finale Version des Vorlesungsskripts - ZIB

5 Bäume und Wege
/**************************************************************************
* *
* Prim’s Algorithm to Determine a Minimum Spanning Tree *
* in a Complete Graph With n Nodes *
* *
* (G. Reinelt) *
* *
*------------------------------------------------------------------------*
* *
* Input: *
* *
* There are four ways to input the edge weights of the complete *
* graph K_n. In any case we assume that first two numbers are given: *
* *
* n = number of nodes *
* mode = input mode *
* *
* Mode specifies the input mode for the edge weights. All edge weights *
* have to be integers. *
* *
* Mode=0 : The full matrix of edge weights is given. The entries are *
* stored row by row. The lower diagonal and the diagonal *
* entries are ignored. *
* *
* Mode=1 : The matrix of edge weights is given as upper triangular *
* matrix. The entries are stored row by row. *
* *
* Mode=2 : The matrix of edge weights is given as lower triangular *
* matrix. The entries are stored row by row. *
* *
* Mode=3 : The edge weights are given in an edge list of the *
* form: 1st endnode, 2nd endnode, edge weight. Edges which *
* are not present are assumed to have ’infinite’ weight. *
* The input is ended if the first endnode is less than 1. *
* *
**************************************************************************/
CONST max_n = 100; { maximum number of nodes }
max_n2 = 4950; { max_n choose 2 = number of edges of K_n}
{ to process larger graphs only max_n and
max-n2 have to be changed }
inf = maxint; { infinity }
TYPE arrn2 = ARRAY[1..max_n2] OF integer;
arrn = ARRAY[1..max_n] OF integer;
VAR i, j,
mode, { input mode of weights:
0 : full matrix
1 : upper triangular matrix
2 : lower triangular matrix
3 : edge list }
min, { minimum distance }
ind, { index of entering edge }
newnode, { entering tree node }
t1, t2, { entering tree edge }
outnodes, { number of nodes not in tree }
c,
weight, { weight of tree }
nchoose2,
n : integer; { number of nodes }
w : arrn2; { vector of weights }
dope, { dope vector for index calculations }
dist, { shortest distances to non-tree nodes }
in_t, { in-tree node of shortest edge }
out_t : arrn; { out-tree node of shortest edge }
{ minimum tree is also stored in in_t & out_t}
connected : boolean; { true input graph is connected? }
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