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

operations = [
 ["set","A1","2"],
 ["set","B1","=A1+1"],
 ["set","C1","=A1+B1"],
 ["set","A1","5"],
 ["get","C1"]
]
result = ["OK","OK","OK","OK","11"]

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.