Graph Construction (10 points) Suppose you are given a unweighted directed graph G=(V,E) with n vertices and m edges. You are also given a set of constants a_(1)dots,a_(n)inN. Finally, you are given a starting node sinV and an ending node tinV. Describe an algorithm that finds the shortest walk length from s to t, such that there exist variables x_

Question

Graph Construction (10 points) Suppose you are given a unweighted directed graph

G=(V,E)

with

n

vertices and

m

edges. You are also given a set of constants

a_(1)dots,a_(n)inN

. Finally, you are given a starting node

sinV

and an ending node

tinV

. Describe an algorithm that finds the shortest walk length from

s

to

t

, such that there exist variables

x_(1),dots,x_(n)inN

that satisfy

W=a_(1)x_(1) cdots a_(n)x_(n)

, where

W

is the number of steps in the shortest walk. Give a rigorous proof for the correctness of your algorithm and its runtime which should be in

O(n m)

.

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