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Solving 'The Assignment Problem' with Lambda
The Setup The problem is simple. Given a 'cost matrix', assign tasks to workers to minimize total cost needed to complete the tasks. Workers may not perform more than 1 task. Assignment p...
In attached file PQ Assignment2 generates the required rows only
Though, it's slower than djclements initial approach (PQ Assignment1)
Looked at doing it w/o generating the unecessary rows* - that's been a disaster so far 😞
Attached is consequently djclements' approach, automated when it comes to joining tables
* > 2K with an input table of 25 rows
=LET(
x,DROP(REDUCE(0,ROW(D6:D9),LAMBDA(a,d,VSTACK(a,LET(c,ROW(E6:E9)<>d,h,FILTER(ROW(E6:E9),c),
e,HSTACK(d,h,IF(MUNIT(3),,TOROW(h))),
v,IFNA(e,TAKE(e,1)),i,TOCOL(DROP(v,,2)),j,TAKE(v,,2),
HSTACK( SORTBY(VSTACK(j,j),MOD(SEQUENCE(ROWS(TAKE(v,,2))*2)-1,3)+1),FILTER(i,i))-5)))),1),v,INDEX(D6:F9,x,SEQUENCE(,3)),
s,BYROW(v,LAMBDA(a,SUM(a))),
VSTACK(D5:F5,INDEX(C6:C9,FILTER(x,s=MIN(s))),FILTER(v,s=MIN(s))))
x,DROP(REDUCE(0,ROW(D6:D9),LAMBDA(a,d,VSTACK(a,LET(c,ROW(E6:E9)<>d,h,FILTER(ROW(E6:E9),c),
e,HSTACK(d,h,IF(MUNIT(3),,TOROW(h))),
v,IFNA(e,TAKE(e,1)),i,TOCOL(DROP(v,,2)),j,TAKE(v,,2),
HSTACK( SORTBY(VSTACK(j,j),MOD(SEQUENCE(ROWS(TAKE(v,,2))*2)-1,3)+1),FILTER(i,i))-5)))),1),v,INDEX(D6:F9,x,SEQUENCE(,3)),
s,BYROW(v,LAMBDA(a,SUM(a))),
VSTACK(D5:F5,INDEX(C6:C9,FILTER(x,s=MIN(s))),FILTER(v,s=MIN(s))))