Suppose you are given a directed graph G = (V, E) with costs on the edges ce for e ε E and a sink t (costs may be negative). Assume that you also have finite values d(v) for v e V. Someone claims that, for each node v e V, the quantity d(v) is the cost of the minimum-cost path from node v to the sink t.
(a) Give a linear-time algorithm (time O(m) if the graph has m edges) that verifies whether this claim is correct.
(b) Assume that the distances are correct, and d(v) is finite for all v e V. Now you need to compute distances to a different sink tt. Give an O(m log n) algorithm for computing distances d'(v) for all nodes v e V to the sink node t.(Hint: It is useful to consider a new cost function defined as follows: for edge e = (v, w), let c'e = ce — d(v) + d(w). Is there a relation between costs of paths for the two different costs c and c ?)
We need at least 10 more requests to produce the solution.
0 / 10 have requested this problem solution
The more requests, the faster the answer.