Sorted Merge

Pick the smaller of two lists and continually copy

Divide and Conquer

partition the input [two equal sized parts] recursively sort each of the partitions merge the partitions #mergeSort

eg

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19

4 1 7 3 8 6 5 2
---------------
4 1 7 3      8 6 5 2
4 1    7 3    8 6     5 2


4    1     7    3    8    6    5    2 //lists of size one! all in order... xd

^    ^     ^    ^    ^    ^    ^    ^
[1][4]     [3][7]    [6][8]    [2][5]

^^^^^^^^^^^^^^^^^    ^^^^^^^^^^^^^^^^
[1347]               [2568]

// find the smallest of the list
1234567 8


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Time Complexity

Split arrays in two halves, constant recombine – N

T(N) = N + 2T(N/2)

let N := 2^N T(2^N) = 2^N + 2T(2^N / 2) = 2^N + 2T(2^(N-1))

divide by 2^N

T(2^N) / 2^N = 1 + 2T(2^(N-1)) / 2^N = 1 + T(2^(N-1))/ 2^(N-1)

…

= N

T(2^N) = 2^N N T(N) = N log_2 N

Bottom-Up Merge Sort
// a non-recursive
// linear n log n
useful if more data > memory available
Quick Sort
Best pivot?? Median value
Median of Three partitinoning
Pick 3 values
pick the median
quicksort > mergesort generally
3 items, 3! = 6 permutations