/*
* computes the sizes of all subtrees of a tree with root r
*/
void SchnyderLayout::subtreeSizes(
EdgeArray<int>& rValues,
int i,
node r,
NodeArray<int>& size)
{
int sum = 0;
for(adjEntry adj : r->adjEdges) {
if (adj->theEdge()->source() == r && rValues[adj->theEdge()] == i) {
node w = adj->twinNode();
subtreeSizes(rValues, i, w, size);
sum += size[w];
}
}
size[r] = sum + 1;
}
static TVector<TVector<size_t>> CalcSubtreeSizesForTree(const TObliviousTrees& forest, size_t treeIdx) {
const int maxDepth = forest.TreeSizes[treeIdx];
TVector<TVector<size_t>> subtreeSizes(maxDepth + 1);
subtreeSizes[maxDepth].resize(size_t(1) << maxDepth);
for (size_t leafIdx = 0; leafIdx < (size_t(1) << maxDepth); ++leafIdx) {
subtreeSizes[maxDepth][leafIdx] = size_t(forest.LeafWeights[treeIdx][leafIdx] + 0.5);
}
for (int depth = maxDepth - 1; depth >= 0; --depth) {
const size_t nodeCount = size_t(1) << depth;
subtreeSizes[depth].resize(nodeCount);
for (size_t nodeIdx = 0; nodeIdx < nodeCount; ++nodeIdx) {
subtreeSizes[depth][nodeIdx] = subtreeSizes[depth + 1][nodeIdx] + subtreeSizes[depth + 1][nodeIdx ^ (1 << depth)];
}
}
return subtreeSizes;
}
void SchnyderLayout::schnyderEmbedding(
GraphCopy& GC,
GridLayout &gridLayout,
adjEntry adjExternal)
{
NodeArray<int> &xcoord = gridLayout.x();
NodeArray<int> &ycoord = gridLayout.y();
node v;
List<node> L; // (un)contraction order
GraphCopy T = GraphCopy(GC); // the realizer tree (reverse direction of edges!!!)
EdgeArray<int> rValues(T); // the realizer values
// choose outer face a,b,c
adjEntry adja;
if (adjExternal != 0) {
edge eG = adjExternal->theEdge();
edge eGC = GC.copy(eG);
adja = (adjExternal == eG->adjSource()) ? eGC->adjSource() : eGC->adjTarget();
}
else {
adja = GC.firstEdge()->adjSource();
}
adjEntry adjb = adja->faceCyclePred();
adjEntry adjc = adjb->faceCyclePred();
node a = adja->theNode();
node b = adjb->theNode();
node c = adjc->theNode();
node a_in_T = T.copy(GC.original(a));
node b_in_T = T.copy(GC.original(b));
node c_in_T = T.copy(GC.original(c));
contract(GC, a, b, c, L);
realizer(GC, L, a, b, c, rValues, T);
NodeArray<int> t1(T);
NodeArray<int> t2(T);
NodeArray<int> val(T, 1);
NodeArray<int> P1(T);
NodeArray<int> P3(T);
NodeArray<int> v1(T);
NodeArray<int> v2(T);
subtreeSizes(rValues, 1, a_in_T, t1);
subtreeSizes(rValues, 2, b_in_T, t2);
prefixSum(rValues, 1, a_in_T, val, P1);
prefixSum(rValues, 3, c_in_T, val, P3);
// now Pi = depth of all nodes in Tree T(i) (depth[root] = 1)
prefixSum(rValues, 2, b_in_T, t1, v1);
// special treatment for a
v1[a_in_T] = t1[a_in_T];
/*
* v1[v] now is the sum of the
* "count of nodes in t1" minus the "subtree size for node x"
* for every node x on a path from b to v in t2
*/
prefixSum(rValues, 3, c_in_T, t1, val);
// special treatment for a
val[a_in_T] = t1[a_in_T];
/*
* val[v] now is the sum of the
* "count of nodes in t1" minus the "subtree size for node x"
* for every node x on a path from c to v in t3
*/
// r1[v]=v1[v]+val[v]-t1[v] is the number of nodes in region 1 from v
forall_nodes(v, T) {
// calc v1'
v1[v] += val[v] - t1[v] - P3[v];
}
