[Algo] [July] algorithm based on comparison ordering the lower bound is O (NLOGN)

Suppose: There are n numbers that need to be sorted.

The full arrangement of n numbers is a (n,n) = n!

Based on comparison, I<j. in the best case , you can sift half of the n! possible. That is to say, the remaining (N!/2) species is possible.

This comparison is done in K-times. Finally sift out a sort (conforming to the requirements):

n!/(2k) < 1

Formula derivation:

2k > n! I understand that k means how many times to sift, 2k is the possibility of permutation. Then the 2k is larger than n! to ensure that the sieve contains the correct arrangement.

Klog (2) > log (n!) Take the logarithm on both sides

K > Log (n!) Ignore constants

N!<nn = log (n!) ~nlog (N)

Push to:

K > Nlog (N)//So Nlog (n) is the Nether

　　

[Algo] [July] algorithm based on comparison ordering the lower bound is O (NLOGN)