public void CutNodeFromTreeIfNotMinimumAndNoGrandparentTest()
{
var heap = new FibonacciHeap <int, int>();
var node1 = heap.Insert(1, 0);
var node2 = heap.Insert(2, 0);
var node3 = heap.Insert(3, 0);
var node4 = heap.Insert(4, 0);
// Extract the minimum, forcing the construction of an order 2 tree which
// is changed to an order 0 and order 1 tree after the minimum is extracted.
//
// 1
// /| 3--2
// 1--2--3--4 -> 3 2 -> |
// | 4
// 4
//
Assert.Equal(heap.ExtractMinimum(), node1);
// Deleting the node should trigger a cut and cascadingCut on the heap.
heap.Delete(node4);
Assert.Equal(heap.Size, 2);
Assert.Equal(heap.ExtractMinimum(), node2);
Assert.Equal(heap.ExtractMinimum(), node3);
Assert.True(heap.IsEmpty);
}
public void LeavesValidTreeOnFlatHeapTest()
{
var heap = new FibonacciHeap <int, int>();
heap.Insert(13, 0);
heap.Insert(26, 0);
heap.Insert(3, 0);
heap.Insert(-6, 0);
heap.Insert(27, 0);
var node6 = heap.Insert(88, 0);
heap.Insert(59, 0);
heap.Insert(-10, 0);
heap.Insert(16, 0);
heap.DecreaseKey(node6, -8);
Assert.Equal(heap.ExtractMinimum().Key, -10);
Assert.Equal(heap.ExtractMinimum().Key, -8);
Assert.Equal(heap.ExtractMinimum().Key, -6);
Assert.Equal(heap.ExtractMinimum().Key, 3);
Assert.Equal(heap.ExtractMinimum().Key, 13);
Assert.Equal(heap.ExtractMinimum().Key, 16);
Assert.Equal(heap.ExtractMinimum().Key, 26);
Assert.Equal(heap.ExtractMinimum().Key, 27);
Assert.Equal(heap.ExtractMinimum().Key, 59);
}
public void Consolidate8NodesIntoWellFormedOrder2TreeTest()
{
var heap = new FibonacciHeap <int, int>();
var node0 = (FibonacciHeap <int, int> .Node)heap.Insert(0, 0);
var node1 = (FibonacciHeap <int, int> .Node)heap.Insert(1, 0);
var node2 = (FibonacciHeap <int, int> .Node)heap.Insert(2, 0);
var node3 = (FibonacciHeap <int, int> .Node)heap.Insert(3, 0);
var node4 = (FibonacciHeap <int, int> .Node)heap.Insert(4, 0);
// Extracting minimum should trigger consolidate.
//
// 1
// /|
// 0--1--2--3--4 -> 3 2
// |
// 4
//
Assert.Equal(heap.ExtractMinimum(), node0);
Assert.Equal(heap.Size, 4);
Assert.True(node1.Parent == null);
Assert.True(node2.Parent == node1);
Assert.True(node3.Parent == node1);
Assert.True(node4.Parent == node3);
Assert.True(node1.Next == node1);
Assert.True(node2.Next == node3);
Assert.True(node3.Next == node2);
Assert.True(node4.Next == node4);
Assert.True(node1.Child == node2);
Assert.True(node2.Child == null);
Assert.True(node3.Child == node4);
Assert.True(node4.Child == null);
}
public void DeleteNoesInFlatHeapTest()
{
var heap = new FibonacciHeap <int, int>();
var node3 = heap.Insert(13, 0);
var node4 = heap.Insert(26, 0);
var node2 = heap.Insert(3, 0);
var node1 = heap.Insert(-6, 0);
var node5 = heap.Insert(27, 0);
Assert.Equal(heap.Size, 5);
heap.Delete(node3);
Assert.Equal(heap.Size, 4);
Assert.Equal(heap.ExtractMinimum(), node1);
Assert.Equal(heap.ExtractMinimum(), node2);
Assert.Equal(heap.ExtractMinimum(), node4);
Assert.Equal(heap.ExtractMinimum(), node5);
Assert.True(heap.IsEmpty);
}
public void LeavesValidTreeOnConsolidatedHeapTest()
{
var heap = new FibonacciHeap <int, int>();
var node0 = (FibonacciHeap <int, int> .Node)heap.Insert(0, 0);
var node1 = (FibonacciHeap <int, int> .Node)heap.Insert(1, 0);
var node2 = (FibonacciHeap <int, int> .Node)heap.Insert(2, 0);
var node3 = (FibonacciHeap <int, int> .Node)heap.Insert(3, 0);
var node4 = (FibonacciHeap <int, int> .Node)heap.Insert(4, 0);
var node5 = (FibonacciHeap <int, int> .Node)heap.Insert(5, 0);
var node6 = (FibonacciHeap <int, int> .Node)heap.Insert(6, 0);
var node7 = (FibonacciHeap <int, int> .Node)heap.Insert(7, 0);
var node8 = (FibonacciHeap <int, int> .Node)heap.Insert(8, 0);
// Extracting minimum should trigger consolidate.
