METYCSSA (#5): Mergesort

• Mergesort algorithm

  • split list in half, sort first half, sort second half, merge together

• T(1) <= b

T(n) <= 2T(n/2) + cn if n > 1

• Analysis

T(n) <= 2T(n/2) + cn

<= 2(2T(n/4) + c(n/2)) + cn

= 4T(n/4) + cn + cn

<= 4(2T(n/8) + c(n/4)) + cn + cn

= 8T(n/8) + cn + cn + cn

<= 2kT(n/2k) + kcn (extrapolating 1 < k ? n)

<= nT(1) + cn log n (for 2k = n or k = log n)

• T(n) ?

Previous slide

Next slide

Back to first slide

View graphic version