(Latest Revision: Nov 13, 2022 )
mstProbSoln.txt
mstProbSoln.txt
Original list - the edges of a connected, undirected graph
edge weight
{07,12} 01
{01,08} 02
{07,08} 03
{01,12} 04
{08,12} 05
{03,10} 06
{05,10} 07
{03,05} 08
{05,07} 09
{01,05} 10
{05,08} 11
{03,08} 12
{06,09} 13
{04,11} 14
{01,07} 15
{02,09} 16
{02,06} 17
{08,09} 18
{08,10} 19
{06,11} 20
{09,07} 21
{04,07} 22
{04,06} 23
{06,12} 24
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WORK SET ONE - Kruskal List
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Using Kruskal's Algorithm to find the edges of a minimum cost spanning tree.
Initial singleton sets {01} {02} {03} {04} {05} {06} {07} {08} {09} {10} {11} {12}
{07,12} 1 accept {01} {02} {03} {04} {05} {06} {07,12} {08} {09} {10} {11} 1 edge
{01,08} 2 accept {01,08} {02} {03} {04} {05} {06} {07,12} {09} {10} {11} 2 edges
{07,08} 3 accept {01,07,08,12} {02} {03} {04} {05} {06} {09} {10} {11} 3 edges
{01,12} 4 reject {01,07,08,12} {02} {03} {04} {05} {06} {09} {10} {11}
{08,12} 5 reject {01,07,08,12} {02} {03} {04} {05} {06} {09} {10} {11}
{03,10} 6 accept {01,07,08,12} {02} {03,10} {04} {05} {06} {09} {11} 4 edges
{05,10} 7 accept {01,07,08,12} {02} {03,05,10} {04} {06} {09} {11} 5 edges
{03,05} 8 reject {01,07,08,12} {02} {03,05,10} {04} {06} {09} {11}
{05,07} 9 accept {01,03,05,07,08,10,12} {02} {04} {06} {09} {11} 6 edges
{01,05} 10 reject {01,03,05,07,08,10,12} {02} {04} {06} {09} {11}
{05,08} 11 reject {01,03,05,07,08,10,12} {02} {04} {06} {09} {11}
{03,08} 12 reject {01,03,05,07,08,10,12} {02} {04} {06} {09} {11}
{06,09} 13 accept {01,03,05,07,08,10,12} {02} {04} {06,09} {11} 7 edges
{04,11} 14 accept {01,03,05,07,08,10,12} {02} {04,11} {06,09} 8 edges
{01,07} 15 reject {01,03,05,07,08,10,12} {02} {04,11} {06,09}
{02,09} 16 accept {01,03,05,07,08,10,12} {02,06,09} {04,11} 9 edges
{02,06} 17 reject {01,03,05,07,08,10,12} {02,06,09} {04,11}
{08,09} 18 accept {01,02,03,05,06,07,08,09,10,12} {04,11} 10 edges
{08,10} 19 reject {01,02,03,05,06,07,08,09,10,12} {04,11}
{06,11} 20 accept {01,02,03,04,05,06,07,08,09,10,11,12} 11 edges
{09,07} 21
{04,07} 22
{04,06} 23
{06,12} 24
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(Sum of the weights is 1+2+3+6+7+9+13+14+16+18+20=109)
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WORK SET TWO - Prim List
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Using the weight-ordered edge list of the graph to find the order in which
Prim's Algorithm would select the edges of a minimum cost spanning tree.
{07,12} 1 Prim #3 (cheapest edge leaving S={01,07,08} Now S={01,07,08,12})
{01,08} 2 Prim #1 (cheapest edge leaving S={01} Now S={01,08})
{07,08} 3 Prim #2 (cheapest edge leaving S={01,08} Now S={01,07,08})
{01,12} 4
{08,12} 5
{03,10} 6 Prim #6 (cheapest edge leaving S={01,05,07,08,10,12} Now S={01,03,05,07,08,10,12})
{05,10} 7 Prim #5 (cheapest edge leaving S={01,05,07,08,12} Now S={01,05,07,08,10,12})
{03,05} 8
{05,07} 9 Prim #4 (cheapest edge leaving S={01,07,08,12} Now S={01,05,07,08,12})
{01,05} 10
{05,08} 11
{03,08} 12
{06,09} 13 Prim #8 (cheapest edge leaving S={01,03,05,07,08,09,10,12} Now S={01,03,05,06,07,08,09,10,12})
{04,11} 14 Prim #11 (cheapest edge leaving S={01,02,03,05,06,07,08,09,10,11,12} Now S={01,02,03,04,05,06,07,08,09,10,11,12})
{01,07} 15
{02,09} 16 Prim #9 (cheapest edge leaving S={01,03,05,06,07,08,09,10,12} Now S={01,02,03,05,06,07,08,09,10,12})
{02,06} 17
{08,09} 18 Prim #7 (cheapest edge leaving S={01,03,05,07,08,10,12} Now S={01,03,05,07,08,09,10,12})
{08,10} 19
{06,11} 20 Prim #10 (cheapest edge leaving S={01,02,03,05,06,07,08,09,10,12} Now S={01,02,03,05,06,07,08,09,10,11,12})
{09,07} 21
{04,07} 22
{04,06} 23
{06,12} 24
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(Same set of edges as before, same sum of the weights
= 1+2+3+6+7+9+13+14+16+18+20=109)
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