Count the Number of Infection Sequences — LeetCode 2954 Python Solution

The problem

You are given an integer n and an array sick sorted in increasing order, representing positions of infected people in a line of n people. At each step, one uninfected person adjacent to an infected person gets infected.

Python solution

mod = 10**9 + 7
mx = 10**5
fac = [1] * (mx + 1)
for i in range(2, mx + 1):
    fac[i] = fac[i - 1] * i % mod


class Solution:
    def numberOfSequence(self, n: int, sick: List[int]) -> int:
        nums = [b - a - 1 for a, b in pairwise([-1] + sick + [n])]
        ans = 1
        s = sum(nums)
        ans = fac[s]
        for x in nums:
            if x:
                ans = ans * pow(fac[x], mod - 2, mod) % mod
        for x in nums[1:-1]:
            if x > 1:
                ans = ans * pow(2, x - 1, mod) % mod
        return ans

Complexity

Pattern: Math and Number Theory

Find the closed form, the invariant, or the modular identity — and skip the loop entirely. LeetCode 2954. Count the Number of Infection Sequences is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Math and Combinatorics.

The math and number theory guide has the Python template for the pattern and the 485 LeetCode problems that use it.

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