CS 162 Intro to Programming II

1. CS 162Intro to Programming II MergeSort

2. MergeSort • Suppose you have 2 sorted arrays • How do you merge them into a sorted array? • Just look at the first element in both arrays • Put the smaller element into the new array. • Then look at the next element in the array that the smaller element came from and compare with the current element in the other array • Repeat… 4 15 8 16 42 23

3. Merging 4 4 4 15 4 15 4 4 15 4 15 8 16 8 16 8 16 16 8 8 8 42 23 42 23 23 42 23 42 15

4. Merging 15 4 16 15 16 4 4 15 4 16 4 4 16 8 23 16 8 16 23 8 8 8 8 42 23 15 42 23 15 23 15 42 42 The complexity of merge sort is O(n)

5. MergeSort • But wait a second…you aren’t given two already sorted arrays • Recursion to the rescue! • Keep dividing the array in half (until the subarraysize is 1) • Asubarray of size 1 is sorted • Merge the sorted halves together

6. MergeSort Illustrated 3 1 7 4 2 2 5 6 2 6 6 7 5 7 1 5 2 3 2 1 3 2 4 4 5 4 1 2 3 6 2 7

7. MergeSort Illustrated 3 1 7 4 2 2 5 6 6 7 6 7 2 3 1 1 4 2 2 4 5 3 5 2 2 4 1 2 3 6 5 7

8. Complexity • Each recursive call operates on an array that is half the size of the original array • How many level’s to get to arrays size of 1? About O(log n)

9. Complexity • Each recursive call operates on an array that is half the size of the original array • Each time you do a sort() you do a merge which is O(n). Each level is O(n).

10. Complexity O(n) O(n) O(n) For O(log n) levels Total complexity is O(n log n) Best and worst case