Добавил первую лабораторную работу

1 files changed, 135 insertions, 0 deletions

diff --git a/lab1/lab1.py b/lab1/lab1.py
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+++ b/lab1/lab1.py
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+import numpy as np
+from dataclasses import dataclass
+
+
+@dataclass
+class BinaryRelation:
+    matrix: np.array
+    reflexive: bool = False
+    antireflexive: bool = False
+    symmetric: bool = False
+    antisymmetric: bool = False
+    transitive: bool = False
+
+
+def check_reflexivity(relation: BinaryRelation):
+    diagonal = np.diagonal(relation.matrix)
+    result = diagonal[diagonal == True].shape[0] == diagonal.shape[0]
+    relation.reflexive = result
+
+
+def check_antireflexivity(relation: BinaryRelation):
+    diagonal = np.diagonal(relation.matrix)
+    result = diagonal[diagonal == False].shape[0] == diagonal.shape[0]
+    relation.antireflexive = result
+
+
+def check_symmetry(relation: BinaryRelation):
+    relation.symmetric = (relation.matrix == relation.matrix.T).all()
+
+
+def check_antisymmetry(relation: BinaryRelation):
+    relation.antisymmetric = True
+    multiplied = relation.matrix @ relation.matrix.T
+    n = multiplied.shape[0]
+    for i in range(n):
+        for j in range(n):
+            if i != j and multiplied[i][j] != False:
+                relation.antisymmetric = False
+
+
+def check_transitivity(relation: BinaryRelation):
+    multiplied = relation.matrix @ relation.matrix
+    relation.transitive = (multiplied <= relation.matrix).all()
+
+
+def is_equivalence(relation: BinaryRelation) -> bool:
+    return relation.reflexive and relation.symmetric and relation.transitive
+
+
+def is_quasiorder(relation: BinaryRelation) -> bool:
+    return relation.reflexive and relation.transitive
+
+
+def is_partial_order(relation: BinaryRelation) -> bool:
+    return relation.reflexive and relation.antisymmetric and relation.transitive
+
+
+def is_strict_order(relation: BinaryRelation) -> bool:
+    return relation.antireflexive and relation.antisymmetric and relation.transitive
+
+
+def reflexive_closure(relation: BinaryRelation) -> BinaryRelation:
+    matrix = np.copy(relation.matrix)
+    for i in range(matrix.shape[0]):
+        matrix[i][i] = True
+    return BinaryRelation(matrix)
+
+
+def symmetric_closure(relation: BinaryRelation) -> BinaryRelation:
+    matrix = np.copy(relation.matrix)
+    n = matrix.shape[0]
+    for i in range(n):
+        for j in range(n):
+            if matrix[i][j]:
+                matrix[j][i] = True
+    return BinaryRelation(matrix)
+
+
+def transitive_closure(relation: BinaryRelation) -> BinaryRelation:
+    matrix = np.copy(relation.matrix)
+    n = matrix.shape[0]
+    for _ in range(n):
+        for i in range(n):
+            for j in range(n):
+                for k in range(n):
+                    if matrix[i][k] and matrix[k][j]:
+                        matrix[i][j] = True
+    return BinaryRelation(matrix)
+
+
+def main():
+    n = int(input("Введите размер матрицы: "))
+    l = []
+    print(f"На следующих {n} строках введите матрицу:")
+    for _ in range(n):
+        l.extend(map(int, input().split()))
+    matrix = np.array(l, dtype=np.bool8).reshape(n, n)
+
+    relation = BinaryRelation(matrix)
+    check_reflexivity(relation)
+    check_antireflexivity(relation)
+    check_symmetry(relation)
+    check_antisymmetry(relation)
+    check_transitivity(relation)
+
+    print("Указанное бинарное отношение обладает следующими свойствами:")
+    if relation.reflexive: print("- Рефлексивность;")
+    if relation.antireflexive: print("- Антирефлексивность;")
+    if relation.symmetric: print("- Симметричность;")
+    if relation.antisymmetric: print("- Антисимметричность;")
+    if relation.transitive: print("- Транзитивность.")
+
+    classes = []
+    if is_equivalence(relation): classes.append("эквивалентностью")
+    if is_quasiorder(relation): classes.append("квазипорядком")
+    if is_partial_order(relation): classes.append("частичным порядком")
+    if is_strict_order(relation): classes.append("строгим порядком")
+    if classes:
+        print(f"Отношение является {', '.join(classes)}")
+    else:
+        print("Отношение не относится ни к какому особому виду")
+    
+    print("Рефлексивное замыкание:")
+    print(np.array(reflexive_closure(relation).matrix, dtype=np.int8))
+    print("Симметричное замыкание:")
+    print(np.array(symmetric_closure(relation).matrix, dtype=np.int8))
+    print("Транзитивное замыкание:")
+    print(np.array(transitive_closure(relation).matrix, dtype=np.int8))
+    print("Эквивалентное замыкание:")
+    eq = transitive_closure(symmetric_closure(reflexive_closure(relation)))
+    print(np.array(eq.matrix, dtype=np.int8))
+
+
+if __name__ == "__main__":
+    main()