Leetcode #2376: Count Special Integers
In this guide, we solve Leetcode #2376 Count Special Integers 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
We call a positive integer special if all of its digits are distinct. Given a positive integer n, return the number of special integers that belong to the interval [1, n].
Quick Facts
- Difficulty: Hard
- Premium: No
- Tags: Math, 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: n = 20
Output: 19
Explanation: All the integers from 1 to 20, except 11, are special. Thus, there are 19 special integers.
Python Solution
class Solution:
def countSpecialNumbers(self, n: int) -> int:
def dfs(i: int, mask: int, lead: bool, limit: bool) -> int:
if i >= len(s):
return int(lead ^ 1)
up = int(s[i]) if limit else 9
ans = 0
for j in range(up + 1):
if mask >> j & 1:
continue
if lead and j == 0:
ans += dfs(i + 1, mask, True, limit and j == up)
else:
ans += dfs(i + 1, mask | 1 << j, False, limit and j == up)
return ans
s = str(n)
return dfs(0, 0, True, True)
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.