Define “cyclic data structures”

Question

At the JSON site it says

JSON does not support cyclic data structures, so be careful to not give cyclical structures to the JSON stringifier.

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Answer 1

I guess the textbook example of a cyclic structure is the doubly-linked list. Each element points to the previous and next elements in the list. This means each element forms a cycle with the previous and next element.

A --> B  --> C
A <-- B  <-- C

(Here each A, B, C although written twice is one object.)

A points to B, as next in the list. B points to A as previous in the list. So there is a cycle from A to B and back to A. The same is true for every element in the list, with elements not at the head or tail beloning to two cycles.

One solution to serializing lists like this is to use IDs to represent each object. This removes the cycles in the structure. We could then write out

  list: {
     items:
      { id:"a", value1: ... etc },
      { id:"b", values .... },
      { id:"c", values .... }
     links:
       { elem:"a", next:"b" },
       { elem:"b", next:"c", prev: "a"},
       { elem:"c", prev:"b" }
  }