#####   ######  #####    ###    #   #  ###  #   #  ######
##  ##  ##      ##  ##  ## ##   #   #   #   #   #  ##
#####   ####    #####   #   #   #   #   #   #   #  ####
##  #   ##      ##      ## ##    # #    #    # #   ##
##   #  ######  ##       ###      #    ###    #    ######

$ curl repovive.com/roadmaps/data-structures/link-cut-trees/findroot-operation

░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░██████████████████████████████████████████████████████████████████████████████

#####   ######  #####    ###    #   #  ###  #   #  ######
##  ##  ##      ##  ##  ## ##   #   #   #   #   #  ##
#####   ####    #####   #   #   #   #   #   #   #  ####
##  #   ##      ##      ## ##    # #    #    # #   ##
##   #  ######  ##       ###      #    ###    #    ######

$ curl repovive.com/roadmaps/data-structures/link-cut-trees/findroot-operation

Repovive

FindRoot Operation - Link-Cut Trees | Data Structures | Repovive

Repovive.

Data Structures19 sections · 729 units49h total

Open in Course

FindRoot Operation

Find tree root

Find the root of the tree containing v:

function findRoot(v)
    access(v)
    // Root is leftmost node in auxiliary tree
    while v.left is not null
        v := v.left
    splay(v)
    return v

After access(v), the path from v to root is in one auxiliary tree. The root is the leftmost node (shallowest depth).

Time: $O(\log n)$ amortized.

This replaces Union-Find's find operation but with more power.