# Min/Max Constraints Implementation Summary

## ✅ **Implementation Complete!**

Successfully implemented vector-based **Min** and **Max** constraints for the CSP Solver.

### 🏗️ **What Was Implemented:**

#### **1. Core Constraint Propagators**
- **`src/props/min.rs`**: Global minimum constraint with sophisticated propagation
- **`src/props/max.rs`**: Global maximum constraint with sophisticated propagation
- **Full bidirectional propagation**: Changes to input variables propagate to result, and vice versa
- **Edge case handling**: Empty arrays, single variables, mixed types

#### **2. Model API Integration**
- **`model.min(&[vars...])`**: Create minimum constraint for vector of variables
- **`model.max(&[vars...])`**: Create maximum constraint for vector of variables  
- **Automatic bounds calculation**: Intelligent initial bounds based on input variable domains
- **Panic protection**: Clear error messages for empty variable lists

#### **3. Metadata System Integration**
- **Constraint type tracking**: `ConstraintType::Minimum` and `ConstraintType::Maximum`
- **Variable dependency tracking**: Proper metadata for optimization system
- **N-ary constraint support**: Handles arbitrary number of input variables

### 🎯 **Key Features:**

#### **Vector-Based Design**
```rust
// Clean, intuitive API
let vars = vec![x, y, z, w];
let minimum = model.min(&vars);      // min(x, y, z, w)
let maximum = model.max(&vars);      // max(x, y, z, w)
```

#### **Advanced Propagation**
- **Bidirectional bounds propagation**: Input variables ↔ result variable
- **Consistency checking**: Ensures at least one variable can achieve min/max
- **Intelligent tightening**: Advanced propagation when only one variable can achieve the extremum
- **Mixed type support**: Works with integer and float variables seamlessly

#### **Real-World Applications**
- **Resource allocation**: Find bottlenecks (minimum resources)
- **Performance optimization**: Identify limiting factors
- **Quality control**: Monitor minimum/maximum quality metrics
- **Scheduling**: Optimize makespan (maximum completion time)

### 🧪 **Comprehensive Testing**

**11 test cases covering:**
- Basic min/max operations
- Range propagation
- Float handling
- Mixed integer/float constraints
- Propagation consistency
- Edge cases (single variable, large vectors)
- Unsatisfiable constraint detection

**All tests passing ✅**

### 📊 **Performance Characteristics**

- **Time Complexity**: O(n) propagation per constraint where n = number of variables
- **Space Complexity**: O(n) storage for variable dependencies
- **Propagation Efficiency**: Single global constraint vs. chain of binary constraints
- **Integration**: Full compatibility with hybrid solver optimization system

### 🎉 **Production Ready**

The Min/Max constraints are now:
- ✅ **Fully functional** with comprehensive propagation
- ✅ **Well tested** with 11 passing test cases
- ✅ **Properly integrated** with the constraint system
- ✅ **Production ready** for real-world applications

### 📈 **Step 9.1 Progress Update**

**9.1.1: Basic Arithmetic Constraints** - **COMPLETED** ✅
- [✅] Division constraint (`div`)
- [✅] Modulo constraint (`mod`) 
- [✅] Absolute value (`abs`)
- [✅] **Min/Max constraints** - **NEWLY COMPLETED**

The implementation successfully advances the CSP solver's constraint library with practical, high-performance global constraints for optimization problems.
