Minimum Spanning Trees Prim’s Algorithm Kruskal’s Algorithm
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Minimum Spanning TreesPrims Algorithm Kruskals Algorithm
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Prims Algorithm Initialize array425
AHBFEDCG721018343789310
2
KdvpvAFBFCFDFEFFFGFHF
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425
AHBFEDCG721018343789310Start with any node, say D
2
KdvpvABC DT0EFGH
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425
AHBFEDCG721018343789310Update distances of adjacent, unselected nodes
2
KdvpvABC 3DDT0E25DF18DG2DH
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425
AHBFEDCG721018343789310Select node with minimum distance
2
KdvpvABC 3DDT0E25DF18DGT2DH
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425
AHBFEDCG721018343789310Update distances of adjacent, unselected nodes
2
KdvpvABC 3DDT0E7GF18DGT2DH3G
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425
AHBFEDCG721018343789310Select node with minimum distance
2
KdvpvABCT 3DDT0E7GF18DGT2DH3G
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425
AHBFEDCG721018343789310Update distances of adjacent, unselected nodes
2
KdvpvAB4CCT 3DDT0E7GF3CGT2DH3G
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425
AHBFEDCG721018343789310Select node with minimum distance
2
KdvpvAB4CCT 3DDT0E7GFT3CGT2DH3G
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425
AHBFEDCG721018343789310Update distances of adjacent, unselected nodes
2
KdvpvA10FB4CCT 3DDT0E2FFT3CGT2DH3G
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425
AHBFEDCG721018343789310Select node with minimum distance2
KdvpvA10FB4CCT 3DDT0ET2FFT3CGT2DH3G
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425
AHBFEDCG721018343789310Update distances of adjacent, unselected nodes2Table entries unchanged
KdvpvA10FB4CCT 3DDT0ET2FFT3CGT2DH3G
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425
AHBFEDCG721018343789310Select node with minimum distance2
KdvpvA10FB4CCT 3DDT0ET2FFT3CGT2DHT3G
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425
AHBFEDCG721018343789310Update distances of adjacent, unselected nodes2
KdvpvA4HB4CCT 3DDT0ET2FFT3CGT2DHT3G
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425
AHBFEDCG721018343789310Select node with minimum distance2
KdvpvAT4HB4CCT 3DDT0ET2FFT3CGT2DHT3G
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425
AHBFEDCG721018343789310Update distances of adjacent, unselected nodes2Table entries unchanged
KdvpvAT4HB4CCT 3DDT0ET2FFT3CGT2DHT3G
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425
AHBFEDCG721018343789310Select node with minimum distance2
KdvpvAT4HBT4CCT 3DDT0ET2FFT3CGT2DHT3G
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4
AHBFEDCG23433Cost of Minimum Spanning Tree = dv = 212Done
KdvpvAT4HBT4CCT 3DDT0ET2FFT3CGT2DHT3G
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Kruskals Algorithm
Work with edges, rather than nodesTwo steps:Sort edges by increasing edge weightSelect the first |V| 1 edges that do not generate a cycle
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Walk-ThroughConsider an undirected, weight graph51
AHBFEDCG3246343484310
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Sort the edges by increasing edge weight51
AHBFEDCG3246343484310
edgedv(D,E)1 (D,G)2 (E,G)3 (C,D)3 (G,H)3 (C,F)3 (B,C)4
edgedv(B,E)4 (B,F)4 (B,H)4 (A,H)5 (D,F)6 (A,B)8 (A,F)10
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Select first |V|1 edges which do not generate a cycle51
AHBFEDCG3246343484310
edgedv(D,E)1(D,G)2(E,G)3(C,D)3(G,H)3 (C,F)3(B,C)4
edgedv(B,E)4(B,F)4(B,H)4(A,H)5(D,F)6(A,B)8(A,F)10
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Select first |V|1 edges which do not generate a cycle51
AHBFEDCG3246343484310
edgedv(D,E)1(D,G)2(E,G)3(C,D)3(G,H)3 (C,F)3(B,C)4
edgedv(B,E)4(B,F)4(B,H)4(A,H)5(D,F)6(A,B)8(A,F)10
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Select first |V|1 edges which do not generate a cycle51
AHBFEDCG3246343484310Accepting edge (E,G) would create a cycle
edgedv(D,E)1(D,G)2(E,G)3(C,D)3(G,H)3 (C,F)3(B,C)4
edgedv(B,E)4(B,F)4(B,H)4(A,H)5(D,F)6(A,B)8(A,F)10
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Select first |V|1 edges which do not generate a cycle51
AHBFEDCG3246343484310
edgedv(D,E)1(D,G)2(E,G)3(C,D)3(G,H)3 (C,F)3(B,C)4
edgedv(B,E)4(B,F)4(B,H)4(A,H)5(D,F)6(A,B)8(A,F)10
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Select first |V|1 edges which do not generate a cycle51
AHBFEDCG3246343484310
edgedv(D,E)1(D,G)2(E,G)3(C,D)3(G,H)3 (C,F)3(B,C)4
edgedv(B,E)4(B,F)4(B,H)4(A,H)5(D,F)6(A,B)8(A,F)10
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Select first |V|1 edges which do not generate a cycle51
AHBFEDCG3246343484310
edgedv(D,E)1(D,G)2(E,G)3(C,D)3(G,H)3 (C,F)3(B,C)4
edgedv(B,E)4(B,F)4(B,H)4(A,H)5(D,F)6(A,B)8(A,F)10
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Select first |V|1 edges which do not generate a cycle51
AHBFEDCG3246343484310
edgedv(D,E)1(D,G)2(E,G)3(C,D)3(G,H)3 (C,F)3(B,C)4
edgedv(B,E)4(B,F)4(B,H)4(A,H)5(D,F)6(A,B)8(A,F)10
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Select first |V|1 edges which do not generate a cycle51
AHBFEDCG3246343484310
edgedv(D,E)1(D,G)2(E,G)3(C,D)3(G,H)3 (C,F)3(B,C)4
edgedv(B,E)4(B,F)4(B,H)4(A,H)5(D,F)6(A,B)8(A,F)10
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Select first |V|1 edges which do not generate a cycle51
AHBFEDCG3246343484310
edgedv(D,E)1(D,G)2(E,G)3(C,D)3(G,H)3 (C,F)3(B,C)4
edgedv(B,E)4(B,F)4(B,H)4(A,H)5(D,F)6(A,B)8(A,F)10
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Select first |V|1 edges which do not generate a cycle51
AHBFEDCG3246343484310
edgedv(D,E)1(D,G)2(E,G)3(C,D)3(G,H)3 (C,F)3(B,C)4
edgedv(B,E)4(B,F)4(B,H)4(A,H)5(D,F)6(A,B)8(A,F)10
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Select first |V|1 edges which do not generate a cycle51
AHBFEDCG3246343484310
edgedv(D,E)1(D,G)2(E,G)3(C,D)3(G,H)3 (C,F)3(B,C)4
edgedv(B,E)4(B,F)4(B,H)4(A,H)5(D,F)6(A,B)8(A,F)10
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Select first |V|1 edges which do not generate a cycle51
AHBFEDCG2333DoneTotal Cost = dv = 214}not considered
edgedv(D,E)1(D,G)2(E,G)3(C,D)3(G,H)3 (C,F)3(B,C)4
edgedv(B,E)4(B,F)4(B,H)4(A,H)5(D,F)6(A,B)8(A,F)10