Clash of the Titans

Each map below represents a city about to be ravaged by giant monsters, with each region representing a building. These cities are meticulously designed; every building has an integer height between 1 and 7 inclusive, and any horizontal or vertical line through the city passes through seven buildings of different heights (excepting lines that pass through corners of buildings).

Numbered arrows pointing into a city indicate how many buildings can be seen directly along that line, with taller buildings obscuring the view of any shorter buildings behind them. For example, if an arrow pointed toward buildings of heights 3, 1, 2, 5, 4, 7, and 6, in that order, three buildings would be visible (the 3-, 5-, and 7-story buildings).

Once you've built up the cities to specifications, the real fun can begin. Godzilla and Mechagodzilla have five itineraries, each for a different city, listed below in no particular order. For each city, each monster chooses an itinerary and begins by destroying a building adjacent to the city's border. (NOTE: In these instructions, "adjacent" means sharing an edge; two areas that only touch at a single point are not adjacent.)

The monster then continues to destroy buildings, making a path in which each destroyed building is adjacent to the last. The plus/minus modifiers in the itinerary indicate how much taller or shorter each building is than the previous one. No monster destroys the same building twice. In some cases, there may be more than one possible path a monster can follow, but all legal paths will have the same starting and ending point.

In each city, after following their individual paths (which don't intersect or overlap), Godzilla and Mechagodzilla have a cataclysmic battle in which they destroy the only building adjacent to the last buildings in both of their paths, no matter how tall that building may be. They then return from whence they came... until the sequel...