Number of Beautiful Integers in the Range — LeetCode 2827 Python Solution
HardMathDynamic Programming
- Problem
- #2827
- Pattern
- Dynamic Programming
- Reading time
- 4 min
- Source
- leetcode.com
The problem
You are given positive integers low, high, and k. A number is beautiful if it meets both of the following conditions: The count of even digits in the number is equal to the count of odd digits.
Example
- Input
- low = 10, high = 20, k = 3
- Output
- 2
- Explanation
- There are 2 beautiful integers in the given range: [12,18].
Python solution
Python
class Solution:
def numberOfBeautifulIntegers(self, low: int, high: int, k: int) -> int:
@cache
def dfs(pos: int, mod: int, diff: int, lead: int, limit: int) -> int:
if pos >= len(s):
return mod == 0 and diff == 10
up = int(s[pos]) if limit else 9
ans = 0
for i in range(up + 1):
if i == 0 and lead:
ans += dfs(pos + 1, mod, diff, 1, limit and i == up)
else:
nxt = diff + (1 if i % 2 == 1 else -1)
ans += dfs(pos + 1, (mod * 10 + i) % k, nxt, 0, limit and i == up)
return ans
s = str(high)
a = dfs(0, 0, 10, 1, 1)
dfs.cache_clear()
s = str(low - 1)
b = dfs(0, 0, 10, 1, 1)
return a - bComplexity
| Measure | Complexity |
|---|---|
| Time | O((\log M)^2 \times k \times |\Sigma|) |
| Space | O((\log M)^2 \times k), where M represents the size of the number high, and |\Sigma| represents the digit set auxiliary |
Pattern: Dynamic Programming
Define a state, write the transition, and stop recomputing the same subproblem. LeetCode 2827. Number of Beautiful Integers in the Range 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.
Related problems
Frequently asked questions
- How hard is LeetCode 2827. Number of Beautiful Integers in the Range?
- LeetCode 2827. Number of Beautiful Integers in the Range is rated Hard on LeetCode.
- What is the time complexity of LeetCode 2827. Number of Beautiful Integers in the Range?
- The Python solution on this page runs in O((\log M)^2 \times k \times |\Sigma|).
- What is the space complexity of LeetCode 2827. Number of Beautiful Integers in the Range?
- The Python solution on this page uses O((\log M)^2 \times k), where M represents the size of the number high, and |\Sigma| represents the digit set auxiliary space.
- What topics does LeetCode 2827. Number of Beautiful Integers in the Range cover?
- LeetCode 2827. Number of Beautiful Integers in the Range is tagged Math and Dynamic Programming on LeetCode.