//
// __1
// / /|
// 5 3 2
// 0--1--2--3--4--5--6--7--8 -> /| |
// 7 6 4
// |
// 8
//
Assert.Equal(heap.ExtractMinimum(), node0);
// Decrease node 8 to 0
//
// __1
// / /| __1--0
// 5 3 2 / /|
// /| | -> 5 3 2
// 7 6 4 /| |
// | 7 6 4
// 8
//
heap.DecreaseKey(node8, 0);
Assert.True(node1.Next == node8);
Assert.Equal(heap.Size, 8);
Assert.True(heap.ExtractMinimum() == node8);
Assert.True(heap.ExtractMinimum() == node1);
Assert.True(heap.ExtractMinimum() == node2);
Assert.True(heap.ExtractMinimum() == node3);
Assert.True(heap.ExtractMinimum() == node4);
Assert.True(heap.ExtractMinimum() == node5);
Assert.True(heap.ExtractMinimum() == node6);
Assert.True(heap.ExtractMinimum() == node7);
Assert.True(heap.IsEmpty);
}
public void CutNodeFromTreeIfNotMinimumAndHasGrandparentTest()
{
var heap = new FibonacciHeap <int, int>();
var node0 = heap.Insert(0, 0);
var node1 = heap.Insert(1, 0);
var node2 = heap.Insert(2, 0);
var node3 = heap.Insert(3, 0);
var node4 = heap.Insert(4, 0);
var node5 = heap.Insert(5, 0);
var node6 = heap.Insert(6, 0);
var node7 = heap.Insert(7, 0);
var node8 = heap.Insert(8, 0);
// extractMinimum on 0 should trigger a cut and cascadingCut on the heap.
//
// __1
// / /|
// 5 3 2
// 0--1--2--3--4--5--6--7--8 -> /| |
// 7 6 4
// |
// 8
//
Assert.Equal(heap.ExtractMinimum(), node0);
// Delete node 8
//
// __1
// / /| __1
// 5 3 2 / /|
// /| | -> 5 3 2
// 7 6 4 /| |
// | 7 6 4
// 8
//
heap.Delete(node8);
Assert.Equal(heap.Size, 7);
Assert.Equal(heap.ExtractMinimum(), node1);
Assert.Equal(heap.ExtractMinimum(), node2);
Assert.Equal(heap.ExtractMinimum(), node3);
Assert.Equal(heap.ExtractMinimum(), node4);
Assert.Equal(heap.ExtractMinimum(), node5);
Assert.Equal(heap.ExtractMinimum(), node6);
Assert.Equal(heap.ExtractMinimum(), node7);
Assert.True(heap.IsEmpty);
}
public void Consolidate8NodesIntoWellFormedOrder3TreeTest()
{
var heap = new FibonacciHeap <int, int>();
var node0 = (FibonacciHeap <int, int> .Node)heap.Insert(0, 0);
var node1 = (FibonacciHeap <int, int> .Node)heap.Insert(1, 0);
var node2 = (FibonacciHeap <int, int> .Node)heap.Insert(2, 0);
var node3 = (FibonacciHeap <int, int> .Node)heap.Insert(3, 0);
var node4 = (FibonacciHeap <int, int> .Node)heap.Insert(4, 0);
var node5 = (FibonacciHeap <int, int> .Node)heap.Insert(5, 0);
var node6 = (FibonacciHeap <int, int> .Node)heap.Insert(6, 0);
var node7 = (FibonacciHeap <int, int> .Node)heap.Insert(7, 0);
var node8 = (FibonacciHeap <int, int> .Node)heap.Insert(8, 0);
// Extracting minimum should trigger consolidate.
