feat: add Single Number II explanation

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

Author: TechnoBlogger14o3

neetcode-150/bit-manipulation/single-number-ii/explanation.md

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+# Single Number II
+
+## Problem Statement
+
+Given an integer array `nums` where every element appears three times except for one, which appears exactly once. Find the single element and return it.
+
+You must implement a solution with a linear runtime complexity and use only constant extra space.
+
+## Examples
+
+**Example 1:**
+```
+Input: nums = [2,2,3,2]
+Output: 3
+```
+
+## Approach
+
+### Method 1: Bit Manipulation (Recommended)
+1. Use bit manipulation to count bits
+2. For each bit position, count occurrences
+3. If count % 3 != 0, set that bit in result
+4. Most efficient approach
+
+**Time Complexity:** O(n) - Single pass
+**Space Complexity:** O(1) - No extra space
+
+### Method 2: Hash Map
+1. Use hash map to count occurrences
+2. Find element with count 1
+3. Less efficient than bit manipulation
+
+**Time Complexity:** O(n) - Single pass
+**Space Complexity:** O(n) - Hash map
+
+## Algorithm
+
+```
+1. Initialize result = 0
+2. For each bit position (0 to 31):
+   a. Count = 0
+   b. For each num in nums:
+      - If (num >> i) & 1: count++
+   c. If count % 3 != 0: result |= (1 << i)
+3. Return result
+```
+
+## Key Insights
+
+- **Bit Counting**: Count bits at each position
+- **Modulo 3**: Use modulo 3 to find single element
+- **Local Optimum**: Count bits efficiently
+- **Global Optimum**: Find single element
+
+## Alternative Approaches
+
+1. **Hash Map**: Use hash map for counting
+2. **Sorting**: Sort and find single element
+3. **Mathematical**: Use mathematical properties
+
+## Edge Cases
+
+- Single element: Return that element
+- All same: Return that element
+- Large arrays: Handle efficiently
+- Negative numbers: Handle appropriately
+
+## Applications
+
+- Bit manipulation
+- Array algorithms
+- Algorithm design patterns
+- Interview preparation
+- System design
+
+## Optimization Opportunities
+
+- **Bit Manipulation**: Most efficient approach
+- **Space Optimization**: O(1) space complexity
+- **Linear Time**: O(n) time complexity
+- **No Extra Space**: Use only necessary space