What is the formula for Josephus problem?
The Equations Write n as n = 2m + k, where 2m is the largest power of two less than or equal to n. k people need to be eliminated to reduce the problem to a power of two, which means 2k people must be passed over. The next person in the circle, person 2k + 1, will be the winner.
Which position does Josephus need to stand to survive with 41 soldiers and himself using the scheme indicated?
Josephus had 40 other soldiers with him, so his value for n was 41. This gives the value for 2^k as 32 and the value for m as 9. Therefore, Josephus must sit in position 2m+1 = 2(9)+1 = 19 to be spared.
Who is Josephus in math?
The Josephus problem is based around Josephus Flavius; a Jewish soldier and historian who inspired an interesting set of mathematical problems. In 67 C.E., Josephus and 40 fellow soldiers were surrounded by a group of Roman soldiers who were intent on capturing them.
Where is Josephus problem used?
In computer science and mathematics, the Josephus Problem (or Josephus permutation) is a theoretical problem. Following is the problem statement: There are n people standing in a circle waiting to be executed. The counting out begins at some point in the circle and proceeds around the circle in a fixed direction.
Why does YouTube freeze 301?
YouTube freezes the public counter at 301 for up to half a day or more while verification takes place. Internally, YouTube’s counters are continuing to count views. Once the traffic is verified, the total number of views is added back onto the public counter. None are missed.
How did Josephus survive?
According to Josephus’ account of the siege of Yodfat, he and his 40 soldiers were trapped in a cave by Roman soldiers. They chose suicide over capture, and settled on a serial method of committing suicide by drawing lots.
Why do videos stop at 301 views?
YouTube starts to freeze the views of videos temporarily, once they reach 301 views. This is done as a measure to verify that all the views are from real viewers, instead of bots. If the views on the video are from real viewers, the view count will shortly update.
Is Brady Haran a doctor?
On July 20, 2016, I received an honorary doctorate from the University of Nottingham. It was a Doctor of Letters honoris causa. It was a really great day and I’m grateful to everyone involved.
How old is Brady Haran?
45 years (June 18, 1976)Brady Haran / Age
How to solve the Josephus problem with n 1 persons?
So we call josephus (n – 1, k) to get the position with n-1 persons. But the position returned by josephus (n – 1, k) will consider the position starting from k%n + 1. So, we must make adjustments to the position returned by josephus (n – 1, k). Following is simple recursive implementation of the Josephus problem.
Is there a simple analytical solution to Josephus’problem?
Despite the simple form of the problem and a large number of articles on this and related problems, a simple analytical representation of the solution of Josephus’ problem has not yet been found.
What is the value of Josephus (n – 1 K)?
josephus(n, k) = (josephus(n – 1, k) + k-1) % n + 1 josephus(1, k) = 1. After the first person (kth from beginning) is killed, n-1 persons are left. So we call josephus(n – 1, k) to get the position with n-1 persons.
What is the position returned by Josephus (n – 1 K)?
After the first person (kth from beginning) is killed, n-1 persons are left. So we call josephus (n – 1, k) to get the position with n-1 persons. But the position returned by josephus (n – 1, k) will consider the position starting from k%n + 1.