Leetcode #1955: Count Number of Special Subsequences
In this guide, we solve Leetcode #1955 Count Number of Special Subsequences 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
A sequence is special if it consists of a positive number of 0s, followed by a positive number of 1s, then a positive number of 2s. For example, [0,1,2] and [0,0,1,1,1,2] are special.
Quick Facts
- Difficulty: Hard
- Premium: No
- Tags: Array, Dynamic Programming
Intuition
The problem breaks into overlapping subproblems, so caching results prevents exponential repetition.
A carefully chosen DP state captures exactly what we need to build the final answer.
Approach
Define the DP state and recurrence, then compute states in the correct order.
Optionally compress space once the recurrence is clear.
Steps:
- Choose a DP state definition.
- Write the recurrence and base cases.
- Compute states in the correct order.
Example
Input: nums = [0,1,2,2]
Output: 3
Explanation: The special subsequences are bolded [0,1,2,2], [0,1,2,2], and [0,1,2,2].
Python Solution
class Solution:
def countSpecialSubsequences(self, nums: List[int]) -> int:
mod = 10**9 + 7
n = len(nums)
f = [[0] * 3 for _ in range(n)]
f[0][0] = nums[0] == 0
for i in range(1, n):
if nums[i] == 0:
f[i][0] = (2 * f[i - 1][0] + 1) % mod
f[i][1] = f[i - 1][1]
f[i][2] = f[i - 1][2]
elif nums[i] == 1:
f[i][0] = f[i - 1][0]
f[i][1] = (f[i - 1][0] + 2 * f[i - 1][1]) % mod
f[i][2] = f[i - 1][2]
else:
f[i][0] = f[i - 1][0]
f[i][1] = f[i - 1][1]
f[i][2] = (f[i - 1][1] + 2 * f[i - 1][2]) % mod
return f[n - 1][2]
Complexity
The time complexity is , and the space complexity is . 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.