Point Q_matrix::getOptimalPoint(Edge *e)
{
if (IS_VISITED(e->v1)) return (*(e->v1)); // Check for sharp vertices
if (IS_VISITED(e->v2)) return (*(e->v2));
Point n;
if (getMinimizer(&(n.x), &(n.y), &(n.z))) return n;
// If not invertible, choose the best among mid, v1 and v2
return bestAmongMidAndEndpoints(e);
}
Point Q_matrix::bestAmongMidAndEndpoints(Edge *e)
{
if (IS_VISITED(e->v1)) return (*(e->v1)); // Check for sharp vertices
if (IS_VISITED(e->v2)) return (*(e->v2));
Point mp = e->getMidPoint(); // Get Edge Midpoint
double erm = getError(&mp, e); // Error at midpoint
double er1 = getError(e->v1, e); // Error at v1
double er2 = getError(e->v2, e); // Error at v2
if (erm <= er1 && erm <= er2) return mp;
if (er1 <= erm && er1 <= er2) return (*(e->v1));
return (*(e->v2));
}
int directed_MST(int root)
{
int i, j, k;
int has_cycle;
int weight, weight_contracted = 0;
int in_edge_weight[MAX_N];
int in_edge_src[MAX_N];
int v_in_cycle[MAX_N];
int contracted[MAX_N];
memset(contracted, 0, sizeof(contracted));
for (;;)
{
for (i = 0; i < n; i++)
{
in_edge_weight[i] = 0x7fffffff;
in_edge_src[i] = -1;
}
/* STEP 1 */
for (i = 0; i < m; i++)
{
/* The edges should be ingored, but condition 1 & 2 are removed in the other place */
/* 1. no edge to itself: e[i].s != e[i].d */
/* 2. no edge to root: e[i].d != root */
/* 3. has the lowest weight in all in-edge */
if (e[i].w < in_edge_weight[e[i].d])
{
in_edge_src[e[i].d] = e[i].s;
in_edge_weight[e[i].d] = e[i].w;
}
}
/* STEP 2 */
weight = 0;
has_cycle = 0;
for (i = 0; i < n; i++)
{
if (contracted[i] == 1)
continue;
if (in_edge_src[i] == -1 && i != root)
{
return -1; /* no MST */
}
if (in_edge_src[i] != -1)
weight += in_edge_weight[i];
/* if three is a cycle in the graph and v[i] is one of vertex connected to the cycle,
the final j won't be -1. */
RESET_VISITED();
for (j = i;
j != -1 && !IS_VISITED(j);
j = in_edge_src[j])
{
SET_VISITED(j);
}
if (j != -1 && IS_VISITED(j))
{
has_cycle = 1;
for (k = 0; k < n; k++)
v_in_cycle[k] = -1;
v_in_cycle[j] = j;
weight_contracted += in_edge_weight[j];
for (k = in_edge_src[j]; k != j; k = in_edge_src[k])
{
v_in_cycle[k] = j;
contracted[k] = 1;
weight_contracted += in_edge_weight[k];
}
break;
}
}
if (has_cycle == 0)
{
break;
}
/* STEP 3:
all vertexs in the cycle are contracted in to one vertex
For an edge e not in the cycle: the new weight will be updated to 'e.w - in_edge_weight[e.d]'.
It means if the edge is add to the MST, the edge from in_edge_src[e.d] to e.d would be removed.
*/
for (i = 0; i < m ; i++)
{
if (v_in_cycle[e[i].d] >= 0)
{
e[i].w -= in_edge_weight[e[i].d];
e[i].d = v_in_cycle[e[i].d];
}
if (v_in_cycle[e[i].s] >= 0)
{
e[i].s = v_in_cycle[e[i].s];
}
/* an edge to itself would be removed */
if (e[i].s == e[i].d)
{
e[i--] = e[--m];
}
}
}
return weight + weight_contracted;
}