Example Run
| Image | U | possible edges | V \ U | Description |
|---|---|---|---|---|
| {} | {A,B,C,D,E,F,G} | This is our original weighted graph. The numbers near the edges indicate their weight. | ||
| {D} | {D,A} = 5 V {D,B} = 9 {D,E} = 15 {D,F} = 6 |
{A,B,C,E,F,G} | Vertex D has been arbitrarily chosen as a starting point. Vertices A, B, E and F are connected to D through a single edge. A is the vertex nearest to D and will be chosen as the second vertex along with the edge AD. | |
| {A,D} | {D,B} = 9 {D,E} = 15 {D,F} = 6 V {A,B} = 7 |
{B,C,E,F,G} | The next vertex chosen is the vertex nearest to either D or A. B is 9 away from D and 7 away from A, E is 15, and F is 6. F is the smallest distance away, so we highlight the vertex F and the edge DF. | |
| {A,D,F} | {D,B} = 9 {D,E} = 15 {A,B} = 7 V {F,E} = 8 {F,G} = 11 |
{B,C,E,G} | The algorithm carries on as above. Vertex B, which is 7 away from A, is highlighted. | |
| {A,B,D,F} | {B,C} = 8 {B,E} = 7 V {D,B} = 9 cycle {D,E} = 15 {F,E} = 8 {F,G} = 11 |
{C,E,G} | In this case, we can choose between C, E, and G. C is 8 away from B, E is 7 away from B, and G is 11 away from F. E is nearest, so we highlight the vertex E and the edge BE. | |
| {A,B,D,E,F} | {B,C} = 8 {D,B} = 9 cycle {D,E} = 15 cycle {E,C} = 5 V {E,G} = 9 {F,E} = 8 cycle {F,G} = 11 |
{C,G} | Here, the only vertices available are C and G. C is 5 away from E, and G is 9 away from E. C is chosen, so it is highlighted along with the edge EC. | |
| {A,B,C,D,E,F} | {B,C} = 8 cycle {D,B} = 9 cycle {D,E} = 15 cycle {E,G} = 9 V {F,E} = 8 cycle {F,G} = 11 |
{G} | Vertex G is the only remaining vertex. It is 11 away from F, and 9 away from E. E is nearer, so we highlight G and the edge EG. | |
| {A,B,C,D,E,F,G} | {B,C} = 8 cycle {D,B} = 9 cycle {D,E} = 15 cycle {F,E} = 8 cycle {F,G} = 11 cycle |
{} | Now all the vertices have been selected and the minimum spanning tree is shown in green. In this case, it has weight 39. |
Read more about this topic: Prim's Algorithm
Famous quotes containing the word run:
“The city is a fact in nature, like a cave, a run of mackerel or an ant-heap. But it is also a conscious work of art, and it holds within its communal framework many simpler and more personal forms of art. Mind takes form in the city; and in turn, urban forms condition mind.”
—Lewis Mumford (1895–1990)
“We perversely see mother love as the problem—when it is all we have to sustain us—rather than blaming the fathers who have run out on our mothers and on us. We seem willing to forgive fathers for loving too little even as we still shrink in terror from mothers who love too much.”
—Frank Pittman (20th century)