Spreadsheet with Formulas

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Problem

Spreadsheet engines are a classic dependency-tracking problem: change one cell and every cell that depends on it must update. You will implement the engine in two phases - lazy evaluation on read, then eager propagation on write - and add cycle detection to both.

Each cell holds an expression: a literal number ("5", "-3", "2.5"), a cell reference ("A1"), or arithmetic combining them (+, -, *, / with standard precedence). Unset cells evaluate to 0. Division by zero propagates ZeroDivisionError.

Level 1 - Evaluate on write

set_cell parses and evaluates the formula immediately, resolving cell references and caching the result; get_cell returns that cached value (an unset cell is 0). Errors surface at write time: dividing by zero raises ZeroDivisionError, and a self-reference (A1 = A1) raises CycleError.

class CycleError(Exception):
    pass

Example:

sheet.set_cell("A1", "7")
sheet.set_cell("A2", "A1")
sheet.get_cell("A2")   # 7.0 -- A1 was resolved when A2 was set

Level 2 - Propagate changes to dependents

When a cell changes, every cell that transitively depends on it must be recomputed too, in dependency order - so re-setting an input updates all of its downstream cells. get_cell stays a single dict lookup.

Example:

sheet.set_cell("A1", "1")
sheet.set_cell("A2", "A1 * 2")
sheet.set_cell("A1", "10")
sheet.get_cell("A2")   # 20.0 -- A2 already propagated when A1 changed

Level 3 - Cycle detection on set_cell

With eager propagation, a cycle would cause infinite recursion. Detect cycles before committing the new formula. If the update would introduce a cycle, raise CycleError and leave the spreadsheet unchanged.

Example:

sheet.set_cell("A1", "5")
sheet.set_cell("A2", "A1")
sheet.set_cell("A1", "A2")   # raises CycleError; sheet unchanged
sheet.get_cell("A1")         # still 5.0

Mastery checklist

Check	Why it matters
Unset cell defaults to 0, doesn't raise	Mirrors Excel; lets references-into-the-future work
Cycle detection on `set_cell`, not just `get_cell`	Otherwise infinite recursion when eager propagation kicks in
Failed `set_cell` leaves the sheet unchanged	Standard transaction semantics
Recompute downstream in topological order	A cell must be recomputed after its dependencies, never before
Operator precedence: `*`/`/` before `+`/`-`	The most common parser bug; left-to-right is wrong for `"2 + 3 * 4"`

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