A LAMBDA Exercise

Patrick2788 

As variant

weekdayMultiplier=
LAMBDA( weekday, CHOOSE(weekday, 1.5, 1, 1, 1, 1, 1, 1.5) );

weekdayHours= 
LAMBDA( vector, weekday,
    SCAN(0, vector,
        LAMBDA(a,v,
            IF( v= 4, 16, // with simplified holidays
            IF( v = "", 0,
            IF( ISTEXT(v), a, 8*weekdayMultiplier(weekday)) ) ) ) )
);
weekdayPersonHours=
LAMBDA( vector, weekday, name,
    SUM( weekdayHours(vector, weekday)*(vector=name) ));

monthPersonHours=
LAMBDA( month, name,
        REDUCE(0, SEQUENCE(7), LAMBDA( a,v,
            a + weekdayPersonHours( CHOOSECOLS( month,v), v, name) ))
);

GrossPay=
LAMBDA( month, names, rates,
    SCAN(0, names, LAMBDA(a,v, monthPersonHours(month, v) ) )*
    rates
);

Patrick2788 Maybe I'm missing some of the challenge but I didn't use Lambda:

=(1.5*COUNTIFS(july,staff)-0.5*COUNTIFS(WkDays,staff)+COUNTIFS(holiday,staff))*8*rate

I added 2 Names: WkDays = the range of the month M-F and holiday = July 4

Patrick2788 

I was undecided whether to delicately unwrap the calendar format into meaningful arrays or to simply hit it with a blunt instrument, COUNTIFS in the present case.  I came to the conclusion that the latter was sufficient, provided I was allowed to mark the holiday as a named range.

Worksheet formula
= rate * MAP(staff, Hoursλ);

Hoursλ = LAMBDA(s,
    8 * SUM(COUNTIFS(holiday, s), dayRate * BYCOL(july, LAMBDA(day, COUNTIFS(day, s))))
);

dayRate = {1.5, 1, 1, 1, 1, 1, 1.5};

One thing that I would observe about Patrick's original solution, is that 'hours()' is a Lambda function and therefore will accept parameters directly from the helper functions without the use of an additional Lambda to pass parameters.  I only realised that once I had reduced my own formula by naming its Lambda function to be "Hoursλ".

Patrick2788 

I think I made this exercise too easy.  mtarler struck it with a blunt instrument (COUNTIFS) and got the job done.  PeterBartholomew1 - I thought I made this one a pain with the holiday pay but you seem to have resolved this one easily working COUNTIFS into your LAMBDA.

I believe SergeiBaklan has a solution that can be scaled to include 3D referencing.

I had to do it. I've updated the workbook, so it now includes 3 months.  I've made some design changes: the number for the day of the week is now a true date and a list of holidays is included in the summary sheet.

Patrick2788 

This is not an independent solution since I started of by examining SergeiBaklan's solution and only then started to play.  The initial manipulation of the 3D Range is truly amazing, I am only beginning to get to grips with some of the new array shaping functions.

I liked Sergei's use of nested Lambda functions; I am moving towards using such functions wherever possible rather than wherever necessary to improve the structure and self-documenting character of solutions, but I have not got there yet!  I did think the use of SCAN to multiply the hourly rates was something of overkill though.

My formulas were

Worksheet formula
= rate * MAP(staff, BillableHoursλ);

BillableHoursλ=
LAMBDA(name,
    LET(
        stack,      SORT(WRAPROWS(TOCOL(calendar, , 1), 3)),
        dates,      TAKE(stack,,1),
        holiday?,   COUNTIFS(holidays,dates),
        weekend?,   WEEKDAY(dates,2)>5,
        time,       1 + 0.5*weekend? + holiday?,
        staff,      TAKE(stack,,-2),
        onshift?,   BYROW(staff,LAMBDA(s,OR(s=name))),
        SUM( IF(onshift?, 8*time) )
    )
);

Patrick2788 

I have used your challenge as a further exercise.  I note that the formula that Sergei introduced to restructure the 3D Range, that contains the calendar, is recalculated in its entirety once for each staff member.  Provided the calculation is fast that is not a problem, but out of interest I set out to limit the calculation step to a single occurrence.  That meant I could not use a defined Name or a Thunk to pass the restructured array 'stack'.

I could create a monolithic block of code and place the calculation of 'stack' before the MAP that determines the eligible hours for each staff member.  To move away from such monolithic code, I wanted to use a further nested Lambda function.  This could either be defined within the outer Lambda function by using LET, in which case it would be within scope of the formula-local name, or 'stack' itself could be passed as a parameter.  I implemented each, but chose the second option.

GrossPayλ 
= LAMBDA(calendar, names, rate,
    LET(
        stack, SORT(WRAPROWS(TOCOL(calendar, , 1), 3)),
        rate * MAP(staff, EquivalentHoursλ(stack))
    )
);

EquivalentHoursλ 
= LAMBDA(stack,
    LAMBDA(name,
        LET(
            dates,    TAKE(stack, , 1),
            holiday?, COUNTIFS(holidays, dates),
            weekend?, WEEKDAY(dates, 2) > 5,
            time,     1 + 0.5 * weekend? + holiday?,
            assigned, TAKE(stack, , -2),
            onshift?, BYROW(assigned, LAMBDA(s, OR(s = name))),
            SUM(IF(onshift?, 8 * time))
        )
    )
);

In order to pass the additional parameter into the MAP construct I needed to define the function 'EquivalentHoursλ' in a Curried form, passing one parameter at a time by using multiple nested LAMBDAs.

I am sorry if this reads like complete gobbledegook; I have tried my best to express the ideas clearly, but I am not convinced I have succeeded!