Home » 国际竞赛 » Details

2023-2024年USACO首次月考题目出炉！白金级第一题真题及解析

Category: 国际竞赛, 翰林严选, 计算机国际竞赛 Date: 2024年1月2日上午11:14

2023-2024赛季的USACO考试已于12月18日正式结束，晋级赛的最新试题也已经公布。近日，USACO官方公布了2023-2024赛季首场月赛的晋级分数线。如果没有晋级，12月可以当做一个练手+熟悉赛制的环节，1、2月的月赛持续发力，USACO可以重复挑战。

今天给大家分享白金级试题和解析，参赛的同学来看看解题思路，没参赛的同学来看看难度如何？

USACO 2023年12月白金级第一题

Farmer John has N (2≤N≤10⁵) cows labeled 1…N, where the connections between cows are described by a tree. Unfortunately, there is a sickness spreading throughout.

Initially, some cows start off infected. Every night, an infected cow spreads the sickness to their neighbors. Once a cow is infected, she stays infected. After some amount of nights, Farmer John realizes that there is an issue so he tests his cows to determine who has the sickness.

You are given Q(1≤Q≤20) different values for the number of nights, each an integer in the range [0,N].
For each number of nights, determine the minimum number of cows that could have started with the illness, or that the number of nights is inconsistent with the given information.

INPUT FORMAT (pipe stdin)：

The first line contains N.

The next line contains a bit string of length N, where the ith bit is 1 if the ith cow is infected and 0 otherwise. At least one cow is infected.

The next N−1 lines contain the edges of the tree.

Then Q, followed by the Q values for the number of nights.

OUTPUT FORMAT (pipe stdout)：

Q lines, the answers for each number of nights, or −1 if impossible.

SAMPLE INPUT：

5
11111
1 2
2 3
3 4
4 5
6
5
4
3
2
1
0

SAMPLE OUTPUT：

1
1
1
1
2
5

For the first four queries, one possibility is that just cow 3 started with the illness. For the fifth query (1 night), one possibility is that cows 2 and 4 started with the illness. For the sixth query (0 nights), one possibility is that all five cows started with the illness.

SAMPLE INPUT：

10
1111111111
1 2
2 3
2 4
2 5
2 6
6 7
7 8
8 9
9 10
11
0
1
2
3
4
5
6
7
8
9
10

SAMPLE OUTPUT：

10
3
2
1
1
1
1
1
1
1
1

For the first query (0 nights), one possibility is that all ten cows started with the illness. For the second query (1 night), one possibility is that cows 2, 7, and 9 started with the illness. For the third query (2 nights), one possibility is that cows 2 and 9 started with the illness. For the fourth to eleventh queries, one possibility is that just cow 7 started with the illness.

SAMPLE INPUT：

5
11100
1 2
2 3
3 4
4 5
6
0
1
2
3
4
5

SAMPLE OUTPUT：

3
1
1
-1
-1
-1

For the first query (0 nights), one possibility is that cows 1, 2, and 3 started with the illness. For the second query (1 night), one possibility is that just cow 2 started with the illness. For the third query (2 nights), one possibility is that just cow 1 started with the illness. For the fourth through sixth queries, there is no consistent possibility.

SCORING：

Inputs 4-5： N≤10
Inputs 6-8： All cows are infected.
Inputs 9-11： N≤400
Inputs 12-23： No additional restrictions.
Problem credits： Suhas Nagar and Brandon Wang

部分代码截图：