static bool AllKnownOut(const Tree &tree, EdgeInfo **EIs, unsigned uNodeFrom,
unsigned uNodeTo)
{
const unsigned uNeighborCount = tree.GetNeighborCount(uNodeTo);
for (unsigned uSub = 0; uSub < uNeighborCount; ++uSub)
{
unsigned uNeighborIndex = tree.GetNeighbor(uNodeTo, uSub);
if (uNeighborIndex == uNodeFrom)
continue;
if (!EIs[uNodeTo][uSub].m_bSet)
return false;
}
return true;
}
void ApplyMinEdgeLength(Tree &tree, double dMinEdgeLength)
{
const unsigned uNodeCount = tree.GetNodeCount();
for (unsigned uNodeIndex = 0; uNodeIndex < uNodeCount; ++uNodeIndex)
{
const unsigned uNeighborCount = tree.GetNeighborCount(uNodeIndex);
for (unsigned n = 0; n < uNeighborCount; ++n)
{
const unsigned uNeighborNodeIndex = tree.GetNeighbor(uNodeIndex, n);
if (!tree.HasEdgeLength(uNodeIndex, uNeighborNodeIndex))
continue;
if (tree.GetEdgeLength(uNodeIndex, uNeighborNodeIndex) < dMinEdgeLength)
tree.SetEdgeLength(uNodeIndex, uNeighborNodeIndex, dMinEdgeLength);
}
}
}
static void CalcInfo(const Tree &tree, unsigned uNode1, unsigned uNode2, EdgeInfo **EIs)
{
const unsigned uNeighborIndex = tree.GetNeighborSubscript(uNode1, uNode2);
EdgeInfo &EI = EIs[uNode1][uNeighborIndex];
EI.m_uNode1 = uNode1;
EI.m_uNode2 = uNode2;
if (tree.IsLeaf(uNode2))
{
EI.m_dMaxDistToLeaf = 0;
EI.m_dTotalDistToLeaves = 0;
EI.m_uMaxStep = NULL_NEIGHBOR;
EI.m_uMostDistantLeaf = uNode2;
EI.m_uLeafCount = 1;
EI.m_bSet = true;
return;
}
double dMaxDistToLeaf = -1e29;
double dTotalDistToLeaves = 0.0;
unsigned uLeafCount = 0;
unsigned uMostDistantLeaf = NULL_NEIGHBOR;
unsigned uMaxStep = NULL_NEIGHBOR;
const unsigned uNeighborCount = tree.GetNeighborCount(uNode2);
for (unsigned uSub = 0; uSub < uNeighborCount; ++uSub)
{
const unsigned uNode3 = tree.GetNeighbor(uNode2, uSub);
if (uNode3 == uNode1)
continue;
const EdgeInfo &EINext = EIs[uNode2][uSub];
if (!EINext.m_bSet)
Quit("CalcInfo: internal error, dist %u->%u not known",
uNode2, uNode3);
uLeafCount += EINext.m_uLeafCount;
const double dEdgeLength = tree.GetEdgeLength(uNode2, uNode3);
const double dTotalDist = EINext.m_dTotalDistToLeaves +
EINext.m_uLeafCount*dEdgeLength;
dTotalDistToLeaves += dTotalDist;
const double dDist = EINext.m_dMaxDistToLeaf + dEdgeLength;
if (dDist > dMaxDistToLeaf)
{
dMaxDistToLeaf = dDist;
uMostDistantLeaf = EINext.m_uMostDistantLeaf;
uMaxStep = uNode3;
}
}
if (NULL_NEIGHBOR == uMaxStep || NULL_NEIGHBOR == uMostDistantLeaf ||
0 == uLeafCount)
Quit("CalcInfo: internal error 2");
const double dThisDist = tree.GetEdgeLength(uNode1, uNode2);
EI.m_dMaxDistToLeaf = dMaxDistToLeaf;
EI.m_dTotalDistToLeaves = dTotalDistToLeaves;
EI.m_uMaxStep = uMaxStep;
EI.m_uMostDistantLeaf = uMostDistantLeaf;
EI.m_uLeafCount = uLeafCount;
EI.m_bSet = true;
}
static void RootByMinAvgLeafDist(const Tree &tree, EdgeInfo **EIs,
unsigned *ptruNode1, unsigned *ptruNode2,
double *ptrdLength1, double *ptrdLength2)
{
const unsigned uNodeCount = tree.GetNodeCount();
const unsigned uLeafCount = tree.GetLeafCount();
unsigned uNode1 = NULL_NEIGHBOR;
unsigned uNode2 = NULL_NEIGHBOR;
double dMinHeight = VERY_LARGE_DOUBLE;
double dBestLength1 = VERY_LARGE_DOUBLE;
double dBestLength2 = VERY_LARGE_DOUBLE;
for (unsigned uNodeIndex = 0; uNodeIndex < uNodeCount; ++uNodeIndex)
{
const unsigned uNeighborCount = tree.GetNeighborCount(uNodeIndex);
for (unsigned uSub = 0; uSub < uNeighborCount; ++uSub)
{
const unsigned uNeighborIndex = tree.GetNeighbor(uNodeIndex, uSub);
// Avoid visiting same edge a second time in reversed order.
