Leetcode #2954: Count the Number of Infection Sequences
In this guide, we solve Leetcode #2954 Count the Number of Infection Sequences in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
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.
Quick Facts
- Difficulty: Hard
- Premium: No
- Tags: Array, Math, Combinatorics
Intuition
There is a mathematical invariant or formula that directly leads to the result.
Using math avoids unnecessary loops and reduces complexity.
Approach
Derive the formula or update rule, then compute the answer directly.
Handle edge cases like overflow or zero carefully.
Steps:
- Identify the math relationship.
- Compute the result with a loop or formula.
- Handle edge cases.
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
The time complexity is , where is the length of the array . The space complexity is .
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.