Understanding O (log2n) and O (nlog2n)

O (LGN) is interpreted as:

Divide a dataset into two halves, then divide each half into two halves, and so on

O (NLGN) is interpreted as:

Divides a dataset into two halves, divides each half into two halves, and so on, iterating through half the data at the same time in the process

In the case of merge sort, the process of sorting can be regarded as an inverted two-fork tree:

From the above, the inverted two-tree leaf node comparison of the number of times, the worst case with the depth of the two-fork tree is the same: from Root to find a leaf node, the complexity of the tree height, that is, log2 N.

The number of times each leaf node is compared can be understood to find every leaf node from root, complexity is tree height * leaf node number, that is log2 n * N.