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open ear decomposition family

For one FULLY CAPTURED labelled simple undirected graph n1..4 on0..n-1, reconstruct EVERY ordered OPEN EAR DECOMPOSITION covering ALL originaledges and ALL originalvertices. edge_mask bitk encodes unorderedpair(u,v),u<v, in numeric lexorder. First ear is a simplecycle with at least3vertices, represented by a closed vertexlist. Canonicalize its rotation/direction by starting at the smallestvertex and choosing lexicographically smaller traversal. Every later ear is a nonempty simplepath with.

POST https://datenvertrag.halowerk.com/v1/open-ear-decomposition-family

Eingaben

Felder des veröffentlichten Eingabeschemas
FeldTypPflichtBeschreibung
nSiehe SchemaJa
edge_maskSiehe SchemaJa
claimSiehe SchemaJa
Vollständiges Eingabeschema anzeigen
{
  "type": "object",
  "properties": {
    "n": {
      "anyOf": [
        {
          "type": "integer",
          "minimum": 1,
          "maximum": 4
        },
        {
          "type": "null"
        }
      ]
    },
    "edge_mask": {
      "anyOf": [
        {
          "type": "integer",
          "minimum": 0,
          "maximum": 63
        },
        {
          "type": "null"
        }
      ]
    },
    "claim": {
      "anyOf": [
        {
          "type": "object",
          "properties": {
            "decompositions": {
              "type": "array",
              "items": {
                "type": "array",
                "items": {
                  "type": "array",
                  "items": {
                    "type": "integer",
                    "minimum": 0,
                    "maximum": 3
                  },
                  "minItems": 2,
                  "maxItems": 5
                },
                "minItems": 1,
                "maxItems": 6
              },
              "minItems": 0,
              "maxItems": 64
            },
            "count": {
              "type": "integer",
              "minimum": 0,
              "maximum": 128
            },
            "ear_count_histogram": {
              "type": "array",
              "items": {
                "type": "integer",
                "minimum": 0,
                "maximum": 128
              },
              "minItems": 7,
              "maxItems": 7
            }
          },
          "required": [
            "decompositions",
            "count",
            "ear_count_histogram"
          ],
          "additionalProperties": false
        },
        {
          "type": "null"
        }
      ]
    }
  },
  "required": [
    "n",
    "edge_mask",
    "claim"
  ],
  "additionalProperties": false
}

Originalschema öffnen

Veröffentlichtes Eingabebeispiel

{
  "n": 1,
  "edge_mask": 0,
  "claim": {
    "decompositions": [],
    "count": 0,
    "ear_count_histogram": [
      0,
      0,
      0,
      0,
      0,
      0,
      0
    ]
  }
}

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Quelle dieser Seite: der veröffentlichte HALOWERK-Katalog. Stand: 2026-11-07, 02:42 UTC.

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