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On a street, there are N individuals (numbered from 1 to N) positioned along the line. Each person's position is denoted by Xi.Here's the situation: among these people, one person is unknowingly carrying the COVID-19 virus. The virus spreads if the distance between an infected person and a healthy person is no more than 2 units. As time goes on, a certain group of individuals (depending on who the initial infected person is) will become infected. Let's refer to the size of this group as the final count of infected people.Your goal is to print the smallest and largest possible number of people who could end up infected. This means finding the minimum and maximum counts of infected individuals, considering both the most favorable and the least favorable scenarios for how the virus spreads among the people on the street.Input FormatThe first line of each test case contains a single integer N.The second line contains N space-separated integers X1, X2, ..., XN.Constraints2 ≤ N ≤ 80 ≤ Xi ≤ 10 for each valid i0 ≤ X1 < X2 < ... < XNOutput FormatPrint a single line containing two space-separated integers ― the minimum and maximum possible final number of infected people.Sample Input 021 2Sample Output 02 2Sample Input 123 6Sample Output 11 1

Question

On a street, there are N individuals (numbered from 1 to N) positioned along the line. Each person's position is denoted by Xi.Here's the situation: among these people, one person is unknowingly carrying the COVID-19 virus. The virus spreads if the distance between an infected person and a healthy person is no more than 2 units. As time goes on, a certain group of individuals (depending on who the initial infected person is) will become infected. Let's refer to the size of this group as the final count of infected people.Your goal is to print the smallest and largest possible number of people who could end up infected. This means finding the minimum and maximum counts of infected individuals, considering both the most favorable and the least favorable scenarios for how the virus spreads among the people on the street.Input FormatThe first line of each test case contains a single integer N.The second line contains N space-separated integers X1, X2, ..., XN.Constraints2 ≤ N ≤ 80 ≤ Xi ≤ 10 for each valid i0 ≤ X1 < X2 < ... < XNOutput FormatPrint a single line containing two space-separated integers ― the minimum and maximum possible final number of infected people.Sample Input 021 2Sample Output 02 2Sample Input 123 6Sample Output 11 1

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Solution

The problem is asking to find the minimum and maximum number of people that could be infected by the COVID-19 virus on a street. The virus spreads if the distance between an infected person and a healthy person is no more than 2 units.

Here are the steps to solve this problem:

  1. First, we need to sort the positions of the individuals in ascending order. This is because the virus spreads to the nearest individuals first.

  2. To find the minimum number of infected people, we can assume that the initial infected person is at one of the ends of the sorted list. This is because the virus can only spread in one direction in this case, either to the left or to the right.

  3. To find the maximum number of infected people, we can assume that the initial infected person is in the middle of the sorted list. This is because the virus can spread in both directions in this case, to the left and to the right.

  4. We can use a loop to iterate through the sorted list and calculate the number of infected people in both scenarios. For the minimum case, we only need to check the distance to the next person. For the maximum case, we need to check the distance to the next person and the previous person.

  5. Finally, we print the minimum and maximum number of infected people.

Here is a Python code snippet that implements these steps:

def solve(N, X):
    X.sort()
    min_infected = max_infected = 1
    left = right = 0
    for i in range(1, N):
        if X[i] - X[i-1] <= 2:
            min_infected += 1
        else:
            max_infected = max(max_infected, min_infected)
            min_infected = 1
    max_infected = max(max_infected, min_infected)
    return min_infected, max_infected

N = int(input())
X = list(map(int, input().split()))
min_infected, max_infected = solve(N, X)
print(min_infected, max_infected)

This code reads the number of individuals and their positions from the input, calls the solve function to calculate the minimum and maximum number of infected people, and then prints the results.

This problem has been solved

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