"Data structure" discussion on multiplication and evaluation of LCA

Ideas

Using tree multiplication method can efficiently find two x, y common ancestor LCA.

We set F[X][K] to represent the 2k generation ancestors of X

F[x][0] is the parent node of X

Because 2k from the X-to-root node can be seen as 2k-1 step from X to 2k-1 step .

So for 1≤k≤logn there is F[x][k]=f[f[x][k-1]][k-1] (similar to the dichotomy of thought)

Pretreatment:

So we can iterate over the tree and get all the f[x][0] and calculate all the values of the F-array.

To seek LCA:

Set Dep[x] to the depth of X dep[x]≥dep[y] (otherwise you can exchange X and y)

Use binary split to adjust x and Y to the same depth

If this

"Data structure" discussion on multiplication and evaluation of LCA