feat: add Missing Number explanation

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

Author: TechnoBlogger14o3

neetcode-150/math-geometry/missing-number/explanation.md

@@ -0,0 +1,76 @@
+# Missing Number
+
+## Problem Statement
+
+Given an array `nums` containing `n` distinct numbers in the range `[0, n]`, return the only number in the range that is missing from the array.
+
+## Examples
+
+**Example 1:**
+```
+Input: nums = [3,0,1]
+Output: 2
+Explanation: n = 3 since there are 3 numbers, so all numbers are in the range [0,3]. 2 is the missing number in the range since it does not appear in nums.
+```
+
+## Approach
+
+### Method 1: Mathematical Sum (Recommended)
+1. Calculate expected sum: n * (n + 1) / 2
+2. Calculate actual sum of array
+3. Return difference
+4. Most efficient approach
+
+**Time Complexity:** O(n) - Single pass
+**Space Complexity:** O(1) - No extra space
+
+### Method 2: XOR Operation
+1. Use XOR properties: a ^ a = 0, a ^ 0 = a
+2. XOR all numbers from 0 to n with array elements
+3. Less efficient than mathematical approach
+
+**Time Complexity:** O(n) - Single pass
+**Space Complexity:** O(1) - No extra space
+
+## Algorithm
+
+```
+1. Calculate expected sum = n * (n + 1) / 2
+2. Calculate actual sum = sum of array elements
+3. Return expected sum - actual sum
+```
+
+## Key Insights
+
+- **Mathematical Sum**: Use arithmetic progression formula
+- **Local Optimum**: Calculate sum efficiently
+- **Global Optimum**: Find missing number
+- **Space Optimization**: Use only necessary space
+
+## Alternative Approaches
+
+1. **XOR Operation**: Use XOR properties
+2. **Sorting**: Sort and find missing number
+3. **Hash Set**: Use hash set for lookup
+
+## Edge Cases
+
+- Single element: Handle appropriately
+- Two elements: Handle appropriately
+- Large arrays: Handle efficiently
+- Empty array: Handle appropriately
+
+## Applications
+
+- Mathematical algorithms
+- Array manipulation
+- Algorithm design patterns
+- Interview preparation
+- System design
+
+## Optimization Opportunities
+
+- **Mathematical Sum**: Most efficient approach
+- **Space Optimization**: O(1) space complexity
+- **Linear Time**: O(n) time complexity
+- **No Extra Space**: Use only necessary space