I know I'm kinda late to the party, but it's really not extremely hard to compute the memory footprint.
Lets take your first example: int c[] = new int[N];
According to the 64-bit memory model, an int is 4 bytes, so all the elements will be 4*N bytes in size. In addition to that, Java has a 24 bytes array overhead and there's also 8 bytes for the actual array object. So that's a total of 32 + 4 * N bytes.
For a 2 dimensional array: int a[][] = new int[N][M];
It's basically the same just that each element in the first array is another array of size M, so instead of 4 we have 32 + 4 * M, so the total size is 32 + (32 + 4 * M) * N.
It's true that a generalization for D dimensions is pretty complicated, but you get the idea.
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