if (uNeighborIndex < uNodeIndex)
continue;
const unsigned uSubRev = tree.GetNeighborSubscript(uNeighborIndex, uNodeIndex);
if (NULL_NEIGHBOR == uSubRev)
Quit("RootByMinAvgLeafDist, internal error 1");
// Get info for edges Node1->Node2 and Node2->Node1 (reversed)
const EdgeInfo &EI = EIs[uNodeIndex][uSub];
const EdgeInfo &EIRev = EIs[uNeighborIndex][uSubRev];
if (EI.m_uNode1 != uNodeIndex || EI.m_uNode2 != uNeighborIndex ||
EIRev.m_uNode1 != uNeighborIndex || EIRev.m_uNode2 != uNodeIndex)
Quit("RootByMinAvgLeafDist, internal error 2");
if (!EI.m_bSet)
Quit("RootByMinAvgLeafDist, internal error 3");
if (uLeafCount != EI.m_uLeafCount + EIRev.m_uLeafCount)
Quit("RootByMinAvgLeafDist, internal error 4");
const double dEdgeLength = tree.GetEdgeLength(uNodeIndex, uNeighborIndex);
if (dEdgeLength != tree.GetEdgeLength(uNeighborIndex, uNodeIndex))
Quit("RootByMinAvgLeafDist, internal error 5");
// Consider point p on edge 12 in tree (1=Node, 2=Neighbor).
//
// ----- ----
// | |
// 1----p--2
// | |
// ----- ----
//
// Define:
// ADLp = average distance to leaves to left of point p.
// ADRp = average distance to leaves to right of point p.
// L = edge length = distance 12
// x = distance 1p
// So distance p2 = L - x.
// Average distance from p to leaves on left of p is:
// ADLp = ADL1 + x
// Average distance from p to leaves on right of p is:
// ADRp = ADR2 + (L - x)
// To be a root, we require these two distances to be equal,
// ADLp = ADRp
// ADL1 + x = ADR2 + (L - x)
// Solving for x,
// x = (ADR2 - ADL1 + L)/2
// If 0 <= x <= L, we can place the root on edge 12.
