To summarize the work you have done above, write a function Percentages$\_$CSA using a LAMBDA

that inputs a column of names $($e$.$g$.,$ season names$)$ and produces a row of percentages for the

alphabetically sorted unique names. The percentages specify the fraction of total rows containing

a unique name $($e$.$g$.,$ Winter$).$ Test your function with the Season data in the Festivals worksheet.

Notice that the length of the row of percentages depends on the data and needs to be computed

dynamically. Use two implementations to write your function Percentages$\_$CSA, the first using

FILTER and the second using the function Percentages$\_$from$\_0\_1\_$table$\_$CSA given below. We

give you almost a complete FILTER solution because FILTER will be covered in detail in the next

topic. Call the function with the FILTER implementation Percentages$\_$FILTER$\_$CSA. Call the

function with the $0\_1\_$table as an intermediate result Percentages$\_0\_1\_$table$\_$CSA.

$=$LAMBDA$($Names$,$LET$($

SortedUnique,SORT$($UNIQUE$($UNKNOWN$\_1)),$

CountOne,LAMBDA$($s$,$ROWS$($FILTER$($Names$,$Names$=$s$))),$

CountsFILTER,MAP$($SortedUnique$,$ UNKNOWN$\_2),$

Percentages,CountsFILTER$/$SUM$($UNKNOWN$\_3),$

Show,IFERROR$($HSTACK$($SortedUnique$,$CountsFILTER,Percentages$),""),$

Result,TRANSPOSE$($CHOOSECOLS$($Show$,1,3)),$

Result$))(\{"$Winter$"$;"Summer";"Winter";"Spring";"Fall";"Winter";"Summer"$\})$

You complete this LAMBDA by changing UNKNOWN$\_1,$ UNKNOWN$\_2,$ UNKNOWN$\_3$ to the

correct names. For example, UNKNOWN$\_1$ needs to be the formal argument Names.

To test the function CountOne, I used the following LAMBDA.

$=$LAMBDA$($Names$,$LET$($

Comment$1,$"FunctionToTest",

CountOne,LAMBDA$($s$,$ROWS$($FILTER$($Names$,$Names$=$s$))),$

PartialResult$1,$ Names$=$"Winter",

PartialResult$2,$FILTER$($Names$,$Names$=$"Winter"$),$

Test$\_1,$ CountOne$("$Winter$"),$

Test$\_2,$ CountOne$("$Summer$"),$

ArrayHeaders,HSTACK$("*$Names$","*$PartialResult$1","*$PartialResult$2","*$Test$\_1","*$Test$\_2"),$

Show,IFERROR$($VSTACK$($ArrayHeaders$,$

HSTACK$($Names$,$PartialResult$1,$ PartialResult$2,$ Test$\_1,$ Test$\_2)),""),$

Show$))(\{"$Winter$"$;"Summer";"Winter";"Spring";"Fall";"Winter"$\})$

The above LAMBDA for testing uses one Names column with six rows to show partial results

inside CountOne and run CountOne for "Winter" and "Summer". Your LAMBDA should look

like LAMBDA$($Names$,$ LET$(...)),$ where in the LET, you compute the intermediate results that

eventually lead to the final result. Document your function Percentages$\_$FILTER$\_$CSA using the

design recipe linked in the syllabus prefix.

To simplify the implementation of your function Percentages$\_0\_1\_$table$\_$CSA, we provide you

with a function called Percentages$\_$from$\_0\_1\_$table$\_$CSA. It takes a table of $0$ and $1$ as input,

and it returns the percentage of the sum of all $1$s per column across all columns.

$=$LAMBDA$($T$\_0\_1,$ LET$($

counts,BYCOL$($T$\_0\_1,$LAMBDA$($D$,$SUM$($D$))),$

percentages,counts$/$SUM$($counts$),$

percentages$))$

Learning to understand a formula written by someone else is a common task. Your task is to

learn from the Excel documentation or ChatGPT how BYCOL is defined and to use it to imple$-$

ment Percentages$\_$CSA by first producing a table of $0$ and $1$ and then processing it with Percent$-$

ages$\_$from$\_0\_1\_$table$\_$CSA. In other words, we break Percentages$\_$CSA into two steps: producing

and consuming a table of $0$ and $1.$

Put the function Percentages$\_$from$\_0\_1\_$table$\_$CSA into a separate worksheet but you don$$t have

to formally document it using the design recipe.