Package g2901_3000.s2954_count_the_number_of_infection_sequences

Class Solution

java.lang.Object
g2901_3000.s2954_count_the_number_of_infection_sequences.Solution
public class Solution extends java.lang.Object
2954 - Count the Number of Infection Sequences.

Hard

You are given an integer n and a 0-indexed integer array sick which is sorted in increasing order.

There are n children standing in a queue with positions 0 to n - 1 assigned to them. The array sick contains the positions of the children who are infected with an infectious disease. An infected child at position i can spread the disease to either of its immediate neighboring children at positions i - 1 and i + 1 if they exist and are currently not infected. At most one child who was previously not infected can get infected with the disease in one second.

It can be shown that after a finite number of seconds, all the children in the queue will get infected with the disease. An infection sequence is the sequential order of positions in which all of the non-infected children get infected with the disease. Return the total number of possible infection sequences.

Since the answer may be large, return it modulo 109 + 7.

Note that an infection sequence does not contain positions of children who were already infected with the disease in the beginning.

Example 1:

Input: n = 5, sick = [0,4]

Output: 4

Explanation: Children at positions 1, 2, and 3 are not infected in the beginning. There are 4 possible infection sequences:

  • The children at positions 1 and 3 can get infected since their positions are adjacent to the infected children 0 and 4. The child at position 1 gets infected first.

Now, the child at position 2 is adjacent to the child at position 1 who is infected and the child at position 3 is adjacent to the child at position 4 who is infected, hence either of them can get infected. The child at position 2 gets infected. Finally, the child at position 3 gets infected because it is adjacent to children at positions 2 and 4 who are infected. The infection sequence is [1,2,3].

  • The children at positions 1 and 3 can get infected because their positions are adjacent to the infected children 0 and 4. The child at position 1 gets infected first.

Now, the child at position 2 is adjacent to the child at position 1 who is infected and the child at position 3 is adjacent to the child at position 4 who is infected, hence either of them can get infected. The child at position 3 gets infected.

Finally, the child at position 2 gets infected because it is adjacent to children at positions 1 and 3 who are infected. The infection sequence is [1,3,2].

  • The infection sequence is [3,1,2]. The order of infection of disease in the children can be seen as: [0,1,2,3,4] => [0,1,2,3,4] => [0,1,2,3,4] => [0,1,2,3,4].
  • The infection sequence is [3,2,1]. The order of infection of disease in the children can be seen as: [0,1,2,3,4] => [0,1,2,3,4] => [0,1,2,3,4] => [0,1,2,3,4].

Example 2:

Input: n = 4, sick = [1]

Output: 3

Explanation: Children at positions 0, 2, and 3 are not infected in the beginning. There are 3 possible infection sequences:

  • The infection sequence is [0,2,3]. The order of infection of disease in the children can be seen as: [0,1,2,3] => [0,1,2,3] => [0,1,2,3] => [0,1,2,3].
  • The infection sequence is [2,0,3]. The order of infection of disease in the children can be seen as: [0,1,2,3] => [0,1,2,3] => [0,1,2,3] => [0,1,2,3].
  • The infection sequence is [2,3,0]. The order of infection of disease in the children can be seen as: [0,1,2,3] => [0,1,2,3] => [0,1,2,3] => [0,1,2,3].

Constraints:

  • 2 <= n <= 105
  • 1 <= sick.length <= n - 1
  • 0 <= sick[i] <= n - 1
  • sick is sorted in increasing order.

  • Constructor Summary

    Constructors
    Constructor
    Description
    Solution()
     

  • Method Summary

    Modifier and Type
    Method
    Description
    int
    numberOfSequence(int n, int[] sick)
     

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Constructor Details

    • Solution

      public Solution()

  • Method Details

    • numberOfSequence

      public int numberOfSequence(int n, int[] sick)