mergesort explanation

1. 4
Abstract in-place merge demo
Goal: Given two sorted subarrays a[lo] to a[mid] and a[mid+1] to a[hi],
replace with sorted subarray a[lo] to a[hi].

2. 5
Abstract in-place merge demo
Goal: Given two sorted subarrays a[lo] to a[mid] and a[mid+1] to a[hi],
replace with sorted subarray a[lo] to a[hi].
E E G M R A C E R Ta[]
midlo mid+1 hi

3. 6
Abstract in-place merge demo
Goal: Given two sorted subarrays a[lo] to a[mid] and a[mid+1] to a[hi],
replace with sorted subarray a[lo] to a[hi].
E E G M R A C E R Ta[]
midlo mid+1 hi
copy to auxiliary array
aux[] E E G M R A C E R T

4. 7
Abstract in-place merge demo
Goal: Given two sorted subarrays a[lo] to a[mid] and a[mid+1] to a[hi],
replace with sorted subarray a[lo] to a[hi].
E E G M R A C E R Ta[]
mid
k
mid+1 hi
copy to auxiliary array
aux[] E E G M R A C E R T
i j
sorted result

5. 8
Abstract in-place merge demo
Goal: Given two sorted subarrays a[lo] to a[mid] and a[mid+1] to a[hi],
replace with sorted subarray a[lo] to a[hi].
E E G M R A C E R Ta[]
mid
k
mid+1 hi
compare minimum in each subarray
aux[] E E G M R A C E R T
i j

6. 9
Abstract in-place merge demo
Goal: Given two sorted subarrays a[lo] to a[mid] and a[mid+1] to a[hi],
replace with sorted subarray a[lo] to a[hi].
E E G M R A C E R Ta[]
mid
k
mid+1 hi
compare minimum in each subarray
aux[] E E G M R A C E R T
i j
A

7. 10
Abstract in-place merge demo
Goal: Given two sorted subarrays a[lo] to a[mid] and a[mid+1] to a[hi],
replace with sorted subarray a[lo] to a[hi].
E E G M R A C E R Ta[]
mid
k
mid+1 hi
compare minimum in each subarray
aux[] E E G M R A C E R T
i j
A

8. 11
Abstract in-place merge demo
Goal: Given two sorted subarrays a[lo] to a[mid] and a[mid+1] to a[hi],
replace with sorted subarray a[lo] to a[hi].
E E G M R A C E R Ta[]
mid
k
mid+1 hi
compare minimum in each subarray
aux[] E E G M R A C E R T
i j
A C

9. 12
Abstract in-place merge demo
Goal: Given two sorted subarrays a[lo] to a[mid] and a[mid+1] to a[hi],
replace with sorted subarray a[lo] to a[hi].
E E G M R A C E R Ta[]
mid
k
mid+1 hi
compare minimum in each subarray
aux[] E E G M R A C E R T
i j
A C

10. 13
Abstract in-place merge demo
Goal: Given two sorted subarrays a[lo] to a[mid] and a[mid+1] to a[hi],
replace with sorted subarray a[lo] to a[hi].
E E E M R A C E R Ta[]
mid
k
mid+1 hi
compare minimum in each subarray
aux[] E E G M R A C E R T
i j
A C

11. 14
Abstract in-place merge demo
Goal: Given two sorted subarrays a[lo] to a[mid] and a[mid+1] to a[hi],
replace with sorted subarray a[lo] to a[hi].
E E E M R A C E R Ta[]
mid
k
mid+1 hi
compare minimum in each subarray
aux[] E E G M R A C E R T
i j
A C

12. 15
Abstract in-place merge demo
Goal: Given two sorted subarrays a[lo] to a[mid] and a[mid+1] to a[hi],
replace with sorted subarray a[lo] to a[hi].
E E E E R A C E R Ta[]
mid
k
mid+1 hi
compare minimum in each subarray
aux[] E E G M R A C E R T
i j
A C

