портирован на Java / jgrapht, образец питона на эту страницу с @Michael Clerx:
import java.util.ArrayList;
import java.util.List;
import java.util.Set;
import org.jgrapht.DirectedGraph;
public class TransitiveReduction<V, E> {
final private List<V> vertices;
final private int [][] pathMatrix;
private final DirectedGraph<V, E> graph;
public TransitiveReduction(DirectedGraph<V, E> graph) {
super();
this.graph = graph;
this.vertices = new ArrayList<V>(graph.vertexSet());
int n = vertices.size();
int[][] original = new int[n][n];
// initialize matrix with zeros
// --> 0 is the default value for int arrays
// initialize matrix with edges
Set<E> edges = graph.edgeSet();
for (E edge : edges) {
V v1 = graph.getEdgeSource(edge);
V v2 = graph.getEdgeTarget(edge);
int v_1 = vertices.indexOf(v1);
int v_2 = vertices.indexOf(v2);
original[v_1][v_2] = 1;
}
this.pathMatrix = original;
transformToPathMatrix(this.pathMatrix);
}
// (package visible for unit testing)
static void transformToPathMatrix(int[][] matrix) {
// compute path matrix
for (int i = 0; i < matrix.length; i++) {
for (int j = 0; j < matrix.length; j++) {
if (i == j) {
continue;
}
if (matrix[j][i] > 0 ){
for (int k = 0; k < matrix.length; k++) {
if (matrix[j][k] == 0) {
matrix[j][k] = matrix[i][k];
}
}
}
}
}
}
// (package visible for unit testing)
static void transitiveReduction(int[][] pathMatrix) {
// transitively reduce
for (int j = 0; j < pathMatrix.length; j++) {
for (int i = 0; i < pathMatrix.length; i++) {
if (pathMatrix[i][j] > 0){
for (int k = 0; k < pathMatrix.length; k++) {
if (pathMatrix[j][k] > 0) {
pathMatrix[i][k] = 0;
}
}
}
}
}
}
public void reduce() {
int n = pathMatrix.length;
int[][] transitivelyReducedMatrix = new int[n][n];
System.arraycopy(pathMatrix, 0, transitivelyReducedMatrix, 0, pathMatrix.length);
transitiveReduction(transitivelyReducedMatrix);
for (int i = 0; i <n; i++) {
for (int j = 0; j < n; j++) {
if (transitivelyReducedMatrix[i][j] == 0) {
// System.out.println("removing "+vertices.get(i)+" -> "+vertices.get(j));
graph.removeEdge(graph.getEdge(vertices.get(i), vertices.get(j)));
}
}
}
}
}
модульный тест :
import java.util.Arrays;
import org.junit.Assert;
import org.junit.Test;
public class TransitiveReductionTest {
@Test
public void test() {
int[][] matrix = new int[][] {
{0, 1, 1, 0, 0},
{0, 0, 0, 0, 0},
{0, 0, 0, 1, 1},
{0, 0, 0, 0, 1},
{0, 1, 0, 0, 0}
};
int[][] expected_path_matrix = new int[][] {
{0, 1, 1, 1, 1},
{0, 0, 0, 0, 0},
{0, 1, 0, 1, 1},
{0, 1, 0, 0, 1},
{0, 1, 0, 0, 0}
};
int[][] expected_transitively_reduced_matrix = new int[][] {
{0, 0, 1, 0, 0},
{0, 0, 0, 0, 0},
{0, 0, 0, 1, 0},
{0, 0, 0, 0, 1},
{0, 1, 0, 0, 0}
};
System.out.println(Arrays.deepToString(matrix) + " original matrix");
int n = matrix.length;
// calc path matrix
int[][] path_matrix = new int[n][n];
{
System.arraycopy(matrix, 0, path_matrix, 0, matrix.length);
TransitiveReduction.transformToPathMatrix(path_matrix);
System.out.println(Arrays.deepToString(path_matrix) + " path matrix");
Assert.assertArrayEquals(expected_path_matrix, path_matrix);
}
// calc transitive reduction
{
int[][] transitively_reduced_matrix = new int[n][n];
System.arraycopy(path_matrix, 0, transitively_reduced_matrix, 0, matrix.length);
TransitiveReduction.transitiveReduction(transitively_reduced_matrix);
System.out.println(Arrays.deepToString(transitively_reduced_matrix) + " transitive reduction");
Assert.assertArrayEquals(expected_transitively_reduced_matrix, transitively_reduced_matrix);
}
}
}
тест Ouput
[[0, 1, 1, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 1, 1], [0, 0, 0, 0, 1], [0, 1, 0, 0, 0]] original matrix
[[0, 1, 1, 1, 1], [0, 0, 0, 0, 0], [0, 1, 0, 1, 1], [0, 1, 0, 0, 1], [0, 1, 0, 0, 0]] path matrix
[[0, 0, 1, 0, 0], [0, 0, 0, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1], [0, 1, 0, 0, 0]] transitive reduction
