Consider a 2 x 2 x **height** stack of cube-shaped boxes of identical size. The stack has **height** levels of boxes, each level containing 4 boxes arranged in a 2 x 2 pattern. Each box has a 50% probability of containing dynamite and a 50% probability of being empty. Two dynamite-filled boxes, A and B, are in the same dynamite cluster if:
- a face of A touches a face of B
- OR a face of A touches a face of some box C, and C is in the same
*dynamite cluster* as B.
A stack is *dangerous* if it contains a *dynamite cluster* that contains at least **dangerousClusterSize** boxes. Given **height** and **dangerousClusterSize**, compute the probability that the stack is *dangerous*. |