From f1ea7f0cb60bc0313ca8a7ec1e28df21fb29312f Mon Sep 17 00:00:00 2001
From: Nao Pross <np@0hm.ch>
Date: Tue, 17 Oct 2023 19:38:38 +0200
Subject: Pass TestFiniteRelationRepresentation, TestFiniteRelationCompose,
 TestFiniteRelationProperties

---
 src/act4e_solutions/relations.py                | 52 +++++++++++++++++++---
 src/act4e_solutions/relations_representation.py | 58 +++++++++++++++++++++++--
 2 files changed, 102 insertions(+), 8 deletions(-)

diff --git a/src/act4e_solutions/relations.py b/src/act4e_solutions/relations.py
index 26f90a7..c538d4d 100644
--- a/src/act4e_solutions/relations.py
+++ b/src/act4e_solutions/relations.py
@@ -3,6 +3,8 @@ from typing import Any, TypeVar
 import act4e_interfaces as I
 from act4e_interfaces import FiniteRelation
 
+from .relations_representation import MyFiniteRelation
+
 E1 = TypeVar("E1")
 E2 = TypeVar("E2")
 E3 = TypeVar("E3")
@@ -14,16 +16,46 @@ B = TypeVar("B")
 
 class SolFiniteRelationProperties(I.FiniteRelationProperties):
     def is_surjective(self, fr: I.FiniteRelation[Any, Any]) -> bool:
-        raise NotImplementedError()
+        # for all y in B there is an x in A s.t. x R y
+        # converse: there is a y in B s.t. for all x in A there is no x R y
+        for y in fr.target().elements():
+            there_is_one = any([fr.holds(x, y) for x in fr.source().elements()])
+            if not there_is_one:
+                return False
+        return True
 
     def is_defined_everywhere(self, fr: I.FiniteRelation[Any, Any]) -> bool:
-        raise NotImplementedError()
+        # for all x in A there is a y in B s.t. x R y
+        # converse: there is an x in A s.t. for all y in B there is no x R y
+        for x in fr.source().elements():
+            there_is_one = any([fr.holds(x, y) for y in fr.target().elements()])
+            if not there_is_one:
+                return False
+        return True
 
     def is_injective(self, fr: I.FiniteRelation[Any, Any]) -> bool:
-        raise NotImplementedError()
+        # x R y and z R y implies z = x
+        # converse: there is a z neq y such that x R y and z R y
+        image = []
+        for y in fr.target().elements():
+            for x in fr.source().elements():
+                if fr.holds(x, y):
+                    if y in image:
+                        return False
+                    image.append(y)
+        return True
 
     def is_single_valued(self, fr: I.FiniteRelation[Any, Any]) -> bool:
-        raise NotImplementedError()
+        # x R y and x R u imply y = u
+        # converse: there is an y neq u such that x R y and x R u
+        domain = []
+        for x in fr.source().elements():
+            for y in fr.target().elements():
+                if fr.holds(x, y):
+                    if x in domain:
+                        return False
+                    domain.append(x)
+        return True
 
 
 class SolFiniteRelationOperations(I.FiniteRelationOperations):
@@ -61,4 +93,14 @@ class SolFiniteEndorelationOperations(I.FiniteEndorelationOperations):
 
 class SolFiniteRelationCompose(I.FiniteRelationCompose):
     def compose(self, fr1: FiniteRelation[E1, E2], fr2: FiniteRelation[E2, E3]) -> I.FiniteRelation[E1, E3]:
-        raise NotImplementedError()
+        values = []
+        # Yeah O(n^3), i really should do this better
+        for a in fr1.source().elements():
+            for b in fr1.target().elements():
+                for c in fr2.target().elements():
+                    if fr1.holds(a, b) and fr2.holds(b, c):
+                        values.append([a, c])
+
+        return MyFiniteRelation(fr1.source(), fr2.target(), values)
+
+
diff --git a/src/act4e_solutions/relations_representation.py b/src/act4e_solutions/relations_representation.py
index 69ccdf0..a7fec7f 100644
--- a/src/act4e_solutions/relations_representation.py
+++ b/src/act4e_solutions/relations_representation.py
@@ -1,14 +1,66 @@
-from typing import TypeVar
+from typing import TypeVar, List, Tuple
 
 import act4e_interfaces as I
+from .sets_representation import SolFiniteSetRepresentation
 
 A = TypeVar("A")
 B = TypeVar("B")
 
+class MyFiniteRelation(I.FiniteRelation[A,B]):
+    _source: I.FiniteSet[A]
+    _target: I.FiniteSet[B]
+    _values: List[Tuple[A,B]]
+
+    def __init__(self, source: I.FiniteSet[A], target: I.FiniteSet[B], values: List[Tuple[A,B]]):
+        self._source = source
+        self._target = target
+        self._values = values
+
+    def source(self) -> I.FiniteSet[A]:
+        return self._source
+
+    def target(self) -> I.FiniteSet[B]:
+        return self._target
+
+    def holds(self, a: A, b: B) -> bool:
+        for v, u in self._values:
+            if self._source.equal(v, a) and self._target.equal(u, b):
+                return True
+        return False
+
 
 class SolFiniteRelationRepresentation(I.FiniteRelationRepresentation):
     def load(self, h: I.IOHelper, data: I.FiniteRelation_desc) -> I.FiniteRelation[A, B]:
-        raise NotImplementedError()
+        fsr = SolFiniteSetRepresentation()
+        src = fsr.load(h, data["source"])
+        dst = fsr.load(h, data["target"])
+        values = []
+        
+        for v in data["values"]:
+            a, b = src.load(h, v[0]), dst.load(h, v[1])
+
+            if not src.contains(a):
+                raise I.InvalidFormat()
+
+            if not dst.contains(b):
+                raise I.InvalidFormat()
+
+            values.append([a, b])
+
+        return MyFiniteRelation(src, dst, values)
 
     def save(self, h: I.IOHelper, f: I.FiniteRelation[A, B]) -> I.FiniteRelation_desc:
-        raise NotImplementedError()
+        fsr = SolFiniteSetRepresentation()
+        d = {
+            "source": fsr.save(h, f.source()),
+            "target": fsr.save(h, f.target()),
+            "values": [],
+        }
+
+        for a in f.source().elements():
+            for b in f.target().elements():
+                if f.holds(a, b):
+                    d["values"].append([
+                        f.source().save(h, a),
+                        f.target().save(h, b)])
+        return d
-- 
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