Spreadsheet Formulas with Dependency Updates

Implement spreadsheet_get_results(row_count: int, column_count: int, operations: list[list[str]]) -> list[int].

The spreadsheet initially contains zeros. Process operations in order and return the value produced by every GET.

Operation Format

• ["SET", cell, value] stores the signed decimal integer value in cell and removes any formula previously stored there.
• ["SUM", cell, reference1, ...] stores a dynamic sum formula in cell. Each reference is one cell such as "B3" or an inclusive rectangle such as "A1:C2".
• ["GET", cell] reads the cell's current value.

Input Domain

• 1 <= row_count <= 1,000 and 1 <= column_count <= 26.
• Cell names use columns A through the configured final column and one-based rows.
• 0 <= len(operations) <= 20,000.
• Every operation and reference is valid, and each SUM has at least one reference.
• A SUM operation never creates a direct or indirect dependency cycle.

Output Rules

• Formulas remain live: changing a referenced cell changes all dependent results.
• Each appearance of a cell contributes once, so overlapping or repeated references contribute repeatedly.
• SUM and SET replace the target's prior literal or formula.
• Preserve GET order; return an empty list when there are no GET operations.
• All intermediate and returned values fit signed 64-bit integers.

Constraints

• Do not recompute every spreadsheet cell after each operation.
• Exact values and dependency semantics are required.

Examples

Example 1

Input: row_count = 3, column_count = 3, operations = [["SET","A1","2"],["SUM","C3","A1","A1:B2"],["GET","C3"],["SET","B2","3"],["GET","C3"]]

Output: [4,7]

Example 2

Input: row_count = 2, column_count = 2, operations = [["SUM","B2","A1:A2"],["SET","A1","5"],["GET","B2"],["SET","B2","4"],["SET","A2","7"],["GET","B2"]]

Output: [5,4]

Hint: Store dependency multiplicity

Expand formula references into source-cell counts, and either propagate value deltas through reverse dependencies or evaluate the acyclic graph with invalidation.