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Joined 2026-09-21 Message
Incoming links: Amortized time complexity
Use a history dynamic array and a cursor between elements. If the cursor is behind the history's end, The representation invariant is , with history exactly the prefix already consumed from the original source. The logical unread sequence is the history suffix starting at
next replays history; otherwise it pulls a new element from the source. prev moves the cursor left and returns the element crossed, so prev followed by next returns the same element twice and restores the cursor.def genBiIter[T](it: Iter[T]): BiIter[T] = new BiIter[T] {
private val history = scala.collection.mutable.ArrayBuffer.empty[T]
private var pos = 0
def hasPrev: Boolean = pos > 0
def hasNext: Boolean = pos < history.length || it.hasNext
def next(): T = {
if (pos < history.length) {
val v = history(pos); pos += 1; v
} else if (it.hasNext) {
val v = it.next()
history += v; pos += 1; v
} else {
throw new NoSuchElementException("BiIter.next")
}
}
def prev(): T = {
if (!hasPrev) throw new NoSuchElementException("BiIter.prev")
pos -= 1
history(pos)
}
}pos, followed by the source's remaining sequence. The logical backward history is the prefix before pos. Every operation preserves this model, including alternating backward and forward moves after source exhaustion.This bidirectional iterator uses storage after consuming distinct source elements. Replay and backward moves take constant time; appending has amortized time complexity under the usual dynamic array model. The input iterator must not be advanced separately.Original article in Journal of the ACM 32(3), pp. 652–686. Author-hosted publication record and abstract: www.cs.cmu.edu/~sleator/papers/Self-Adjusting.htm
The article introduces splay trees and proves a logarithmic amortized time complexity for their standard operations.
Splay tree 2026-10-31
A splay tree is a binary search tree whose access operations use splaying to move a selected key to the root through tree rotations. It stores no explicit balance or height information. A single access can take linear time, while the standard operations have logarithmic amortized time complexity. The distinction matters: amortized analysis bounds the total cost of an operation sequence, not the worst cost of every individual operation.[ref]
Self-Adjusting Binary Search Trees by Daniel Sleator and Robert Tarjan. Author-hosted abstract: representation, operations and amortized logarithmic bound