Past exam of the short options course of the University of Oxford / 2017 / 7 / a / ii / Solution

A shortest path from $u$ to $v$ is a graph path $P$ joining these endpoints such thatfor every other $uv$-path $P^{\prime }$ in $G$, where $w(P)$ is the sum of its edge weights. Here paths have no repeated vertices; minimizing over unrestricted walks is a different problem when negative edge weights occur.