state1 = [0, 1, 2, 0, 2] state2 = [1, 1, 1, 1, 1]

Difference index = 0.065.

In computing, an index is a data structure that improves the speed of data retrieval operations on a database table. Think of it like the index at the back of a book: instead of flipping through every page to find a topic, you go to the index, find the page number, and jump directly there.

( H ) has index 2 iff ( H ) is a proper subgroup and for any ( g \notin H ), ( g^2 \in H ).

Aggregate to domain level, then to overall divergence index (0 = identical, 1 = maximum possible divergence).

class TwoStateIndex: def __init__(self, size): self.size = size self.bitmap = 0 # integer as bitset def set_state(self, index, state): """Set state: 0 or 1 at given index""" if state == 1: self.bitmap |= (1 << index) else: self.bitmap &= ~(1 << index)