3. Give an example of a simple directed, weighted graph G = (V, E, w: E R) and vertices s, t V such that Dijkstras algortihm started at s does not find the shortest s t path. Hint: You will need to use negative edge weights. (Note: this shows that for finding shortest paths, the greedy choice property fails in the presence of negative edge weights. Do you see why?)

3. Give an example of a simple directed, weighted graph G = (V, E, w: E + R) and vertices st EV such that Dijkstra's algortihm started at s does not find the shortest S t path. Hint: You will need to use negative edge weights. (Note: this shows that for finding shortest paths, the greedy choice property fails in the presence of negative edge weights. Do you see why?) 3. Give an example of a simple directed, weighted graph G = (V, E, w: E + R) and vertices st EV such that Dijkstra's algortihm started at s does not find the shortest S t path. Hint: You will need to use negative edge weights. (Note: this shows that for finding shortest paths, the greedy choice property fails in the presence of negative edge weights. Do you see why?)