The median m of a sequence of n elements is the element that would fall in the middle if the sequence was sorted. That is, e ≤ m for half the elements, and m ≤ e for the others. Clearly, one can obtain the median by sorting the sequence, but one can do quite a bit better with the following algorithm that finds the kth element of a sequence between a (inclusive) and b (exclusive). (For the median, use k = n/2, a = 0, and b = n.) select(k, a, b) Pick a pivot p in the subsequence between a and b. Partition the subsequence elements into three subsequences: the elements p Let n1, n2, n3 be the sizes of each of these subsequences. if k < n1 return select(k, 0, n1). else if (k > n1 + n2) return select(k, n1 + n2, n). else return p. c++
The median m of a sequence of n elements is the element that would fall in the middle if the sequence was sorted. That is, e ≤ m for half the elements, and m ≤ e for the others. Clearly, one can obtain the median by sorting the sequence, but one can do quite a bit better with the following
select(k, a, b)
Pick a pivot p in the subsequence between a and b.
Partition the subsequence elements into three subsequences: the elements <p, =p, >p
Let n1, n2, n3 be the sizes of each of these subsequences.
if k < n1
return select(k, 0, n1).
else if (k > n1 + n2)
return select(k, n1 + n2, n).
else
return p. c++
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