A street sweeper starts at P, ends at S, and must traverse every street at least once. Edge lengths in km are shown. Find the minimum total distance in integer km.
Total edge length is $PQ+PR+QR+QS+RS=2+3+4+3+1=13$ km. Initially Q and R are odd-degree vertices; a route beginning P and ending S needs P and S odd instead. Minimum duplicated paths pair P with Q (2 km) and R with S (1 km),adding3. The competing pairing P–R and Q–S adds6; pairing P–S and Q–R adds8. A 16 km route exists, for example P–Q–P–R–Q–S–R–S. Thus **16 km**.
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