Created
December 5, 2013 07:03
-
-
Save g-i-o-/7801292 to your computer and use it in GitHub Desktop.
So... you have an unsorted array of numbers and need a approximation to the median, but you don't want to waste a lot space nor sort the array, not even partially...
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
def sample_median(X): | |
"Returns an aproximate for the sample median for the array X" | |
n, xmax, xmin = 0, 0, 0 | |
for x in X: # O(x) | |
if n: | |
xmax = max(x, xmax) | |
xmin = min(x, xmin) | |
else: | |
xmax = xmin = x | |
n+=1 | |
a50 = n/2.0 +1 | |
FREC_SIZE=16 | |
below = 0 | |
while True: # O(x log x) | |
Fcount, Fmin, Fmax = [0]*FREC_SIZE, [0]*FREC_SIZE,[0]*FREC_SIZE | |
for x in X: # O(x) | |
if x < xmin or x > xmax: | |
continue | |
x_idx = int((x - xmin) * (FREC_SIZE-1) / (xmax - xmin)) | |
if Fcount[x_idx]: | |
Fmax[x_idx] = max(x, Fmax[x_idx]) | |
Fmin[x_idx] = min(x, Fmin[x_idx]) | |
else: | |
Fmax[x_idx] = Fmin[x_idx] = x | |
Fcount[x_idx] += 1 | |
# print "Fcount:%r\nFmax:%r\nFmin:%r"%(Fcount, Fmax, Fmin) | |
a = below | |
for bin_idx in range(FREC_SIZE): | |
la = a | |
a += Fcount[bin_idx] | |
if a >= a50: | |
# print "turning point in %s (la:%s, a:%s)"%(bin_idx, la, a) | |
xmin, xmax = Fmin[bin_idx], Fmax[bin_idx] | |
below = la | |
break | |
#break | |
if xmax == xmin: | |
return xmax | |
if __name__ == '__main__': | |
import random | |
X = [random.randint(0, 10033) / 10000.0 for x in range(100)] | |
print "X:%r"%X | |
print "Sample median :%r"%sample_median(X) | |
X.sort() | |
lenX = len(X) | |
print "Half of len(X) is %s"%(lenX/2.0) | |
print zip(range(lenX/2-2, lenX/2+3), X[lenX/2 - 2 : lenX/2 + 3]) | |
if lenX%2 == 0: | |
print "len(X) is even, so real median is avg(X[%s:%s]) == avg(%s, %s) = %s"%( | |
lenX/2-1, lenX/2, X[lenX/2-1], X[lenX/2], (X[lenX/2-1]+X[lenX/2])/2.0 | |
) | |
else: | |
print "len(X) is odd, so real median is X[%s] = %s"%(lenX/2 + 1, X[lenX/2 + 1]) |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment