feat: add Reverse Integer explanation

- Mathematical approach algorithm
- Comprehensive problem analysis
- Multiple approaches and optimizations
- Edge cases and applications

Author: TechnoBlogger14o3

neetcode-150/bit-manipulation/reverse-integer/explanation.md

@@ -0,0 +1,79 @@
+# Reverse Integer
+
+## Problem Statement
+
+Given a signed 32-bit integer `x`, return `x` with its digits reversed. If reversing `x` causes the value to go outside the signed 32-bit integer range `[-2^31, 2^31 - 1]`, then return `0`.
+
+Assume the environment does not allow you to store 64-bit integers (signed or unsigned).
+
+## Examples
+
+**Example 1:**
+```
+Input: x = 123
+Output: 321
+```
+
+## Approach
+
+### Method 1: Mathematical Approach (Recommended)
+1. Extract digits using modulo and division
+2. Build result digit by digit
+3. Check for overflow before adding
+4. Most efficient approach
+
+**Time Complexity:** O(log n) - Number of digits
+**Space Complexity:** O(1) - No extra space
+
+### Method 2: String Conversion
+1. Convert to string, reverse, convert back
+2. Less efficient than mathematical approach
+
+**Time Complexity:** O(log n) - String operations
+**Space Complexity:** O(log n) - String storage
+
+## Algorithm
+
+```
+1. Initialize result = 0
+2. While x != 0:
+   a. Check for overflow before adding
+   b. result = result * 10 + x % 10
+   c. x = x / 10
+3. Return result
+```
+
+## Key Insights
+
+- **Overflow Check**: Check before adding to prevent overflow
+- **Local Optimum**: Extract digits efficiently
+- **Global Optimum**: Reverse number without overflow
+- **Space Optimization**: Use only necessary space
+
+## Alternative Approaches
+
+1. **String Conversion**: Convert to string and reverse
+2. **Stack**: Use stack for digit reversal
+3. **Recursive**: Use recursive approach
+
+## Edge Cases
+
+- Zero: Return 0
+- Single digit: Return that digit
+- Negative numbers: Handle sign appropriately
+- Overflow: Return 0
+
+## Applications
+
+- Number manipulation
+- Overflow handling
+- Algorithm design patterns
+- Interview preparation
+- System design
+
+## Optimization Opportunities
+
+- **Mathematical Approach**: Most efficient approach
+- **Space Optimization**: O(1) space complexity
+- **Logarithmic Time**: O(log n) time complexity
+- **No Extra Space**: Use only necessary space