const double ADL1 = EI.m_dTotalDistToLeaves / EI.m_uLeafCount;
const double ADR2 = EIRev.m_dTotalDistToLeaves / EIRev.m_uLeafCount;
const double x = (ADR2 - ADL1 + dEdgeLength)/2.0;
if (x >= 0 && x <= dEdgeLength)
{
const double dLength1 = x;
const double dLength2 = dEdgeLength - x;
const double dHeight1 = EI.m_dMaxDistToLeaf + dLength1;
const double dHeight2 = EIRev.m_dMaxDistToLeaf + dLength2;
const double dHeight = dHeight1 >= dHeight2 ? dHeight1 : dHeight2;
#if TRACE
Log("Candidate root Node1=%u Node2=%u Height=%g\n",
uNodeIndex, uNeighborIndex, dHeight);
#endif
if (dHeight < dMinHeight)
{
uNode1 = uNodeIndex;
uNode2 = uNeighborIndex;
dBestLength1 = dLength1;
dBestLength2 = dLength2;
dMinHeight = dHeight;
}
}
}
}
if (NULL_NEIGHBOR == uNode1 || NULL_NEIGHBOR == uNode2)
Quit("RootByMinAvgLeafDist, internal error 6");
#if TRACE
Log("Best root Node1=%u Node2=%u Length1=%g Length2=%g Height=%g\n",
uNode1, uNode2, dBestLength1, dBestLength2, dMinHeight);
#endif
*ptruNode1 = uNode1;
*ptruNode2 = uNode2;
*ptrdLength1 = dBestLength1;
*ptrdLength2 = dBestLength2;
}
void FindRoot(const Tree &tree, unsigned *ptruNode1, unsigned *ptruNode2,
double *ptrdLength1, double *ptrdLength2,
ROOT RootMethod)
{
#if TRACE
tree.LogMe();
#endif
if (tree.IsRooted())
Quit("FindRoot: tree already rooted");
const unsigned uNodeCount = tree.GetNodeCount();
const unsigned uLeafCount = tree.GetLeafCount();
if (uNodeCount < 2)
Quit("Root: don't support trees with < 2 edges");
EdgeInfo **EIs = new EdgeInfo *[uNodeCount];
for (unsigned uNodeIndex = 0; uNodeIndex < uNodeCount; ++uNodeIndex)
EIs[uNodeIndex] = new EdgeInfo[3];
EdgeList Edges;
for (unsigned uNodeIndex = 0; uNodeIndex < uNodeCount; ++uNodeIndex)
if (tree.IsLeaf(uNodeIndex))
{
unsigned uParent = tree.GetNeighbor1(uNodeIndex);
Edges.Add(uParent, uNodeIndex);
}
#if TRACE
Log("Edges: ");
Edges.LogMe();
#endif
// Main loop: iterate until all distances known
double dAllMaxDist = -1e20;
unsigned uMaxFrom = NULL_NEIGHBOR;
unsigned uMaxTo = NULL_NEIGHBOR;
for (;;)
{
EdgeList NextEdges;
#if TRACE
Log("\nTop of main loop\n");
Log("Edges: ");
Edges.LogMe();
Log("MDs:\n");
ListEIs(EIs, uNodeCount);
#endif
// For all edges
const unsigned uEdgeCount = Edges.GetCount();
if (0 == uEdgeCount)
break;
for (unsigned n = 0; n < uEdgeCount; ++n)
{
unsigned uNodeFrom;
unsigned uNodeTo;
Edges.GetEdge(n, &uNodeFrom, &uNodeTo);
CalcInfo(tree, uNodeFrom, uNodeTo, EIs);
#if TRACE
Log("Edge %u -> %u\n", uNodeFrom, uNodeTo);
#endif
const unsigned uNeighborCount = tree.GetNeighborCount(uNodeFrom);
for (unsigned i = 0; i < uNeighborCount; ++i)
{
const unsigned uNeighborIndex = tree.GetNeighbor(uNodeFrom, i);
if (!Known(tree, EIs, uNeighborIndex, uNodeFrom) &&
AllKnownOut(tree, EIs, uNeighborIndex, uNodeFrom))
NextEdges.Add(uNeighborIndex, uNodeFrom);
}
}
Edges.Copy(NextEdges);
}
#if TRACE
ListEIs(EIs, uNodeCount);
#endif
switch (RootMethod)
{
case ROOT_MidLongestSpan:
RootByMidLongestSpan(tree, EIs, ptruNode1, ptruNode2,
ptrdLength1, ptrdLength2);
break;
case ROOT_MinAvgLeafDist:
RootByMinAvgLeafDist(tree, EIs, ptruNode1, ptruNode2,
ptrdLength1, ptrdLength2);
break;
default:
Quit("Invalid RootMethod=%d", RootMethod);
}
for (unsigned uNodeIndex = 0; uNodeIndex < uNodeCount; ++uNodeIndex)
delete[] EIs[uNodeIndex];
delete[] EIs;
}
