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task_graph__binary_tree__bst_path_operation_label

Program Contract

Program: label(path_terminal(binary_search_tree_operation(tree, operation, key))); scene=binary_tree; scope=bst_path_operation_label

Candidate set: the visible graph, tree, network, route, matrix, table, node, edge, label, weight, path, and option elements inside the bst_path_operation_label objective scope. Operands: visible scene state and prompt-bound operands named by path_terminal, binary_search_tree_operation, tree, operation, key, binary_tree, bst_path_operation_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_sequence schema; the prompt/annotation contract defines the minimal visual witnesses. Query ids: single.

Reasoning Operations

Families: topology, state_update

Summary

  1. Domain: graph
  2. Scene: binary_tree
  3. Scene: relation
  4. Task id: task_graph__binary_tree__bst_path_operation_label
  5. Objective: answer label-valued binary-search-tree path operation queries.

Query IDs

  1. bst_search_terminal_label: search for a key in a BST and answer the final visited node label.
  2. bst_insert_parent_label: insert a missing key into a BST and answer the existing parent node label.

Annotation

  1. Answer type: string.
  2. Annotation schema: point_sequence.
  3. Annotation points are the ordered node-center search or insertion path from the root through the answer node.

Generation Notes

  1. Instances render numeric keys in a bounded-depth binary search tree.
  2. Default node count is 7..13.
  3. The renderer is the shared top-down binary_tree scene.
  4. Title and node labels use the role-appropriate shared font pool and readable text styles with recorded contrast metadata.
  5. 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.