Symmetrization

You may use biometrics in your devices.

O(1) is crucial because of K-independent hashing, but there is the bug.

i≠ j, k=1

Symmetrization is the optimization to solve this difficulty.

There are two shapes.

The associated symmetric form may take half-integer values.

(p+q)/2

A set of point pairs {(p1,q1),・・・,(pm,qm)} is given on the boundary of a shape.

T is transformation.

T=(Θ,d)

T'(p+dp)=q+dq

∴

E is still expectation. The boundary will be getting smaller like your fingerprints or DNA. O(1) is the worst-case execution time (WCET). I have quantum computers in my brain because of O(1), but nobody cares. You need the faster one to count prime numbers, although XP is enough for me. C++ is hard to use in Windows 10. I believe in your evolution.