Editing Persistent data structure (section)

===Path copying===
With the path copying method a copy of all nodes is made on the path to any node which is about to be modified. These changes must then be [[Fractional cascading|cascaded]] back through the data structure: all nodes that pointed to the old node must be modified to point to the new node instead. These modifications cause more cascading changes, and so on, until the root node is reached.

====Complexity of path copying====
With m modifications, this costs O(log m) additive [[lookup]] time. Modification time and space are bounded by the size of the longest path in the data structure and the cost of the update in the ephemeral data structure.  In a Balanced Binary Search Tree without parent pointers the worst case modification time complexity is O(log n + update cost). However, in a linked list the worst case modification time complexity is O(n + update cost).