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Tuesday, October 20

Mastermulti-constraint & composite logic

The Binding Circle of Ysmerra Spire

The summoners of Ysmerra Spire hold wild spirits in a chalk binding circle that has room for only so many at once. The Conclave of the Spire posts a bounty for a warden's ledger. The ledger must track which spirits are bound, which have slipped free when their term ran out, and which must be cast out when a new spirit is drawn in.

Write a class BindingCircle. Its constructor takes capacity, an integer >= 0: the most spirits that may be present at once.

Every method takes the current time t, an integer. t never decreases from one call to the next, though several calls may share the same t.

Terms. A spirit bound at time t with duration d (an integer >= 1) is *present* at every time x with t <= x < t + d. At time t + d it is gone, and a gone spirit is forgotten entirely.

Each present spirit has three properties:

  • a power;
  • a summon count;
  • a last-touched mark.

A spirit is *touched* by a bind or by a successful summon. Recency is decided by the order in which operations were made, not by t.

Methods:

  • bind(name, power, duration, t) returns a string.
  • If name is present at t: set its power to power and its term to end at t + duration, and mark it touched. Its summon count is unchanged. Nothing is evicted. Return "".
  • Otherwise, if capacity is 0: store nothing and return "".
  • Otherwise, if the number of spirits present at t equals capacity: evict one present spirit. Choose the one with the fewest summons; break ties by the one touched least recently. Then bind the new spirit with summon count 0, mark it touched, and return the evicted spirit's name.
  • Otherwise: bind the new spirit with summon count 0, mark it touched, and return "".
  • Spirits that left because their term ended are never reported as evicted.
  • summon(name, t) returns an integer.
  • If name is present at t: increase its summon count by 1, mark it touched, and return its power.
  • Otherwise: return -1 and change nothing.
  • count(t) returns the number of spirits present at t.

Names are non-empty strings. Powers are non-negative integers.

  • stateful objects with eviction rules
  • Master

examples

  1. case 1capacity 2; at t=0 bind Ash (power 5, duration 100); at t=1 bind Bram (power 7, duration 100); at t=2 summon Ash; at t=3 bind Cinder (power 9, duration 100)summon Ash returns 5; bind Cinder returns "Bram" (Bram has 0 summons, Ash has 1)
  2. case 2capacity 2; at t=0 bind Ash and bind Bram (duration 50 each); at t=1 summon Ash; at t=2 summon Bram; at t=3 bind Cinderbind Cinder returns "Ash": both have 1 summon, and Ash was touched less recently
  3. case 3capacity 2; at t=0 bind Ash (power 4, duration 5) and Bram (power 6, duration 100); at t=5 summon Ash; at t=6 bind Cindersummon Ash returns -1 because Ash's term ended at t=5; bind Cinder returns "", since Ash left on its own and there was room
  4. case 4capacity 0; bind Ash (power 1, duration 10) at t=0; summon Ash at t=1; count at t=1bind returns "", summon returns -1, count returns 0
reward
540 XP
signature
BindingCircle
not yet run

TypeScript, run as ES2022 — types are stripped, not checked. If a JS engine would run it, so will we.

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  • fewest summons is evicted
  • tie broken by least recent touch
  • rebind refreshes recency and power
  • expired spirits leave quietly at the boundary
  • rebinding after expiry resets summons
  • rebinding a present spirit keeps its summons
  • rebind renews the term
  • capacity zero holds nothing
  • capacity one always evicts the sole spirit
The Binding Circle of Ysmerra Spire · bitwick