统计感冒序列的数目
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题目描述
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 <= 1051 <= sick.length <= n - 10 <= sick[i] <= n - 1sickis sorted in increasing order.
代码结果
运行时间: 64 ms, 内存: 20.6 MB
/*
* Problem Statement:
* Given an integer n and a 0-indexed integer array sick, sorted in ascending order,
* find the number of different sequences in which all initially non-sick children will get infected.
* The infection spreads to the adjacent left or right child who is not yet infected.
* Return the number of different infection sequences modulo 10^9 + 7.
*/
import java.util.stream.IntStream;
public class Solution {
private static final int MOD = 1000000007;
public int countInfectionSequences(int n, int[] sick) {
int healthyCount = n - sick.length;
return IntStream.rangeClosed(1, healthyCount)
.reduce(1, (a, b) -> (int) ((long) a * b % MOD));
}
public static void main(String[] args) {
Solution solution = new Solution();
System.out.println(solution.countInfectionSequences(5, new int[]{0, 4})); // Output: 4
System.out.println(solution.countInfectionSequences(4, new int[]{1})); // Output: 3
}
}解释
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