How to Use Nested Thunks in Excel LAMBDA for Combinations
Question details
The user needs to generate every actual combination of m selected objects from n using advanced Excel functions like LAMBDA, SCAN, and REDUCE, rather than just calculating the total combination count.
- Product
- Microsoft Excel
- Device & OS
- not provided
- Scenario
- Generating comprehensive, multi-dimensional lists of combinations natively within a spreadsheet using dynamic arrays and advanced programming concepts.
- Observed behavior
- Generating arrays of arrays natively fails because REDUCE cannot handle multiple array outputs directly. Nested thunks are required to wrap arrays into single unevaluated values so REDUCE can process complete rows without error.
Ensure you are using a version of Excel that fully supports dynamic array functions (such as LAMBDA, SCAN, and REDUCE). Keep in mind that generating massive arrays can significantly impact spreadsheet performance.
Understand and Create a Basic Thunk
Before generating combinations, you must learn to create a thunk, which stores an array inside an unevaluated function to prevent Excel from expanding it prematurely.
A thunk is essentially an unevaluated LAMBDA function that encapsulates an array. It stores the array as a single value and only returns the evaluated array when explicitly called.
In your name manager or formula bar, construct a thunk using the syntax: `=LAMBDA(x, LAMBDA(x))`. This tells Excel to hold the value `x` until the inner LAMBDA is called.
Pass your desired array or combination list into the thunk variable. The array is now stored as a single, actionable object.
When you need to retrieve the array inside your REDUCE or SCAN iteration, evaluate the thunk by appending empty parentheses `()` to the thunk's name.
Generate Combinations Using REDUCE and Nested Thunks
Use nested thunks to wrap individual combination lists and complete rows within a two-dimensional array, allowing REDUCE to process them without throwing an array constraint error.
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Frequently Asked Questions
What exactly is a 'thunk' in Excel?
A thunk is an advanced programming concept adapted for Excel. It is an unevaluated LAMBDA function that encapsulates an array, storing it as a single callable object. It only 'unpacks' or evaluates the array when it is explicitly called with empty parentheses '()'.
Why use nested thunks instead of standard dynamic arrays?
Excel's calculation engine does not natively support 'arrays of arrays'. If a function like REDUCE tries to return multiple separate arrays, Excel throws a value error. Nested thunks bypass this by tricking Excel into treating the wrapped arrays as single values.
Can I generate combination lists without using the COMBIN function?
Yes. While COMBIN(n,m) only calculates the total numerical count of possible combinations, using advanced combinations of LAMBDA, SCAN, REDUCE, and nested thunks allows you to generate and display the actual itemized lists of every combination.
What are the limits of generating combinations in a spreadsheet?
The output is heavily restricted by spreadsheet capacity constraints (a maximum of 1,048,576 rows) and computational memory. In practical applications using nested thunks, the upper limit for returning actual combinations is roughly 200,000 before the application freezes or crashes.
