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9 Cards in this Set

  • Front
  • Back

Merge Sort run times

best/worst/average: all big theta n log n

quick sort run times

best/average: big theta n log n


worst case: big theta n^2

bubble sort run times

best/worst/average: big theta n^2

binary search run times

best case: big theta (1)


average case: big theta log n


worst case: big theta log n

insertion sort search

best case: big theta (n)


worst case: big theta n^2


average case: big theta n^2

Big O notation

*represents upper bound-run time will never go over this


*element to the left must be less than element to right


example:


n is an element of O(n^2)


n^3 is NOT an element of O(n^2)

Big Omega notation

*represents the lower bound-run time will never go below this


*element to the left must be greater than element to the right


example:


n^3 is an element of n^2


n is not an element of n^2

Big Theta notation

*represents the tight bound-run time is equal/close to equal


*elements on right and left should be equal


example:


n^2 + sin (n) is an element of n^2

Master Theorem

T(n) = aT (n/b) + f(n) then a = b^d