13. 16
Abstract in-place merge demo
Goal: Given two sorted subarrays a[lo] to a[mid] and a[mid+1] to a[hi],
replace with sorted subarray a[lo] to a[hi].
E E E E R A C E R Ta[]
mid
k
mid+1 hi
compare minimum in each subarray
aux[] E E G M R A C E R T
i j
A C

14. 17
Abstract in-place merge demo
Goal: Given two sorted subarrays a[lo] to a[mid] and a[mid+1] to a[hi],
replace with sorted subarray a[lo] to a[hi].
E E E E E A C E R Ta[]
mid
k
mid+1 hi
compare minimum in each subarray
aux[] E E G M R A C E R T
i j
A C

15. 18
Abstract in-place merge demo
Goal: Given two sorted subarrays a[lo] to a[mid] and a[mid+1] to a[hi],
replace with sorted subarray a[lo] to a[hi].
E E E E E A C E R Ta[]
mid
k
mid+1 hi
compare minimum in each subarray
aux[] E E G M R A C E R T
i j
A C

16. 19
Abstract in-place merge demo
Goal: Given two sorted subarrays a[lo] to a[mid] and a[mid+1] to a[hi],
replace with sorted subarray a[lo] to a[hi].
E E E E E G C E R Ta[]
mid
k
mid+1 hi
compare minimum in each subarray
aux[] E E G M R A C E R T
i j
A C

17. 20
Abstract in-place merge demo
Goal: Given two sorted subarrays a[lo] to a[mid] and a[mid+1] to a[hi],
replace with sorted subarray a[lo] to a[hi].
E E E E E G C E R Ta[]
mid
k
mid+1 hi
compare minimum in each subarray
aux[] E E G M R A C E R T
i j
A C

18. 21
Abstract in-place merge demo
Goal: Given two sorted subarrays a[lo] to a[mid] and a[mid+1] to a[hi],
replace with sorted subarray a[lo] to a[hi].
E E E E E G M E R Ta[]
mid
k
mid+1 hi
compare minimum in each subarray
aux[] E E G M R A C E R T
i j
A C

19. 22
Abstract in-place merge demo
Goal: Given two sorted subarrays a[lo] to a[mid] and a[mid+1] to a[hi],
replace with sorted subarray a[lo] to a[hi].
E E E E E G M E R Ta[]
mid
k
mid+1 hi
compare minimum in each subarray
aux[] E E G M R A C E R T
i j
A C

20. 23
Abstract in-place merge demo
Goal: Given two sorted subarrays a[lo] to a[mid] and a[mid+1] to a[hi],
replace with sorted subarray a[lo] to a[hi].
E E E E E G M R R Ta[]
mid
k
mid+1 hi
compare minimum in each subarray
aux[] E E G M R A C E R T
i j
A C

21. 24
Abstract in-place merge demo
Goal: Given two sorted subarrays a[lo] to a[mid] and a[mid+1] to a[hi],
replace with sorted subarray a[lo] to a[hi].
E E E E E G M R R Ta[]
mid
k
mid+1 hi
compare minimum in each subarray
aux[] E E G M R A C E R T
i j
A C

22. 25
Abstract in-place merge demo
Goal: Given two sorted subarrays a[lo] to a[mid] and a[mid+1] to a[hi],
replace with sorted subarray a[lo] to a[hi].
E E E E E G M R R Ra[]
mid
k
mid+1 hi
compare minimum in each subarray
aux[] E E G M R A C E R R
i j
A C
j
k

23. 26
Abstract in-place merge demo
Goal: Given two sorted subarrays a[lo] to a[mid] and a[mid+1] to a[hi],
replace with sorted subarray a[lo] to a[hi].
E E E E E G M R R Ra[]
mid mid+1 hi
abstract in-place mergesort complete using auxiliary array
aux[] E E G M R A C E R R
A C