//
// __1
// / /|
// 5 3 2
// 1--2--3--4--5--6--7--8 -> /| |
// 7 6 4
// |
// 8
//
Assert.Equal(heap.ExtractMinimum(), node0);
Assert.True(node1.Parent == null);
Assert.True(node2.Parent == node1);
Assert.True(node3.Parent == node1);
Assert.True(node4.Parent == node3);
Assert.True(node5.Parent == node1);
Assert.True(node6.Parent == node5);
Assert.True(node7.Parent == node5);
Assert.True(node8.Parent == node7);
Assert.True(node1.Next == node1);
Assert.True(node2.Next == node5);
Assert.True(node3.Next == node2);
Assert.True(node4.Next == node4);
Assert.True(node5.Next == node3);
Assert.True(node6.Next == node7);
Assert.True(node7.Next == node6);
Assert.True(node8.Next == node8);
Assert.True(node1.Child == node2);
Assert.True(node2.Child == null);
Assert.True(node3.Child == node4);
Assert.True(node4.Child == null);
Assert.True(node5.Child == node6);
Assert.True(node6.Child == null);
Assert.True(node7.Child == node8);
Assert.True(node8.Child == null);
}
public void CorrectlyAssignIndirectChildWhenDirectChildIsCutFromParentTest()
{
var heap = new FibonacciHeap <int, int>();
var node0 = (FibonacciHeap <int, int> .Node)heap.Insert(0, 0);
heap.Insert(1, 0);
heap.Insert(2, 0);
heap.Insert(3, 0);
heap.Insert(4, 0);
var node5 = (FibonacciHeap <int, int> .Node)heap.Insert(5, 0);
var node6 = (FibonacciHeap <int, int> .Node)heap.Insert(6, 0);
var node7 = (FibonacciHeap <int, int> .Node)heap.Insert(7, 0);
heap.Insert(8, 0);
// Extracting minimum should trigger consolidate.
//
// __1
// / /|
// 5 3 2
// 0--1--2--3--4--5--6--7--8 -> /| |
// 7 6 4
// |
// 8
//
Assert.Equal(heap.ExtractMinimum(), node0);
// Delete node 6, marking 5
//
// __1 __1
// / /| / /|
// 5 3 2 >5 3 2
// /| | -> / |
// 7 6 4 7 4
// | |
// 8 8
//
heap.Delete(node6);
Assert.True(node5.Child == node7);
}
public void CutNodeFromTreeIfNotMinimumAndHasGrandparentWithMarkedParentTest()
{
var heap = new FibonacciHeap <int, int>();
var node0 = (FibonacciHeap <int, int> .Node)heap.Insert(0, 0);
var node1 = (FibonacciHeap <int, int> .Node)heap.Insert(1, 0);
var node2 = (FibonacciHeap <int, int> .Node)heap.Insert(2, 0);
var node3 = (FibonacciHeap <int, int> .Node)heap.Insert(3, 0);
var node4 = (FibonacciHeap <int, int> .Node)heap.Insert(4, 0);
var node5 = (FibonacciHeap <int, int> .Node)heap.Insert(5, 0);
var node6 = (FibonacciHeap <int, int> .Node)heap.Insert(6, 0);
var node7 = (FibonacciHeap <int, int> .Node)heap.Insert(7, 0);
var node8 = (FibonacciHeap <int, int> .Node)heap.Insert(8, 0);
// Extracting minimum should trigger consolidate.
//
// __1
// / /|
// 5 3 2
// 0--1--2--3--4--5--6--7--8 -> /| |
// 7 6 4
// |
// 8
//
Assert.Equal(heap.ExtractMinimum(), node0);
// Delete node 6, marking 5
//
// __1 __1
// / /| / /|
// 5 3 2 >5 3 2
// /| | -> / |
// 7 6 4 7 4
// | |
// 8 8
//
heap.Delete(node6);
Assert.True(node5.IsMarked);
// Delete node 7, cutting the sub-tree
//
// __1
// / /| 1--5
// >5 3 2 /| |
// / | -> 3 2 8
// 7 4 |
// | 4
// 8
//
heap.Delete(node7);
Assert.True(node5.Next == node1);
Assert.True(node2.Next == node3);
Assert.True(node3.Next == node2);
Assert.Equal(heap.Size, 6);
Assert.True(heap.ExtractMinimum() == node1);
Assert.True(heap.ExtractMinimum() == node2);
Assert.True(heap.ExtractMinimum() == node3);
Assert.True(heap.ExtractMinimum() == node4);
Assert.True(heap.ExtractMinimum() == node5);
Assert.True(heap.ExtractMinimum() == node8);
Assert.True(heap.IsEmpty);
}
