feat: add Insert Interval explanation

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

Author: TechnoBlogger14o3

neetcode-150/intervals/insert-interval/explanation.md

@@ -0,0 +1,81 @@
+# Insert Interval
+
+## Problem Statement
+
+You are given an array of non-overlapping intervals `intervals` where `intervals[i] = [starti, endi]` represent the start and the end of the `ith` interval and `intervals` is sorted in ascending order by `starti`. You are also given an interval `newInterval = [start, end]` that represents the start and end of another interval.
+
+Insert `newInterval` into `intervals` such that the intervals are still sorted in ascending order by `starti` and `intervals` still does not have any overlapping intervals (merge overlapping intervals if necessary).
+
+Return `intervals` after the insertion.
+
+## Examples
+
+**Example 1:**
+```
+Input: intervals = [[1,3],[6,9]], newInterval = [2,5]
+Output: [[1,5],[6,9]]
+```
+
+## Approach
+
+### Method 1: Three Pass Algorithm (Recommended)
+1. First pass: Add all intervals before newInterval
+2. Second pass: Merge overlapping intervals with newInterval
+3. Third pass: Add all intervals after newInterval
+4. Most efficient approach
+
+**Time Complexity:** O(n) - Three passes
+**Space Complexity:** O(1) - In-place modification
+
+### Method 2: Binary Search + Merge
+1. Use binary search to find insertion point
+2. Merge overlapping intervals
+3. Less efficient than three pass approach
+
+**Time Complexity:** O(n) - Merge operation
+**Space Complexity:** O(1) - In-place modification
+
+## Algorithm
+
+```
+1. Initialize result = []
+2. Add all intervals before newInterval
+3. Merge overlapping intervals with newInterval
+4. Add all intervals after newInterval
+5. Return result
+```
+
+## Key Insights
+
+- **Three Passes**: Separate intervals into three categories
+- **Local Optimum**: Merge overlapping intervals optimally
+- **Global Optimum**: Maintain sorted order without overlaps
+- **Space Optimization**: Use only necessary space
+
+## Alternative Approaches
+
+1. **Binary Search**: Use binary search for insertion point
+2. **Single Pass**: Use single pass with complex logic
+3. **Sorting**: Sort all intervals and merge
+
+## Edge Cases
+
+- Empty intervals: Return [newInterval]
+- Single interval: Merge if overlapping
+- No overlaps: Insert in correct position
+- All overlaps: Merge into single interval
+
+## Applications
+
+- Interval algorithms
+- Scheduling problems
+- Algorithm design patterns
+- Interview preparation
+- System design
+
+## Optimization Opportunities
+
+- **Three Pass Algorithm**: Most efficient approach
+- **Space Optimization**: O(1) space complexity
+- **Linear Time**: O(n) time complexity
+- **No Extra Space**: Use only necessary space