In mathematics, an addition chain for computing a positive integer n can be given by a sequence of natural numbers v and a sequence of index pairs w such that each term in v is the sum of two previous terms, the indices of those terms being specified by w:
- v =(v0,...,vs), with v0 = 1 and vs = n
- for each 0< i ≤ s holds: vi = vj + vk, with wi=(j,k) and 0 ≤ j,k ≤ i − 1
Often only v is given since it is easy to extract w from v, but sometimes w is not uniquely reconstructible. An introduction is given by Knuth.
Read more about Addition Chain: Examples, Methods For Computing Addition Chains, Chain Length, Brauer Chain, Scholz Conjecture
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Famous quotes containing the words chain and/or addition:
“It could not have come down to us so far,
Through the interstices of things ajar
On the long bead chain of repeated birth,
To be a bird while we are men on earth,”
—Robert Frost (1874–1963)
“As easy mayst thou fall
A drop of water in the breaking gulf,
And take unmingled thence that drop again,
Without addition or diminishing,
As take from me thyself and not me too.”
—William Shakespeare (1564–1616)