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how to solve this allocation problem
suppose i have a table with three columns
first one denotes the sequence of items to pick each person allowed to pick (here only two and same seq, the front ones will have higher dollar reward) whenever available, rewards is the dollar amount corresponding the sequence of items to pick and column three is whether they allow to pick
since person 1 can pick item 0 which has 300 as he is allowed to pick. then second person cannot pick item 0 as each item for the amount of reward is unique. so he has to skip 1 and second element is 1 which he is allowed to pick then he picks item 1.
The question is if i have a table and row 1 correspond to first person and so on, how can i output the item number each person pick?
pickSeq: (0;1;2);(0;1;2)
rewards:(300;200;100);(300;200;100)
allowToPick:(true;true;true);(true;true;true)
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2 Replies
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If you had the following scenario, you could sort the reward desending, sort the pickSeq ascending and use indices to solve for your problem:
q)n:10
q)people:([]pickSeq:0+til n;person:`$"person",/:string 1+til n;allowedToPick:n?01b)
q)people pickSeq person allowedToPick ------------------------------ 0 person1 1 1 person2 1 2 person3 1 3 person4 1 4 person5 0 5 person6 0 6 person7 0 7 person8 1 8 person9 0 9 person10 0
q)rewards:([]prize:(1+til 10)*100)
q)rewards prize ----- 100 200 300 400 500 600 700 800 900 1000
q)(update ind:i from xdesc[`prize;rewards]) lj `ind xkey update ind:i from select person from xasc[`pickSeq;people] where allowedToPick prize ind person ----------------- 1000 0 person1 900 1 person2 800 2 person3 700 3 person4 600 4 person8 500 5 400 6 300 7 200 8 100 9You could also extract the person and their prize as follows:
q){if[1=count x;x:enlist x]; if[1=count y;y:enlist y]; y!x iasc y}[exec desc prize from rewards;] exec person from xasc[`pickSeq;people] where allowedToPick person1| 1000 person2| 900 person3| 800 person4| 700 person8| 600 -
q)show people:([]pickSeq:neg[n]?n;person:`$"person",/:string 1+til n;allowedToPick:n?01b) pickSeq person allowedToPick ------------------------------ 1 person1 0 8 person2 1 5 person3 0 7 person4 1 0 person5 0 3 person6 1 6 person7 0 4 person8 0 2 person9 1 9 person10 0
q)show prize:100*1+til 8 100 200 300 400 500 600 700 800The winners in order:
q)`pickSeq xasc select from people where allowedToPick pickSeq person allowedToPick ----------------------------- 2 person9 1 3 person6 1 7 person4 1 8 person2 1
And their rewards:
q){select person,reward:count[x]#desc prize from x}`pickSeq xasc people where people`allowedToPick person reward -------------- person9 800 person6 700 person4 600 person2 500Or in vector form:
q){x!count[x]#desc prize}{x iasc y}. flip people[where people`allowedToPick;`person`pickSeq] person9| 800 person6| 700 person4| 600 person2| 500Above,
where people`allowedToPickfinds the winners; and{x iasc y}.sorts the winners names by pick order. The vector form has less work to do:q)ts:1000 {select person,reward:count[x]#desc prize from x}`pickSeq xasc people where people`allowedToPick 12 3184
q)ts:1000 {x!count[x]#desc prize}{x iasc y}. flip people[where people`allowedToPick;`person`pickSeq] 3 3312
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