变成朋友。一共有$m$天,每天晚上有的人要去旅行,去旅行的人必须满足ta有至少$k$个朋友也去旅行
求每天去旅行的最大人数
**输入格式:**
第一行3个整数,表示$n,m,k$
往下m行,每行两个整数$x,y$,表示这天早上$x$和$y$会变成朋友
**输出格式:**
共$m$行,每行一个整数,表示每天晚上最多能去旅游的人数
题目描述
There are $ n $ persons who initially don't know each other. On each morning, two of them, who were not friends before, become friends.
We want to plan a trip for every evening of $ m $ days. On each trip, you have to select a group of people that will go on the trip. For every person, one of the following should hold:
- Either this person does not go on the trip,
- Or at least $ k $ of his friends also go on the trip.
Note that the friendship is not transitive. That is, if $ a $ and $ b $ are friends and $ b $ and $ c $ are friends, it does not necessarily imply that $ a $ and $ c $ are friends.
For each day, find the maximum number of people that can go on the trip on that day.
输入输出格式
输入格式
The first line contains three integers $ n $ , $ m $ , and $ k $ ( $ 2 \leq n \leq 2 \cdot 10^5, 1 \leq m \leq 2 \cdot 10^5 $ , $ 1 \le k < n $ ) — the number of people, the number of days and the number of friends each person on the trip should have in the group.
The $ i $ -th ( $ 1 \leq i \leq m $ ) of the next $ m $ lines contains two integers $ x $ and $ y $ ( $ 1\leq x, y\leq n $ , $ x\ne y $ ), meaning that persons $ x $ and $ y $ become friends on the morning of day $ i $ . It is guaranteed that $ x $ and $ y $ were not friends before.
输出格式
Print exactly $ m $ lines, where the $ i $ -th of them ( $ 1\leq i\leq m $ ) contains the maximum number of people that can go on the trip on the evening of the day $ i $ .
输入输出样例
输入样例 #1
4 4 2
2 3
1 2
1 3
1 4
输出样例 #1
0
0
3
3
输入样例 #2
5 8 2
2 1
4 2
5 4
5 2
4 3
5 1
4 1
3 2
输出样例 #2
0
0
0
3
3
4
4
5
输入样例 #3
5 7 2
1 5
3 2
2 5
3 4
1 2
5 3
1 3
输出样例 #3
0
0
0
0
3
4
4
说明
In the first example,
- $ 1,2,3 $ can go on day $ 3 $ and $ 4 $ .
In the second example,
- $ 2,4,5 $ can go on day $ 4 $ and $ 5 $ .
- $ 1,2,4,5 $ can go on day $ 6 $ and $ 7 $ .
- $ 1,2,3,4,5 $ can go on day $ 8 $ .
In the third example,
- $ 1,2,5 $ can go on day $ 5 $ .
- $ 1,2,3,5 $ can go on day $ 6 $ and $ 7 $ .