Question: For n distinct elements with positive weights x 1 , x 2 , dots, x n with positive weights w 1 , w 2 ,

For n distinct elements with positive weights x1,x2,dots,xn with positive weights w1,w2,dots,wn such that
i=1nwi=1 the weighted lower median is the element xk such that
xi>xk?wi12x1,x2,dots,xnwi=1ni=1,2,dots,nnO(nlogn)O(n)??
For n distinct elements with positive weights x 1

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