Numbers With Repeated Digits — LeetCode 1012 Python Solution

The problem

Given an integer n, return the number of positive integers in the range [1, n] that have at least one repeated digit.

Example

Input

n = 20

Output

1

Explanation

The only positive number (<= 20) with at least 1 repeated digit is 11.

Python solution

class Solution:
    def numDupDigitsAtMostN(self, n: int) -> int:
        @cache
        def dfs(i: int, mask: int, lead: bool, limit: bool) -> int:
            if i >= len(s):
                return lead ^ 1
            up = int(s[i]) if limit else 9
            ans = 0
            for j in range(up + 1):
                if lead and j == 0:
                    ans += dfs(i + 1, mask, True, False)
                elif mask >> j & 1 ^ 1:
                    ans += dfs(i + 1, mask | 1 << j, False, limit and j == up)
            return ans

        s = str(n)
        return n - dfs(0, 0, True, True)

Complexity

Pattern: Dynamic Programming

Define a state, write the transition, and stop recomputing the same subproblem. LeetCode 1012. Numbers With Repeated Digits 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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