public void DirectedAndWeightedGraphShortestPathsCheck()
{
var vertices = new int[] { 1, 2, 3, 4, 5, 6, 7, 8, 9 };
var graph = new DirectedWeightedALGraph <int, int>();
graph.AddVertices(vertices);
// Graph is:
// 1 -> 3, 4
// 1 <- 2
// 2 -> 1, 5
// 2 <- 3, 5, 6
// 3 -> 2, 6
// 3 <- 1, 4
// 4 -> 3, 6
// 4 <- 1, 7
// 5 -> 2, 7, 8
// 5 <- 2, 8
// 6 -> 2
// 6 <- 3, 4
// 7 -> 4
// 7 <- 5, 8
// 8 -> 5, 7
// 8 <- 5
// 9 ->
// 9 <-
// With each edge having a weight of the absolute value of the difference of the vertices
graph.AddEdge(1, 3, 2);
graph.AddEdge(1, 4, 3);
graph.AddEdge(2, 1, 1);
graph.AddEdge(2, 5, 3);
graph.AddEdge(3, 2, 1);
graph.AddEdge(3, 6, 3);
graph.AddEdge(4, 3, 1);
graph.AddEdge(4, 6, 2);
graph.AddEdge(5, 2, 3);
graph.AddEdge(5, 7, 2);
graph.AddEdge(5, 8, 3);
graph.AddEdge(6, 2, 4);
graph.AddEdge(7, 4, 3);
graph.AddEdge(8, 5, 3);
graph.AddEdge(8, 7, 1);
// Expected shortest paths for vertex 1
// 1 to 2 : 1 -> 3 -> 2
// 1 to 3 : 1 -> 3
// 1 to 4 : 1 -> 4
// 1 to 5 : 1 -> 3 -> 2 -> 5
// 1 to 6 : 1 -> 3 -> 6
// 1 to 7 : 1 -> 3 -> 2 -> 5 -> 7
// 1 to 8 : 1 -> 3 -> 2 -> 5 -> 8
// 1 to 9 : no path
var expectedPaths = new int[7][]
{
new int[] { 1, 3, 2 },
new int[] { 1, 3 },
new int[] { 1, 4 },
new int[] { 1, 3, 2, 5 },
new int[] { 1, 3, 6 },
new int[] { 1, 3, 2, 5, 7 },
new int[] { 1, 3, 2, 5, 8 }
};
var expectedEdgesWeights = new int[7][]
{
new int[] { 2, 1 },
new int[] { 2 },
new int[] { 3 },
new int[] { 2, 1, 3 },
new int[] { 2, 3 },
new int[] { 2, 1, 3, 2 },
new int[] { 2, 1, 3, 3 }
};
var paths = graph.BellmanFordShortestPaths(1);
for (int i = 0; i < 7; i++)
{
var curPath = paths.VerticesPathTo(i + 2);
for (int j = 0; j < curPath.Count; j++)
{
if (expectedPaths[i][j] != curPath[j])
{
Assert.Fail();
}
}
var curEdgesPath = paths.EdgesPathTo(i + 2);
for (int j = 0; j < curEdgesPath.Count; j++)
{
if (expectedEdgesWeights[i][j] != curEdgesPath[j].Weight)
{
Assert.Fail();
}
}
}
Assert.IsFalse(paths.HasPathTo(9));
// Expected shortest paths for vertex 8
// 8 to 1 : 8 -> 5 -> 2 -> 1
// 8 to 2 : 8 -> 5 -> 2
// 8 to 3 : 8 -> 7 -> 4 -> 3
// 8 to 4 : 8 -> 7 -> 4
// 8 to 5 : 8 -> 5
// 8 to 6 : 8 -> 7 -> 4 -> 6
// 8 to 7 : 8 -> 7
// 8 to 9 : no path
expectedPaths = new int[7][]
{
new int[] { 8, 5, 2, 1 },
new int[] { 8, 5, 2 },
new int[] { 8, 7, 4, 3 },
new int[] { 8, 7, 4 },
new int[] { 8, 5 },
new int[] { 8, 7, 4, 6 },
new int[] { 8, 7 }
};
expectedEdgesWeights = new int[7][]
{
new int[] { 3, 3, 1 },
new int[] { 3, 3 },
new int[] { 1, 3, 1 },
new int[] { 1, 3 },
new int[] { 3 },
new int[] { 1, 3, 2 },
new int[] { 1 }
};
paths = graph.BellmanFordShortestPaths(8);
for (int i = 0; i < 7; i++)
{
var curPath = paths.VerticesPathTo(i + 1);
for (int j = 0; j < curPath.Count; j++)
{
if (expectedPaths[i][j] != curPath[j])
{
Assert.Fail();
}
}
var curEdgesPath = paths.EdgesPathTo(i + 1);
for (int j = 0; j < curEdgesPath.Count; j++)
{
if (expectedEdgesWeights[i][j] != curEdgesPath[j].Weight)
{
Assert.Fail();
}
}
}
Assert.IsFalse(paths.HasPathTo(9));
}