/Solutions are available.
1. Tallest path
Suppose that each edge uv in a graph G represents a oneway section of the US Interstate highway system spanned by an easilydamaged bridge with clearance c_{uv}. Suppose further that you wish to drive a truck full of heating oil from vertex s to vertex t in G, and that a truck with height h can only safely pass under a bridge with clearance c_{uv} ≥ h. Give the most efficient algorithm you can that computes for each vertex t≠s the height of the tallest truck that can reach t from s.
2. Exchange rates
A currency exchange offers to trade currencies at various exchange rates, giving a table where one unit on the lefthand side of each row buys some number of units on the righthand side:
1 US Dollar 
0.52 British Pounds 
1 US Dollar 
1.31 Canadian Dollars 
1 US Dollar 
1920.00 Venezuelan Bolivars 
1 British Pound 
1.83 US Dollars 
1 Canadian Dollar 
32.13 Indian Rupees 
etc... 

Give the most efficient algorithm you can that determines whether it is possible to make a profit by exchanging money at these rates, where you can start with any currency you like and go through as many intermediate currencies as you like as long as you end with the same currency you started with. Compute its running time as a function of the number of currencies n. Hint: consider taking logarithms.