Eager Spreadsheet Formulas with Constant-Time Reads

Implement a spreadsheet with `set_cell`, `get_cell`, arithmetic formulas, dependency updates, and circular-reference rejection. Each successful write must leave computed values ready so a subsequent `get_cell` is a constant-time cached read. Implement `eager_sheet(operations: string[][]) -> string[]`. Each row is `["set", cell, raw]` or `["get", cell]`. Return one string per operation: - A successful set returns `"OK"`. - A set that would introduce a circular reference returns `"CYCLE"` and leaves the previous sheet unchanged. - A get returns the cell's computed integer in canonical decimal notation, with no leading plus or leading zeros; zero is `"0"`. ### Formula and edit contract The source describes formulas and dependency/cycle handling but does not give a grammar. This practice version explicitly uses: - Cell names are uppercase letters followed by a positive decimal row number with no leading zeros, such as `A1` or `AA10`. - Raw values are signed integer strings or formulas beginning with `=`. - Formula grammar is `term (('+' | '-') term)*`, where a term is a nonnegative integer or a cell reference. Spaces may surround tokens. Unary signs and parentheses inside formulas are excluded. - Unset cells evaluate to zero. Repeated references contribute repeatedly, so `=A1+A1` counts the value twice. - Set replaces the entire previous definition, including its dependency links. It may change a literal to a formula or a formula to a literal. - Direct and indirect cycles are rejected before the edit becomes visible. A failed set preserves both the old definition and every previously computed value. - On a successful set, update every affected dependent value before processing the next operation. Implement get using stored results, without dependency traversal on reads. ### Constraints - There are at most 500 operations and at most 100 terms per formula. - All names and expressions are syntactically valid. - Numeric tokens, stored literals, and all intermediate arithmetic results for an acyclic prospective sheet fit in a signed 32-bit integer. - The sheet starts empty, and operations are processed sequentially. - Cycle-error serialization, unset-cell behavior, grammar, and bounds are explicit practice assumptions. The constant-time-read requirement and the need to consider write-versus-read evaluation come from the reported task. ### Examples ```text operations = [ ["set","A1","2"], ["set","B1","=A1+1"], ["set","C1","=A1+B1"], ["set","A1","5"], ["get","C1"] ] result = ["OK","OK","OK","OK","11"] ``` ```text operations = [ ["set","A1","=B1"], ["set","B1","=A1+1"], ["get","A1"], ["set","A1","3"], ["set","B1","=A1+1"], ["get","B1"] ] result = ["OK","CYCLE","0","OK","OK","4"] ``` The rejected edit in the second example leaves `B1` unset. Replacing `A1` with a literal later removes the dependency that would have completed the cycle. ```hint Keep both graph directions One graph direction identifies a formula's inputs. The other identifies which cached values can change after an input edit. Recompute dependents only after their changed inputs are ready. ```