HardNo. 2376
Count Special Integers — LeetCode 2376 Python Solution
- Pattern
- Dynamic Programming
- Topics
- Math, Dynamic Programming
- Reading time
- 3 min
- Source
- leetcode.com
The problem
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].
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:
@cache
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
- Time
- O(m × 2D × D)
- Space · auxiliary
- O(m × 2D)
Pattern: Dynamic Programming
Define a state, write the transition, and stop recomputing the same subproblem. LeetCode 2376. Count Special Integers is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Dynamic Programming.
The dynamic programming guide has the Python template for the pattern and the 481 LeetCode problems that use it.
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Frequently asked questions
- How hard is LeetCode 2376. Count Special Integers?
LeetCode 2376. Count Special Integers is rated Hard on LeetCode.
- What is the time complexity of LeetCode 2376. Count Special Integers?
The Python solution on this page runs in O(m × 2D × D).
- What is the space complexity of LeetCode 2376. Count Special Integers?
The Python solution on this page uses O(m × 2D) auxiliary space.
- What topics does LeetCode 2376. Count Special Integers cover?
LeetCode 2376. Count Special Integers is tagged Math and Dynamic Programming on LeetCode.