Finding The Median

September 11, 2015

The median of an array is the value in the middle if the array was sorted; if the array has an odd number of items n, the median is the (n+1)/2’th largest item in the array (which is also the (n+1)/2’th smallest item in the array), and if the array has an even number of items n, the median is the arithmetic average of the n/2’th smallest item in the array and the n/2’th largest item in the array. For instance, the median of the array [2,4,5,7,3,6,1] is 4 and the median of the array [5,2,1,6,3,4] is 3.5.

Your task is to write a program that takes an array of 8-bit integers (possibly but not necessarily in sort) and finds the median value in the array; you should find an algorithm that takes linear time and constant space. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

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