Rewrite README with comprehensive documentation

Update README with detailed explanation of interval_map implementation,
including overview, key characteristics, usage examples, build instructions,
and real-world use cases.

Co-Authored-By: Claude Haiku 4.5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01Te4uaebdDpT3hbdtrkcofD

README

@@ -1 +1,75 @@
-This code is a customization of std::map to address some specific needs. Showing in-depth knowledge of standard libraries.
+# Interval Map Implementation
+
+A template-based C++ implementation of an efficient interval map data structure that maps intervals (ranges) of keys to values, rather than individual key-value pairs.
+
+## Overview
+
+`interval_map<K, V>` is a specialized container that associates values with continuous intervals of keys. Instead of storing a value for every single key, it compresses storage by representing contiguous ranges that map to the same value.
+
+### Key Characteristics
+
+- **Efficient Storage**: Stores only the boundaries where values change, reducing memory overhead compared to individual key mappings
+- **Standard Library Integration**: Built on top of `std::map` for reliable performance and familiarity
+- **Template-Based**: Supports any comparable key type (`K`) and any value type (`V`)
+- **Interval Semantics**: Follows C++ conventions with half-open intervals `[keyBegin, keyEnd)`
+
+## How It Works
+
+### Constructor
+```cpp
+interval_map(V const& val, K k_range=1000)
+```
+Initializes the map with a default value that covers the entire key range. Pre-populates the internal map with entries for optimization purposes.
+
+### assign() Method
+```cpp
+void assign(K const& keyBegin, K const& keyEnd, V const& val)
+```
+Assigns a value `val` to the interval `[keyBegin, keyEnd)`.
+- If `keyBegin >= keyEnd`, the interval is empty and nothing is done
+- Overwrites any previous values in this interval
+- Uses `std::map::lower_bound()` for efficient O(log n) interval lookup
+
+### Operator[]
+```cpp
+V const& operator[](K const& key) const
+```
+Performs efficient O(log n) lookup to retrieve the value associated with a given key.
+
+## Usage Example
+
+```cpp
+interval_map<int, char> m('A', 100);  // Initialize with 'A' covering [0, 100)
+m.assign(-10, 50, 'B');                // Assign 'B' to [-10, 50)
+m['25'];                               // Returns 'B'
+m['75'];                               // Returns 'A'
+```
+
+## Building and Running
+
+### Compile
+```bash
+g++ -std=c++11 -o interval_map main.cpp
+```
+
+### Run
+```bash
+./interval_map
+```
+
+## Implementation Details
+
+This implementation demonstrates:
+- Mastery of `std::map` operations (`lower_bound`, `upper_bound`, `insert`)
+- Efficient interval range manipulation
+- Template metaprogramming with multiple template parameters
+- Memory-efficient data structure design
+- Proper use of C++ Standard Library conventions
+
+## Use Cases
+
+- Graphics rendering (color transitions)
+- Time-based event scheduling
+- Segment compression and querying
+- Network routing tables
+- Configuration management with ranges