The Surveyor's Crooked Field Notes

Pinned by the door, in a surveyor's hand.

The terraces above bitwick were levelled last autumn, one line of the notebook per measurement, each line saying how high one stone sits relative to another. Rain got into the book: some lines can no longer be read as measurements at all, and some disagree with lines written earlier. The stonewright needs the differences that still hold.

Write resolveLevels(notes, queries). notes is a list of strings; queries is a list of two-element lists of strings. Return a list with one entry per query, in order — each entry an integer or null (None in Python).

Well-formed notes. Split a note on single space characters (so "a b" yields three pieces, the middle one empty). The note is well-formed only if this yields exactly five pieces t0 t1 t2 t3 t4 with:

• t0 and t4 non-empty — the two stone names, compared exactly;
• t1 equal to is;
• and either t2 a run of one or more digits 0–9 (leading zeros allowed) together with t3 equal to above or below, or t2 equal to level together with t3 equal to with.

A well-formed note asserts, writing h for height in hands and n for the value of t2:

• A is n above B: h(A) = h(B) + n
• A is n below B: h(A) = h(B) − n
• A is level with B: h(A) = h(B)

Accepting. Work through notes in order. Ignore any note that is not well-formed. Ignore any well-formed note whose assertion contradicts the assertions already accepted; a note that merely restates something already forced is accepted. An ignored note has no effect whatsoever.

Answering. For a query [A, B], the entry is h(A) − h(B) when the accepted notes force that value, and null when they do not. If A and B are the same string, the entry is 0, even when that name appears in no accepted note.