New developments in Rubik's Cube: 26 steps are sufficient to crack any Rubik's Cube

Recently, Daniel Kunkle, a computer scientist at the University of northeastern in Boston, proved that any cube can be unlocked in 26 steps. This result breaks all previous records. In the process of solving the cube, he constructed some very enlightening algorithms. This article will briefly introduce these algorithms.
There are about 4.3X10 ^ 19 possible initial states for a cube, and it is impossible for a cow to search for all possibilities. Therefore, Kunkle and his instructor gene Cooperman came up with some strategies for classifying and filtering the status of Rubik's Cube.
Kunkle and cooperman first use a small trick to simplify the problem. If each side of the cube is a color, we think that the cube is unlocked, no matter which side is a color. In other words, the initial states that can be obtained through color replacement between each other are equivalent. In this way, the initial state of "essentially different" is reduced to 10 ^ 18.
Next, they began to look at a more simple problem: how many states can be solved if only half-turn is allowed. In 10 ^ 18 States, only about 15000 states can be cracked with only 180 degrees of rotation. For a common computer, this number is not large. In less than a day, you can search for the minimum number of steps required to unlock more than 15000 cubes. They found that any of these initial states can be resolved within 13 steps.
What they need to do is to find out how many steps are required to convert any State to one of the 15000 special states. To do this, they first divide all the initial states into several equivalence classes, and the States in each equivalence class can be obtained by rotating each other at only 180 degrees. In this way, if any State in the same equivalence class can be changed to one of the special states, the same rotation step can also change all other States of the equivalence class to special states. Finally, they found 1.4x10 ^ 12 different equivalence classes. The number of states to be resolved was reduced from 4.3x10 ^ 19 to 1.4x10 ^ 12. However, 10 ^ 12 is still a horrible number.
Now they use a supercomputer to complete the job and use some skillful decisions to accelerate the search process. The computer needs to spend a lot of time reading data on the hard disk. In order to speed up, Kunkle and cooperman skillfully process the data so that the data arrangement exactly matches the order in which the computer reads data, this saves time for searching hard disks.
"This method can be applied to any combination problem," Kunkle said. He mentioned a series of issues such as checkers, chess, flight schedules, and protein stacking. A similar combination of learning methods has recently been used to find the optimal strategy for checkers.
After 63 hours of computing, the supercomputer got the answer that any State can be converted to 15000 special states within 16 steps. These special states only need 13 steps to reach the final state. Therefore, the final conclusion of this method is that any cube problem can be solved within 29 steps.
However, this number is not enough to create a new record. Last year, Sweden came to the conclusion that it had solved the cube problem in 27 steps. Kunkle and cooperman realized that they still need to take three steps to break this record.
Using their existing algorithms, only 8x10 ^ 7 State sets cannot be able to return solutions within 26 steps. After searching for these relatively few States, they finally found a solution to all the cubes within 26 steps.
They published the results at the Issac (International Symposium on symbolic and algebraic computation, International Conference on symbol and algebra computing) in July 29.
Now Kunkle and cooperman want to reduce the maximum number of steps to 25. They think they can perform a brute force search for all the status that requires 26 steps to find a better solution.
Although they have achieved great success, this result may have room for improvement. Many scholars believe that less than 20 steps can solve any cube, but no one can prove it now.

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