Question: Solve a DAG 3 times with each algorithm then show they fail Problem 2 (20 points) 1. [15 points] Consider a DAG which has already

Solve a DAG 3 times with each algorithm then show they

Solve a DAG 3 times with each algorithm then show they fail

Problem 2 (20 points) 1. [15 points] Consider a DAG which has already been topologically sorted, so edges go from left to right. In the lecture notes, we have seen a Dynamic Programming algorithm that finds the shortest path in a DAG where edges have weights associated with them. Now consider the following greedy strategies. Show that all of them fail to find the shortest path from node 1 to node n by giving appropriate small examples. You should also explain what is the value of the optimal solution compared to the greedy one. Greedy strategy 1 Set i=1 While itn, Pick the edge (i, j) with the largest j Set i=j and repeat Return the weight of the path constructed from node 1 to node n. Greedy strategy 2 Set i=1 . While ihn, Pick the edge (i, j) with the smallest weight Set i=j and repeat Return the weight of the path constructed from node 1 to node n. Greedy strategy 3 Set i=1 While itn, Pick the edge (i, j) with the smallest ratio weight/(-i) Set i=j and repeat Return the weight of the path constructed from node 1 to node n

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