A new friends sort algorithm

Calculation of the Minimum Computational Complexity Based on Information Entropy

“…n n e n n n n ≈ − ≈ Therefore, the minimum computational complexity is O(nlog 2 (n)). The result is the same with that of the merge sort [10]. This fact confirms the correctness of the theory again.…”

“…This computational complexity is the same with that of Bubble sort and insertion sort [10]. These methods are fast enough, however, just as we know, the fastest algorithm is merge sort the computational complexity of which is able to reach O(nlog 2 (n)) [10]. O(nlog 2 (n)) is much smaller than O(n 2 ), this fact indicates that O(n 2 ) is not the minimum computational complexity and O(nlog 2 (n)) takes place of it.…”

“…Therefore, the minimum computational complexity is O(n 2 ). This computational complexity is the same with that of Bubble sort and insertion sort [10]. These methods are fast enough, however, just as we know, the fastest algorithm is merge sort the computational complexity of which is able to reach O(nlog 2 (n)) [10].…”

“…While calculating the computational complexity of the two problems in Section 3, we can find out that the equation is able to be simplified. Because the possibilities of all states are the same and the final information entropy is zero, the equation can be expressed in the following form (n is the number of the states): (10) ) ( log complexity Time 2 n = This simplified equation discloses another characteristic of the states in the models of problems. That is the equality of the states' possibilities.…”

“…In Section 4, the equation to calculate the computational complexity is simplified. According to (10), there is a logarithmic relationship between the minimum computational complexity and the number of the states.…”