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Two more algorithms

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This commit is contained in:
Guilherme Werner
2023-06-19 18:51:24 -03:00
parent d040c33e65
commit 7234d53258
4 changed files with 442 additions and 19 deletions
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333
Source/Graph.cpp
View File

@ -54,7 +54,7 @@ void Graph::Print()
} }
} }
void Graph::TransitiveClosure() void Graph::TransitiveReduction1()
{ {
int m1[length][length]; int m1[length][length];
int m2[length][length]; int m2[length][length];
@ -182,3 +182,334 @@ void Graph::TransitiveClosure()
cout << endl; cout << endl;
} }
} }
void Graph::TransitiveReduction2()
{
int closure[this->length][this->length];
for (auto i = 0; i < this->length; i++)
{
for (auto j = 0; j < this->length; j++)
{
closure[i][j] = 0;
}
}
for (auto i = 0; i < this->length; i++)
{
for (auto j = this->adj[i].begin(); j != this->adj[i].end(); j++)
{
closure[i][*j] = 1;
}
}
cout << "\nG1:" << endl;
for (int i = 0; i < this->length; i++)
{
for (int j = 0; j < this->length; j++)
{
cout << closure[i][j] << " ";
}
cout << endl;
}
for (auto k = 0; k < this->length; k++)
{
for (auto i = 0; i < this->length; i++)
{
for (auto j = 0; j < this->length; j++)
{
if (i == j)
{
closure[i][j] = 1;
}
else
{
closure[i][j] = closure[i][j] || (closure[i][k] && closure[k][j]);
}
}
}
}
cout << "\nTC:" << endl;
for (int i = 0; i < this->length; i++)
{
for (int j = 0; j < this->length; j++)
{
if (i == j)
{
cout << "1 ";
}
else
{
cout << closure[i][j] << " ";
}
}
cout << endl;
}
int reduction[this->length][this->length];
for (auto i = 0; i < this->length; i++)
{
for (auto j = 0; j < this->length; j++)
{
reduction[i][j] = 0;
}
}
for (auto i = 0; i < this->length; i++)
{
for (auto j = adj[i].begin(); j != adj[i].end(); j++)
{
reduction[i][*j] = 1;
}
}
for (auto j = 0; j < this->length; j++)
{
for (auto i = 0; i < this->length; i++)
{
if (reduction[i][j] == 1)
{
for (auto k = 0; k < this->length; k++)
{
if (reduction[j][k] == 1)
{
reduction[i][k] = 0;
}
}
}
}
}
cout << "\nG2:" << endl;
for (int i = 0; i < this->length; i++)
{
for (int j = 0; j < this->length; j++)
{
cout << reduction[i][j] << " ";
}
cout << endl;
}
for (auto k = 0; k < this->length; k++)
{
for (auto i = 0; i < this->length; i++)
{
for (auto j = 0; j < this->length; j++)
{
if (i == j)
{
reduction[i][j] = 1;
}
else
{
reduction[i][j] = reduction[i][j] || (reduction[i][k] && reduction[k][j]);
}
}
}
}
cout << "\nTC:" << endl;
for (int i = 0; i < this->length; i++)
{
for (int j = 0; j < this->length; j++)
{
if (i == j)
{
cout << "1 ";
}
else
{
cout << reduction[i][j] << " ";
}
}
cout << endl;
}
}
void Graph::TransitiveReduction3()
{
int closure[this->length][this->length];
for (auto i = 0; i < this->length; i++)
{
for (auto j = 0; j < this->length; j++)
{
closure[i][j] = 0;
}
}
for (auto i = 0; i < this->length; i++)
{
for (auto j = this->adj[i].begin(); j != this->adj[i].end(); j++)
{
closure[i][*j] = 1;
}
}
cout << "\nG1:" << endl;
for (int i = 0; i < this->length; i++)
{
for (int j = 0; j < this->length; j++)
{
cout << closure[i][j] << " ";
}
cout << endl;
}
for (auto k = 0; k < this->length; k++)
{
for (auto i = 0; i < this->length; i++)
{
for (auto j = 0; j < this->length; j++)
{
if (i == j)
{
closure[i][j] = 1;
}
else
{
closure[i][j] = closure[i][j] || (closure[i][k] && closure[k][j]);
}
}
}
}
cout << "\nTC:" << endl;
for (int i = 0; i < this->length; i++)
{
for (int j = 0; j < this->length; j++)
{
if (i == j)
{
cout << "1 ";
}
else
{
cout << closure[i][j] << " ";
}
}
cout << endl;
}
int reduction[this->length][this->length];
for (auto i = 0; i < this->length; i++)
{
for (auto j = 0; j < this->length; j++)
{
reduction[i][j] = 0;
}
}
for (auto i = 0; i < this->length; i++)
{
for (auto j = adj[i].begin(); j != adj[i].end(); j++)
{
reduction[i][*j] = 1;
}
}
for (int v = 0; v < this->length; ++v)
{
std::vector<std::vector<int>> paths;
// Encontra todos os paths possíveis de v para outros vértices
for (int j = 2; j <= this->length; ++j)
{
std::vector<int> path(j);
for (int i = 0; i < j; ++i)
{
path[i] = i;
}
do
{
if (path[0] == v)
{
paths.push_back(path);
}
} while (std::next_permutation(path.begin(), path.end()));
}
// Verifica se os paths são transitivos
for (const auto &path : paths)
{
for (int i = 0; i < path.size() - 2; ++i)
{
if (reduction[path[i]][path[i + 1]] == 1 && reduction[path[i + 1]][path[i + 2]] == 1)
{
reduction[path[i]][path[i + 2]] = 0;
}
}
}
}
cout << "\nG2:" << endl;
for (int i = 0; i < this->length; i++)
{
for (int j = 0; j < this->length; j++)
{
cout << reduction[i][j] << " ";
}
cout << endl;
}
for (auto k = 0; k < this->length; k++)
{
for (auto i = 0; i < this->length; i++)
{
for (auto j = 0; j < this->length; j++)
{
if (i == j)
{
reduction[i][j] = 1;
}
else
{
reduction[i][j] = reduction[i][j] || (reduction[i][k] && reduction[k][j]);
}
}
}
}
cout << "\nTC:" << endl;
for (int i = 0; i < this->length; i++)
{
for (int j = 0; j < this->length; j++)
{
if (i == j)
{
cout << "1 ";
}
else
{
cout << reduction[i][j] << " ";
}
}
cout << endl;
}
}

