Spreadsheet III

Requirements

• Export Spreadsheet as named and default. Expose set(cell, value), get(cell), and clear(cell). Cell addresses contain one or more letters followed by a positive row integer without leading zeros; trim surrounding whitespace and normalize letters to uppercase. Invalid addresses throw TypeError. Numeric values must be finite.
• set accepts a finite number or a formula string starting with = after trimming. Formulas contain decimal number literals or cell addresses separated by +, -, *, or /. Evaluate operators strictly left to right, without normal arithmetic precedence: =2+3*4 is 20. Whitespace between tokens is allowed.
• Decimal literals may have a leading minus and may use .5 or 2. forms. No whitespace is allowed between a numeric minus sign and its digits. Support subtraction of a negative literal, such as =1--2. No unary plus, negative cell reference, exponent notation, parentheses, ranges, functions, or implicit multiplication is required. Malformed formulas throw SyntaxError when set and leave any previous value unchanged.
• Missing or cleared cells read as 0. References are live: changing a dependency changes the next get result. Formula cells can reference other formulas, forward references, and repeated dependencies. Every get uses current state; memoization must not become a stale cache.
• Retain the exact left-to-right arithmetic grammar from version II. Add dependency-aware persistent caching: cache only successful numeric reads, and invalidate a changed/cleared cell and all its transitive dependents. Keep cached values for unrelated cells. References to currently missing cells still form dependency edges, so later writes invalidate formulas that used the earlier zero.
• set must reject direct or indirect cycles with RangeError before committing. Use the candidate formula’s references against the current graph. A rejected cyclic or malformed write leaves the previous value, dependency edges, and cached results intact. This version detects cycles during writes rather than waiting for get.
• When replacing a formula or clearing a cell, remove its old outgoing dependency edges and add the candidate edges on successful set. Keep incoming edges from other cells even when the referenced cell is cleared. Repeated references count as a single graph edge while still contributing repeatedly during evaluation.
• Division by zero and nonfinite intermediate results throw RangeError during get; do not cache failures. Setting a previously missing/zero dependency or clearing a formula must let valid reads recover. Independent Spreadsheet instances have separate values, graphs, and caches.
• No UI, HTML, CSS, eval, external parser, ranges, parentheses, functions, asynchronous recalculation, or ordinary operator precedence is required. The dependency graph may contain forward references but must remain acyclic after every successful write.

Examples

Input: const s=new Spreadsheet(); s.set("B1","=A1+2"); s.get("B1"); s.set("A1",5); s.get("B1");
Output: 2, then 7 after invalidating the dependent cache.

Input: s.set("A1","=B1+1")
Output: Throws RangeError and retains the previous A1 value because B1 already depends on A1.