Version 5.0 The LEDA User Manual

6.14 Dynamic Trees ( dynamic trees )
1. Definition
An instance D of the data type dynamic trees is a set of dynamically changing rooted
trees. Each edge is directed towards the root and has a weight. Optionally, user defined
information can be stored at the vertices and at the edges.
Remark Dynamic trees are very similar to the data type tree collection. The main difference
is that the former use edge weights instead of the node weights used by the latter.
#include < LEDA/core/dynamic trees.h >
2. Creation
dynamic trees D;
creates an empty instance D of type dynamic trees.
3. Operations
vertex D.make(void ∗ x = nil)
creates a tree containing a single node v which is returned.
The additional user defined information x is
stored at v.
void∗ D.vertex inf(vertex v) returns the additional user defined information at v.
void∗ D.edge inf(vertex v)
vertex D.parent(vertex v)
returns the additional user defined information at
(v,parent(v)) or nil, if v has no parent.
returns the parent of v in the tree or nil.
vertex D.root(vertex v) returns the root of the tree containing v.
double D.cost(vertex v)
vertex D.mincost(vertex v)
returns the cost of (v,parent(v)).
Precondition: v is not a tree root.
returns vertex w closest to root(v) s.t. (w,parent(w))
has minimal cost on the path v → root(v).
Precondition: v is not a tree root.
void D.update(vertex v, double x)
adds x to each edge on the path v → root(v).
void
D.link(vertex v, vertex w, double x, void ∗ e inf = nil)
links the tree root v (prec.) to the vertex w in a different
tree (prec.). The edge e = (v, w) gets weight
x, and the additional user defined information e i nf is
stored at e.
double D.cut(vertex v)
deletes the edge (v,parent(v)) and returns its weight.
Precondition: v is not a tree root.