Complete documentation system with 81 comprehensive notes and updated README index

src/notes/248_strobogrammatic_number_iii.md

@@ -0,0 +1,119 @@
+# Strobogrammatic Number III
+
+[![Problem 248](https://img.shields.io/badge/Problem-248-blue?style=for-the-badge&logo=leetcode)](https://leetcode.com/problems/strobogrammatic-number-iii/)
+[![Difficulty](https://img.shields.io/badge/Difficulty-Hard-red?style=for-the-badge)](https://leetcode.com/problemset/?difficulty=HARD)
+[![LeetCode](https://img.shields.io/badge/LeetCode-View%20Problem-orange?style=for-the-badge&logo=leetcode)](https://leetcode.com/problems/strobogrammatic-number-iii/)
+
+**Problem Number:** [248](https://leetcode.com/problems/strobogrammatic-number-iii/)
+**Difficulty:** [Hard](https://leetcode.com/problemset/?difficulty=HARD)
+**Category:** Math, Recursion, String
+**LeetCode Link:** [https://leetcode.com/problems/strobogrammatic-number-iii/](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](../exercises/248.strobogrammatic-number-iii.py).
+
+**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.
+
+---
+
+[![Back to Index](../../README.md#-problem-index)](../../README.md#-problem-index) | [![View Solution](../exercises/248.strobogrammatic-number-iii.py)](../exercises/248.strobogrammatic-number-iii.py)
+
+*Note: This is a recursive generation problem that demonstrates efficient strobogrammatic number counting in ranges.*