T, e T c(e) = 50 G = (V, E), c(e) Minimum Spanning Tree
Kruskal’s Algorithm: Add cheapest edge that does not create a cycle
Kruskal’s Algorithm: Add cheapest edge that does not create a cycle
Kruskal’s Algorithm: Add cheapest edge that does not create a cycle
Kruskal’s Algorithm: Add cheapest edge that does not create a cycle
Kruskal’s Algorithm: Add cheapest edge that does not create a cycle
Kruskal’s Algorithm: Add cheapest edge that does not create a cycle
Kruskal’s Algorithm: Add cheapest edge that does not create a cycle
Kruskal’s Algorithm: Add cheapest edge that does not create a cycle ?
Kruskal’s Algorithm: Add cheapest edge that does not create a cycle Ignore edges inside components
Kruskal’s Algorithm: Add cheapest edge that does not create a cycle Ignore edges inside components
Kruskal’s Algorithm: Add cheapest edge that does not create a cycle Ignore edges inside components
Kruskal’s Algorithm: Add cheapest edge that does not create a cycle Ignore edges inside components
Prim’s Algorithm: Grow a tree. At each step, add cheapest edge from tree node to non-tree node
Prim’s Algorithm: Grow a tree. At each step, add cheapest edge from tree node to non-tree node
Prim’s Algorithm: Grow a tree. At each step, add cheapest edge from tree node to non-tree node
Prim’s Algorithm: Grow a tree. At each step, add cheapest edge from tree node to non-tree node
Prim’s Algorithm: Grow a tree. At each step, add cheapest edge from tree node to non-tree node
8 5 4 Prim’s Algorithm: Grow a tree. At each step, add cheapest edge from tree node to non-tree node Can remove edges between tree nodes
Prim’s Algorithm: Grow a tree. At each step, add cheapest edge from tree node to non-tree node
Prim’s Algorithm: Grow a tree. At each step, add cheapest edge from tree node to non-tree node
Prim’s Algorithm: Grow a tree. At each step, add cheapest edge from tree node to non-tree node
node-comp array node comp comp-size array comp size Lists of nodes 1 : 1, 2, 6, 7 2 : 3 : 4 : 4 5 : 5 6 : 7 : 8 : 8, 9, 3 9 : Components Data Structure Supporting Find and Merge (Union-Find)
Components Data Structure Supporting Find and Merge (Union-Find) node-comp array node comp comp-size array comp size Lists of nodes 1 : 1 2 : 2 3 : 3 4 : 4 5 : 5 6 : 6 7 : 7 8 : 8 9 : 9
Components Data Structure node-comp array node comp comp-size array comp size Lists of nodes 1 : 1 2 : 2 3 : 3 4 : 4 5 : 5 6 : 6 7 : 7 8 : 8 9 : 9 Merge(1,2)
Components Data Structure node-comp array node comp comp-size array comp size Lists of nodes 1 : 1, 2 2 : 3 : 3 4 : 4 5 : 5 6 : 6 7 : 7 8 : 8 9 : 9 Merge(1,2)
Components Data Structure node-comp array node comp comp-size array comp size Lists of nodes 1 : 1, 2, 6, 7 2 : 3 : 4 : 4 5 : 5 6 : 7 : 8 : 8, 9, 3 9 : Merge(1,8)
Components Data Structure node-comp array node comp comp-size array comp size Lists of nodes 1 : 1, 2, 6, 7 2 : 3 : 4 : 4 5 : 5 6 : 7 : 8 : 8, 9, 3 9 : Merge(1,8)
Components Data Structure node-comp array node comp comp-size array comp size Lists of nodes 1 : 1, 2, 6, 7 2 : 3 : 4 : 4 5 : 5 6 : 7 : 8 : 8, 9, 3 9 : Merge(1,8)
Components Data Structure node-comp array node comp comp-size array comp size Lists of nodes 1 : 1, 2, 6, 7 2 : 3 : 4 : 4 5 : 5 6 : 7 : 8 : 8, 9, 3 9 : Merge(1,8)
Components Data Structure node-comp array node comp comp-size array comp size Lists of nodes 1 : 1, 2, 6, 7 2 : 3 : 4 : 4 5 : 5 6 : 7 : 8 : 8, 9, 3 9 : Merge(1,8)
Components Data Structure node-comp array node comp comp-size array comp size Lists of nodes 1 : 1, 2, 6, 7, 8, 9, 3 2 : 3 : 4 : 4 5 : 5 6 : 7 : 8 : 9 : Merge(1,8)
Components Data Structure Pointer Version 1(1)2(1)6(1)3(1)4(1)5(1)8(1)9(1)7(1) Merge(1,2)
Components Data Structure Pointer Version 1(1) 2 6(1)3(1)4(1)5(1)8(1)9(1)7(1) Merge(1,2)
Components Data Structure Pointer Version 1(2) 2 6(1)3(1)4(1)5(1)8(1)9(1)7(1) Merge(3,4)
Components Data Structure Pointer Version 1(2) 2 6(1) 3 4 5(1)8(1)9(1)7(1) Merge(3,4)
Components Data Structure Pointer Version 1(1) 2 6(1)3(2) 4 5(1)8(1)9(1)7(1) Merge(1,3)
Components Data Structure Pointer Version 1(2) 2 6(1)3(2) 4 5(1)8(1)9(1)7(1) Merge(1,3)