Leetcode #1088: Confusing Number II
In this guide, we solve Leetcode #1088 Confusing Number II 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 confusing number is a number that when rotated 180 degrees becomes a different number with each digit valid. We can rotate digits of a number by 180 degrees to form new digits.
Quick Facts
- Difficulty: Hard
- Premium: Yes
- Tags: Math, Backtracking
Intuition
We must explore combinations of choices, but many branches can be pruned early.
Backtracking enumerates valid candidates while keeping the search space under control.
Approach
Use DFS to build candidates step by step, and backtrack when constraints are violated.
Pruning keeps the exploration practical for typical constraints.
Steps:
- Define the decision tree.
- DFS through choices and backtrack.
- Prune invalid paths early.
Example
Input: n = 20
Output: 6
Explanation: The confusing numbers are [6,9,10,16,18,19].
6 converts to 9.
9 converts to 6.
10 converts to 01 which is just 1.
16 converts to 91.
18 converts to 81.
19 converts to 61.
Python Solution
class Solution:
def confusingNumberII(self, n: int) -> int:
def check(x: int) -> bool:
y, t = 0, x
while t:
t, v = divmod(t, 10)
y = y * 10 + d[v]
return x != y
def dfs(pos: int, limit: bool, x: int) -> int:
if pos >= len(s):
return int(check(x))
up = int(s[pos]) if limit else 9
ans = 0
for i in range(up + 1):
if d[i] != -1:
ans += dfs(pos + 1, limit and i == up, x * 10 + i)
return ans
d = [0, 1, -1, -1, -1, -1, 9, -1, 8, 6]
s = str(n)
return dfs(0, True, 0)
Complexity
The time complexity is Exponential (worst case). The space complexity is O(depth).
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.