Function result of adding or updating children pairs of the node at backwards index index in tree tree

tree

Format:

result of adding or updating children pairs of the node at backwards index index in tree tree

Input:

Output:

Conditional properties that reference this function:

• if the following are true:

  • ((length of stack tree) - 1) - index = back_i
  • the element at index back_i of stack tree = node (value, distance, previous)
  • result of splitting pairs into nodes that exist in the tree tree and new nodes = pair (exists, new)
  • result of updating nodes exists in tree tree with parent index index and parent distance distance = updated

  then result of adding or updating children pairs of the node at backwards index index in tree tree = result of pushing nodes new into tree updated where parent is index and parent distance is distance

  (link)

• if the following are true:

  • children of the node at backwards index i of tree tree in graph graph = children
  • result of adding or updating children children of the node at backwards index i in tree tree = new_tree

  then output of the shortest_path function where the input graph is graph, backwards index is i, and tree is tree = output of the shortest_path function where the input graph is graph, backwards index is (i + 1), and tree is new_tree

  (link)

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