Question

На острове живут 2023 человека. Некоторые из них дружат между собой, если A дружит с B, то B дружит с A, причём у каждого не более 10 друзей. На остров едет бригада врачей которые собираются привить часть жителей. Требуется чтобы у каждого кто останется не привит все друзья были привиты. Какое минимальное количество привитых могло быть среди жителей?

Answer 1

Ответ:

1 человек

Пошаговое объяснение:

Пускай единственные друзья на острове - это А и В. Тогда мы можем привить А, а В оставить непривитым - у того единственный друг А.

А остальные жители не имеют друзей, поэтому их прививать не обязательно.

Answer 2

Problem Analysis

We are given that there are 2023 people living on an island. Some of them are friends with each other, and each person can have a maximum of 10 friends. A team of doctors is coming to the island to vaccinate some of the residents. The goal is to ensure that every person who remains unvaccinated has all their friends vaccinated. We need to determine the minimum number of vaccinated people among the residents.

Solution

To solve this problem, we can use a greedy algorithm. We will start by assuming that all residents are unvaccinated. Then, we will iterate through each resident and check if all their friends are vaccinated. If any friend is unvaccinated, we will mark the resident as vaccinated and increment the count of vaccinated people. We will continue this process until no more residents can be vaccinated.

Let's go through an example to illustrate the algorithm:

1. Assume all 2023 residents are unvaccinated. 2. Start with the first resident (A) and check if all their friends are vaccinated. - If all friends are vaccinated, move to the next resident. - If any friend is unvaccinated, mark resident A as vaccinated and increment the count of vaccinated people. 3. Repeat step 2 for each resident until no more residents can be vaccinated.

Let's implement this algorithm in code:

def min_vaccinated(residents):
    vaccinated = 0
    while True:
        vaccinated_this_round = 0
        for resident in residents:
            if resident['vaccinated']:
                continue
            all_friends_vaccinated = True
            for friend in resident['friends']:
                if not friend['vaccinated']:
                    all_friends_vaccinated = False
                    break
            if all_friends_vaccinated:
                resident['vaccinated'] = True
                vaccinated += 1
                vaccinated_this_round += 1
        if vaccinated_this_round == 0:
            break
    return vaccinated

Now, let's apply this algorithm to the given problem:

residents = [
    {'id': 'A', 'vaccinated': False, 'friends': []},
    {'id': 'B', 'vaccinated': False, 'friends': []},
    ...
    {'id': 'Z', 'vaccinated': False, 'friends': []}
]

# Set the friends for each resident
# residents[i]['friends'] = [residents[j], residents[k], ...]
# where j, k, ... are the indices of the friends of resident i

# Call the function to get the minimum number of vaccinated people
min_vaccinated_count = min_vaccinated(residents)

The variable `min_vaccinated_count` will contain the minimum number of vaccinated people among the residents.

Answer

The minimum number of vaccinated people among the 2023 residents on the island can be determined using the algorithm described above. Unfortunately, the specific details of the island's residents and their friendships are not provided, so we cannot provide an exact answer. However, by implementing the algorithm with the given information, you can determine the minimum number of vaccinated people.