Leetcode #2539: Count the Number of Good Subsequences
In this guide, we solve Leetcode #2539 Count the Number of Good 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 subsequence of a string is good if it is not empty and the frequency of each one of its characters is the same. Given a string s, return the number of good subsequences of s.
Quick Facts
- Difficulty: Medium
- Premium: Yes
- Tags: Hash Table, Math, String, Combinatorics, Counting
Intuition
Fast membership checks and value lookups are the heart of this problem, which makes a hash map the natural choice.
By storing what we have already seen (or counts/indexes), we can answer the question in one pass without backtracking.
Approach
Scan the input once, using the map to detect when the condition is satisfied and to update state as you go.
This keeps the solution linear while remaining easy to explain in an interview setting.
Steps:
- Initialize a hash map for seen items or counts.
- Iterate through the input, querying/updating the map.
- Return the first valid result or the final computed value.
Example
Input: s = "aabb"
Output: 11
Explanation: The total number of subsequences is 24. There are five subsequences which are not good: "aabb", "aabb", "aabb", "aabb", and the empty subsequence. Hence, the number of good subsequences is 24-5 = 11.
Python Solution
N = 10001
MOD = 10**9 + 7
f = [1] * N
g = [1] * N
for i in range(1, N):
f[i] = f[i - 1] * i % MOD
g[i] = pow(f[i], MOD - 2, MOD)
def comb(n, k):
return f[n] * g[k] * g[n - k] % MOD
class Solution:
def countGoodSubsequences(self, s: str) -> int:
cnt = Counter(s)
ans = 0
for i in range(1, max(cnt.values()) + 1):
x = 1
for v in cnt.values():
if v >= i:
x = x * (comb(v, i) + 1) % MOD
ans = (ans + x - 1) % MOD
return ans
Complexity
The time complexity is O(n). The space complexity is O(n).
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.