e-LC011-container.yml · YAML

# Editorial widget: LC 11 Container With Most Water
# Editorial widgets animate ONE specific signature problem at fixed input.
# Preset-only; no randomize, no edit.

id: e-LC011-container
title: "Container With Most Water (LC 11), greedy two-pointer shrink"
type: editorial-single-panel
level: 1
modes: [preset]

# Editorial widgets do not expose user input: the canonical input is the lesson.
caps:
  array_length: { fixed: 9 }       # exactly the canonical input length

commands:
  - name: measureArea
    payload: { l: 'integer', r: 'integer', h_l: 'integer', h_r: 'integer', area: 'integer', best: 'integer' }
    description: "Show min(h[l], h[r]) * (r-l) and compare against running best."
  - name: shrinkShorter
    payload: { which: 'l | r', from_index: 'integer', to_index: 'integer' }
    description: "Advance the pointer on the shorter wall by 1; flash the wall that just got discarded."
  - name: foundBest
    payload: { l: 'integer', r: 'integer', area: 'integer' }
    description: "Latch the best-area pair; cells turn solid green."

static_fallback:
  generator: jsdom
  output: site/static/widgets/e-LC011-container-fallback.svg
  keyframes_used: [0, 2, 4, 8]      # init, the hit at 49, a mid-state, terminate

panels:
  default:
    chapter: "3.0"
    primary_chapter: part-3-pointers-window-prefix/00-two-pointers-opposite
    label: "Container With Most Water, greedy shrink"
    canonical_input: |
      height = [1, 8, 6, 2, 5, 4, 8, 3, 7]
    # Why this input: LC's canonical example. The optimal pair is at indices
    # [1, 8] (values 8 and 7) for area 49, found on step 2. The remaining
    # iterations show why advancing the shorter wall, and only the shorter
    # wall, is the rule: every alternative move strictly shrinks area.
    presets: []                      # editorial widgets are preset-as-canonical-input
    n_steps: 9
    keyframes:
      - step: 0
        kind: init
        state: { l: 0, r: 8, h_l: 1, h_r: 7, area: null, best: 0 }
        narration: "Place pointers at the two ends. l=0 (height 1), r=8 (height 7). Best area so far: 0."
      - step: 1
        kind: measureArea
        payload: { l: 0, r: 8, h_l: 1, h_r: 7, area: 8, best: 8 }
        state: { l: 0, r: 8, area: 8, best: 8 }
        narration: "min(1, 7) * 8 = 8. Best updates to 8. Wall l (height 1) is the shorter; advance l."
      - step: 2
        kind: measureArea
        payload: { l: 1, r: 8, h_l: 8, h_r: 7, area: 49, best: 49 }
        state: { l: 1, r: 8, area: 49, best: 49 }
        narration: "min(8, 7) * 7 = 49. Best updates to 49. The optimal pair, found on the second probe."
      - step: 3
        kind: shrinkShorter
        payload: { which: r, from_index: 8, to_index: 7 }
        state: { l: 1, r: 7, area: null, best: 49 }
        narration: "Wall r (height 7) is now the shorter; advance r to index 7 (height 3)."
      - step: 4
        kind: measureArea
        payload: { l: 1, r: 7, h_l: 8, h_r: 3, area: 18, best: 49 }
        state: { l: 1, r: 7, area: 18, best: 49 }
        narration: "min(8, 3) * 6 = 18. Well below 49. Width has dropped; the bound is the shorter wall."
      - step: 5
        kind: measureArea
        payload: { l: 1, r: 6, h_l: 8, h_r: 8, area: 40, best: 49 }
        state: { l: 1, r: 6, area: 40, best: 49 }
        narration: "min(8, 8) * 5 = 40. Tie on heights; the algorithm advances r (else branch on strict <)."
      - step: 6
        kind: measureArea
        payload: { l: 1, r: 5, h_l: 8, h_r: 4, area: 16, best: 49 }
        state: { l: 1, r: 5, area: 16, best: 49 }
        narration: "min(8, 4) * 4 = 16. Smaller still. Advance the shorter side, r, again."
      - step: 7
        kind: measureArea
        payload: { l: 1, r: 2, h_l: 8, h_r: 6, area: 6, best: 49 }
        state: { l: 1, r: 2, area: 6, best: 49 }
        narration: "Width has collapsed to 1. min(8, 6) * 1 = 6. Best holds at 49."
      - step: 8
        kind: foundBest
        payload: { l: 1, r: 8, area: 49 }
        state: { l: 1, r: 1, area: null, best: 49, result: 49 }
        narration: "Pointers cross. Final answer: 49, the area between walls at indices 1 and 8."

lc_id: 11
difficulty: medium
algorithm: two-pointer-greedy-shrink

notes: |
  Animates the case-analysis proof: at each
  state, advancing the taller wall keeps min(h[l], h[r]) the same or worse
  while strictly shrinking width, so area cannot grow. Only advancing the
  shorter wall opens the possibility of a larger area. The optimal pair is
  found on step 2; the remaining steps confirm no later pair beats it.

  Distinct from chapter widget w-08-two-pointers-3sum, which is the
  configurable two-pointer-on-sorted demo. e-LC011 is preset-only and
  fixed to LC 11's standard test case.