Deshaw Inc Interview Question for Software Developers
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Apparently DESCO asked it. It was faulty, and I am fixing it. The physics was wrong. A mono pole is an abstract magnet with either the north or the south pole of the magnet.
[ en.wikipedia.org/wiki/Magnetic_monopole ]
Imagine you are given such *n* monopoles, all of the same type, say North type. Thus, all of these repel one another. The force of repulsion follows inverse square law :
[ en.wikipedia.org/wiki/Inverse-square_law ]
That is, given two such monopoles with a distance *r* between them, the force of repulsion between them is given by :
F = ( 1.0 ) / ( r ** 2 )
Now, suppose you are also given an array of *n* number of positions over X axis, like : [ 0, 1, 4, 10 , 21 , .. ] where you need to place the monopoles ( imagine they are hold tight there, and do not move away ).- NoOne October 18, 2016 in United States
After placement, you are given another monopole, of different type S, say. Find positions to place the monopole so that it is stable.
Fixes from the original question :
1. Monopoles exhibit inverse square law, not inverse law.
2. It is impossible to have stable configuration using same type monopole, so one must use another type, repulsion is not stable, attraction is.
( Terrible physics mistakes )
PS. Do not try to do binary search here. Binary search assumption is underlying linearity of the structure, thus, effectively there are proportionate elements in left and right. In the classic cases of sorted array, the expectation is 50/50. But here due to non linearity (inverse square) , it won't work.
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