leetcode/src/notes/248_strobogrammatic_number_iii.md

Strobogrammatic Number III

Problem Number: 248 Difficulty: Hard Category: Math, Recursion, String LeetCode Link: https://leetcode.com/problems/strobogrammatic-number-iii/

Problem Description

Given two strings low and high that represent two integers low and high where low <= high, return the number of strobogrammatic numbers in the range [low, high].

A strobogrammatic number is a number that looks the same when rotated 180 degrees (looked at upside down).

Example 1:

Input: low = "50", high = "100"
Output: 3
Explanation: 69, 88, and 96 are three strobogrammatic numbers.

Example 2:

Input: low = "0", high = "0"
Output: 1

Constraints:

• 1 <= low.length, high.length <= 15
• low and high consist of only digits.
• low <= high
• low and high do not contain any leading zeros except itself.

My Approach

I used a Recursive Generation approach to generate all strobogrammatic numbers in the given range. The key insight is to recursively build strobogrammatic numbers of different lengths and count those within the range.

Algorithm:

1. Define recursive function to generate strobogrammatic numbers of given length
2. Base cases: length 0 returns [""], length 1 returns ["0","1","8"]
3. For length > 1: recursively generate shorter numbers and add pairs
4. Generate numbers for all lengths between min and max
5. Count numbers that fall within the range [low, high]

Solution

The solution uses recursive generation to build strobogrammatic numbers and count them in range. See the implementation in the solution file.

Key Points:

• Uses recursion to generate strobogrammatic numbers
• Handles different lengths systematically
• Avoids leading zeros except for single digit
• Counts numbers within specified range

Time & Space Complexity

Time Complexity: O(5^(n/2))

• Recursive generation: O(5^(n/2)) where n is max length
• Range checking: O(k) where k is number of generated numbers
• Total: O(5^(n/2))

Space Complexity: O(5^(n/2))

• Recursive call stack: O(n)
• Generated numbers storage: O(5^(n/2))
• Total: O(5^(n/2))

Key Insights

1. Recursive Generation: Building strobogrammatic numbers recursively is efficient.

2. Length-based Approach: Generate numbers by length to avoid duplicates.

3. Pair Addition: Add valid pairs (11, 88, 69, 96) around shorter numbers.

4. Leading Zero Handling: Avoid leading zeros except for single digit numbers.

5. Range Checking: Convert strings to integers for range comparison.

6. Base Cases: Handle length 0 and 1 as base cases.

Mistakes Made

1. Wrong Generation: Initially might generate invalid strobogrammatic numbers.

2. Leading Zeros: Not properly handling leading zero constraints.

3. Complex Logic: Overcomplicating the recursive generation.

4. Range Issues: Not properly converting strings to integers for comparison.

Related Problems

• Strobogrammatic Number (Problem 246): Check if number is strobogrammatic
• Strobogrammatic Number II (Problem 247): Generate strobogrammatic numbers of given length
• Generate Parentheses (Problem 22): Recursive generation
• Subsets (Problem 78): Generate all subsets

Alternative Approaches

1. Iterative Generation: Use iteration instead of recursion - O(5^(n/2)) time
2. Binary Search: Use binary search on generated numbers - O(n log n) time
3. Mathematical: Use mathematical properties to optimize - O(n) time

Common Pitfalls

1. Wrong Generation: Generating invalid strobogrammatic numbers.
2. Leading Zeros: Not properly handling leading zero constraints.
3. Complex Logic: Overcomplicating the recursive generation.
4. Range Issues: Not properly converting strings to integers.
5. Memory Issues: Not considering exponential space complexity.

---

|

Note: This is a recursive generation problem that demonstrates efficient strobogrammatic number counting in ranges.