# Decisión: traza de backtracking CSP

Problema: `horario-cursos-backtracking`.

## Métricas

| Métrica | Valor |
|---|---:|
| Candidatos brutos | 64 |
| Candidatos tras poda unaria | 16 |
| Nodos visitados | 10 |
| Ramas cortadas | 1 |
| Valores podados por forward checking | 8 |
| Profundidad máxima | 3 |
| Soluciones | 4 |

## Primera decisión MRV

MRV elige `Python` porque su dominio tiene 2 valores tras la poda inicial.

## Soluciones

| Solución |
|---|
| Python=(10, A), IA=(9, A), Datos=(9, B) |
| Python=(10, A), IA=(9, A), Datos=(10, B) |
| Python=(10, A), IA=(9, B), Datos=(10, B) |
| Python=(10, B), IA=(9, A), Datos=(9, B) |

## Primeros eventos de la traza

```jsonl
{"event": "unary_prune", "constraint": "python_hora_10", "variable": "Python", "removed": [[9, "A"], [9, "B"]], "remaining": [[10, "A"], [10, "B"]]}
{"event": "unary_prune", "constraint": "datos_sala_b", "variable": "Datos", "removed": [[9, "A"], [10, "A"]], "remaining": [[9, "B"], [10, "B"]]}
{"event": "choose_variable", "depth": 0, "variable": "Python", "domain_size": 2, "assignment": {}}
{"event": "try_value", "depth": 0, "variable": "Python", "value": [10, "A"], "assignment": {"Python": [10, "A"]}, "consistent": true, "failures": []}
{"event": "forward_prune", "depth": 1, "variable": "IA", "removed": [[10, "A"], [10, "B"]], "assignment": {"Python": [10, "A"]}}
{"event": "choose_variable", "depth": 1, "variable": "IA", "domain_size": 2, "assignment": {"Python": [10, "A"]}}
{"event": "try_value", "depth": 1, "variable": "IA", "value": [9, "A"], "assignment": {"Python": [10, "A"], "IA": [9, "A"]}, "consistent": true, "failures": []}
{"event": "choose_variable", "depth": 2, "variable": "Datos", "domain_size": 2, "assignment": {"Python": [10, "A"], "IA": [9, "A"]}}
```

## Lectura técnica

- La poda unaria reduce el espacio antes de empezar el árbol.
- MRV elige primero las variables con menos margen.
- Forward checking corta valores futuros incompatibles con la asignación actual.
- La traza permite explicar el comportamiento del solver sin depender de intuiciones.