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task_graph__binary_tree__heap_property_violation_label

Program Contract

Program: label(child_node(heap_property_violation(binary_tree))); scene=binary_tree; scope=heap_property_violation_label

Candidate set: the visible graph, tree, network, route, matrix, table, node, edge, label, weight, path, and option elements inside the heap_property_violation_label objective scope. Operands: visible scene state and prompt-bound operands named by child_node, heap_property_violation, binary_tree, heap_property_violation_label. Operation: evaluate label over the candidate set using the visible graph structure, labels, weights, directions, reachability, paths, connectivity, or option-selection constraints encoded in the program expression; generation enforces a unique final answer. Output binding: answer uses the string schema; generation binds a unique final answer. Annotation witnesses: annotation uses the point_map schema; the prompt/annotation contract defines the minimal visual witnesses. Query ids: single.

Reasoning Operations

Families: topology, matching

Summary

  1. Domain: graph
  2. Scene: binary_tree
  3. Scene: relation
  4. Task id: task_graph__binary_tree__heap_property_violation_label
  5. Objective: find the child node that violates a min-heap property.

Query IDs

  1. single: find the child node whose key is smaller than its parent key.

Annotation

  1. Answer type: string.
  2. Annotation schema: point_map.
  3. Annotation uses keys parent and child, with each value a node-center [x,y] pixel point.

Generation Notes

  1. Instances render a complete numeric-key binary tree with exactly one min-heap violation.
  2. Default node count is 7..10 for this task.
  3. The violating child is sampled with a larger numeric gap below its parent so the unique heap violation is visually easier to compare.
  4. The renderer is the shared top-down binary_tree scene.
  5. Title and node labels use the role-appropriate shared font pool and readable text styles with recorded contrast metadata.
  6. Binary-tree rendering includes sampled tree treatments, node shapes/colors, light optional non-answer context text outside the tree content, bounded content jitter before projection, and scene-derived connector styles.