Sort into chain

• To: mathgroup at smc.vnet.net
• Subject: [mg45605] Sort into chain
• From: Goyder Dr HGD <h.g.d.goyder at cranfield.ac.uk>
• Date: Fri, 16 Jan 2004 06:05:23 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Dear Mathgroup,

How do I sort a list of pairs, for example,

a = {{3, 1}, {2, 6}, {7, 3}, {8, 7}, {10, 8}, {6, 11},
{12, 10}, {11, 14}, {15, 12}, {14, 18}, {19, 15},
{18, 20}, {20, 19}, {1, 2}};

Into a list where the second entry in each pair is the same as the first
entry in the next pair. Thus the effect of the sort will give

{{18, 20}, {20, 19}, {19, 15}, {15, 12},
{12, 10}, {10, 8}, {8, 7}, {7, 3}, {3, 1},
{1, 2}, {2, 6}, {6, 11}, {11, 14}, {14, 18}}

The first pair is not important because the pairs form a circular chain.

I have tried

Sort[a, (#1[[2]] == #2[[1]]) &]

{{1, 2}, {20, 19}, {14, 18}, {18, 20}, {19, 15},
{15, 12}, {6, 11}, {11, 14}, {12, 10}, {10, 8},
{8, 7}, {7, 3}, {2, 6}, {3, 1}}

which has a few correct entries but is not finished. I wondered if the
difficulty was due to the circular nature of the chain but if you break the
chain by dropping one pair it still does not work.

Thanks for any assistance

Hugh Goyder

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