UVa 10337 - Flight Planner

Summary
Given a field of windstrengths, you are to find the minimum cost to fly to the destination X. You can move climb, hold at the same height, or sink.

Explanation
This problem is similar to UVa 116 (Undirectional TSP) and is somewhat easier since it only wants the minimum cost. Do a dp from left to right to keep track of the minimum cost for reaching each position. Remember you are on a flight, so you have to land at X, i.e. at the last row (0 altitude according to the problem).

Gotchas

 * You must fly, literally, to the destination. So, you cannot play cheat by skimming through to destination at altitude 0 (plane driving on road?!). Keep the costs at every altitude 0 to be infinity as they are forbidden before the destination.

Input
2 400 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 9 9 1 1 -9 -9 1 1000 9 9  9  9  9  9  9  9  9  9 9  9  9  9  9  9  9  9  9  9 9  9  9  9  9  9  9  9  9  9 9  9  9  9  9  9  9  9  9  9 9  9  9  9  9  9  9  9  9  9 9  9  9  9  9  9  9  9  9  9   7  7  7  7  7  7  7  7  7  7 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -7 -3 -7 -7 -7 -7 -7 -7 -7 -7 -9 -9 -9 -9 -9 -9 -9 -9 -9 -9

Output
120 354