Sum of k-Mirror Numbers - Problem
A k-mirror number is a positive integer without leading zeros that reads the same both forward and backward in base-10 as well as in base-k.
For example, 9 is a 2-mirror number. The representation of 9 in base-10 and base-2 are 9 and 1001 respectively, which read the same both forward and backward.
On the contrary, 4 is not a 2-mirror number. The representation of 4 in base-2 is 100, which does not read the same both forward and backward.
Given the base k and the number n, return the sum of the n smallest k-mirror numbers.
Input & Output
Example 1 — Basic Case
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Input:
k = 2, n = 5
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Output:
25
💡 Note:
The first 5 k-mirror numbers for k=2 are: 1 (base-10: 1, base-2: 1), 3 (base-10: 3, base-2: 11), 5 (base-10: 5, base-2: 101), 7 (base-10: 7, base-2: 111), 9 (base-10: 9, base-2: 1001). Sum = 1+3+5+7+9 = 25
Example 2 — Different Base
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Input:
k = 3, n = 7
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Output:
499
💡 Note:
The first 7 k-mirror numbers for k=3 are palindromes in both base-10 and base-3. We check each candidate systematically until we find 7 valid numbers.
Example 3 — Small Case
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Input:
k = 7, n = 2
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Output:
4
💡 Note:
For k=7, the first 2 k-mirror numbers are 1 and 3. Sum = 1+3 = 4
Constraints
- 2 ≤ k ≤ 9
- 1 ≤ n ≤ 30
Visualization
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Understanding the Visualization
1
Input
Given k=2, n=3 - find first 3 numbers palindromic in both base-10 and base-2
2
Process
Test candidates: 1✓, 2✗, 3✓, 4✗, 5✓, 6✗, 7✓, 8✗, 9✓
3
Output
Sum first 3: 1+3+5 = 9
Key Takeaway
🎯 Key Insight: Generate base-10 palindromes systematically instead of testing every number
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Explanation
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