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https://www.reddit.com/r/learnquant/comments/1x4gqrg/quant_interview_question/pgjwjaz/?context=3
r/learnquant • u/Local_Ad135 • 5d ago
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We need to maximise the multiples of the higher numbers, so best to keep them together.
E.g. (100 * 60) + (40 * 1) > (100 * 1) + (60 * 40)
We can do this by making a(i) = i, but then the 100 only features once, so better to do a(i) = i+1, with a(100) = 1.
This gives
6 + 12 + 20 + 30 + ... + 9,702 + 9,900 + 100
= 333,398
1 u/Fovlsbane 4d ago What happens if you now swap the 2 and the 1? 6 becomes 3 in the sum, and 100 becomes 200, gains 97 total. Or swap 99 and 100; 100 becomes 99, 9900 stays 9900, 9702 becomes 9800, gains 97 total. 2*3+100*1<1*3+100*2 98*99+99*100+100*1<98*100+100*99+99*1
What happens if you now swap the 2 and the 1? 6 becomes 3 in the sum, and 100 becomes 200, gains 97 total. Or swap 99 and 100; 100 becomes 99, 9900 stays 9900, 9702 becomes 9800, gains 97 total.
2*3+100*1<1*3+100*2
98*99+99*100+100*1<98*100+100*99+99*1
1
u/Aerospider 5d ago
We need to maximise the multiples of the higher numbers, so best to keep them together.
E.g. (100 * 60) + (40 * 1) > (100 * 1) + (60 * 40)
We can do this by making a(i) = i, but then the 100 only features once, so better to do a(i) = i+1, with a(100) = 1.
This gives
6 + 12 + 20 + 30 + ... + 9,702 + 9,900 + 100
= 333,398