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Kauratuba's Multiplication Algorithm
Input / Output
IN: two n digit numbers
OUT: numbers multiplied
Kauratuba's Multiplication Algorithm
Runtime
(worst-case
deterministic unless
otherwise specified)
O(n^1.6)
Kauratuba's Multiplication Algorithm
Implementation
Split numbers into four
n/2-digit multiplication, make
three recursive calls and use
FOIL cleverly to get
recurrence of T(n) = 3T(n/2)
+ O(n).
Merge
Input / Output
IN: two sorted lists
OUT: merged sorted list
Merge
O(n)
Merge
Two pointers moving across
the two lists to decide which
number goes next.
Mergesort
IN: unsorted list
OUT: sorted list
Mergesort
O(n log n)
Mergesort
Mergesort
Partition
Partition
Partition
Partition