4
Source/Graph.h
View File

@ -36,6 +36,8 @@ public:
void InsertD(int u, int v); void InsertD(int u, int v);
void Remove(int u, int v); void Remove(int u, int v);
void RemoveD(int u, int v); void RemoveD(int u, int v);
void TransitiveClosure(); void TransitiveReduction1();
void TransitiveReduction2();
void TransitiveReduction3();
Graph *Clone(); Graph *Clone();
}; };

23
Source/Main.cpp
View File

@ -16,25 +16,14 @@ int main()
g1->InsertD(4, 0); g1->InsertD(4, 0);
g1->InsertD(4, 2); g1->InsertD(4, 2);
cout << "-- TRANSITIVE CLOSURE --" << endl; cout << "-- MATRIX --" << endl;
g1->TransitiveClosure(); g1->TransitiveReduction1();
// cout << "M1:" << endl; cout << "\n-- LOOPS --" << endl;
// g1->PrintIncidenceMatrix(); g1->TransitiveReduction2();
// g1->PrintAdjacencyMatrix();
// auto m1 = g1->GetIncidenceMatrix();
// Graph *g2 = g1->ToTransitiveClosure(); cout << "\n-- PERMUTATION --" << endl;
// cout << "M2:" << endl; g1->TransitiveReduction3();
// g2->PrintIncidenceMatrix();
// g2->PrintAdjacencyMatrix();
// auto m2 = g2->GetIncidenceMatrix();
// auto m3 = Graph::MultiplyIncidenceMatrix(m1, m2);
// Graph *g3 = new Graph(m3);
// cout << "M3:" << endl;
// g3->PrintIncidenceMatrix();
// g3->PrintAdjacencyMatrix();
return 0; return 0;
} }

101
Tests.txt Normal file
View File

@ -0,0 +1,101 @@
-- MATRIX --
M1:
0 1 1 1 0 0
0 0 1 1 0 1
0 0 0 1 0 0
0 0 0 0 0 1
1 0 1 0 0 0
0 0 0 0 0 0
M2:
1 1 1 1 0 1
0 1 1 1 0 1
0 0 1 1 0 1
0 0 0 1 0 1
1 1 1 1 1 1
0 0 0 0 0 1
M3:
0 1 2 3 0 3
0 0 1 2 0 3
0 0 0 1 0 1
0 0 0 0 0 1
1 1 2 2 0 2
0 0 0 0 0 0
Gt:
0 1 0 0 0 0
0 0 1 0 0 0
0 0 0 1 0 0
0 0 0 0 0 1
1 0 0 0 0 0
0 0 0 0 0 0
-- LOOPS --
G1:
0 1 1 1 0 0
0 0 1 1 0 1
0 0 0 1 0 0
0 0 0 0 0 1
1 0 1 0 0 0
0 0 0 0 0 0
TC:
1 1 1 1 0 1
0 1 1 1 0 1
0 0 1 1 0 1
0 0 0 1 0 1
1 1 1 1 1 1
0 0 0 0 0 1
G2:
0 1 0 0 0 0
0 0 1 0 0 1
0 0 0 1 0 0
0 0 0 0 0 1
1 0 0 0 0 0
0 0 0 0 0 0
TC:
1 1 1 1 0 1
0 1 1 1 0 1
0 0 1 1 0 1
0 0 0 1 0 1
1 1 1 1 1 1
0 0 0 0 0 1
-- PERMUTATION --
G1:
0 1 1 1 0 0
0 0 1 1 0 1
0 0 0 1 0 0
0 0 0 0 0 1
1 0 1 0 0 0
0 0 0 0 0 0
TC:
1 1 1 1 0 1
0 1 1 1 0 1
0 0 1 1 0 1
0 0 0 1 0 1
1 1 1 1 1 1
0 0 0 0 0 1
G2:
0 1 0 1 0 0
0 0 1 0 0 1
0 0 0 1 0 0
0 0 0 0 0 1
1 0 1 0 0 0
0 0 0 0 0 0
TC:
1 1 1 1 0 1
0 1 1 1 0 1
0 0 1 1 0 1
0 0 0 1 0 1
1 1 1 1 1 1
0 0 0 0 0 1