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August 22, 2008, 01:31

Nice summary. Your pseudo-code for the recursive power algorithm is not quite right. As written, it is still O(n). You don't get the benefit if you make each recursive call twice. For the O(log n) version, try:

Recursive-Power(x, n):
if n == 1
return x
if n is even
y = Recursive-Power(x, n/2)
return y*y
y = Recursive-Power(x, (n-1)/2)
return y*y*x

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