Merge sort
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Merge sort is an algorithm that splits an array into halves, recursively sorts the halves, and then merges the sorted halves into one sorted array. It has a time complexity of O(n log n) in all cases and requires auxiliary space of O(n). The algorithm works by recursively splitting an array into halves until each subarray contains a single element, which is trivially sorted. It then merges the sorted subarrays back together into a single sorted array.
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![Merge Sort
Given a sequence of n elements (also called keys) a[1]……a[n], the
general idea is to imagine them to split into two sets:
a[1]….a[n/2] and a[n/2 +1]…….a[n].
Each set is individually sorted and resulting sorted sequences are
merged to produce single sorted sequence of n elements.](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
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Merge sort
- 1. Merge Sort Dr. Himani Mittal GGDSD College Chandigarh
- 2. Merge Sort Given a sequence of n elements (also called keys) a[1]……a[n], the general idea is to imagine them to split into two sets: a[1]….a[n/2] and a[n/2 +1]…….a[n]. Each set is individually sorted and resulting sorted sequences are merged to produce single sorted sequence of n elements.
- 4. Merge-sort
- 5. Merging two Sorted Sequences
- 6. MergeSort Working 7 9 2 11 3 5 15 30 2 7 9 11 3 5 15 30 2 3 5 7 9 11 15 30 Low=1, high=8 Mid = (1+8)/2 = 4 Low=5, high=8 Mid = (5+8)/2 = 6 Low=1, high=4 Mid = (1+4)/2 = 2 Low=1, high=2 Mid = (1+2)/2 = 1 Low=7, high=8 Mid = (7+8)/2 = 7 Merging
- 7. MergeSort Call Tree (Sort Left, Sort Right, Merge Root – Post Order) Low=1, high=8 Mid = (1+8)/2 = 4 M ergeSort ( 1, 8) M ergeSort ( 1, 4) M ergeSort ( 5, 8) M ergeSort ( 1, 2) M ergeSort ( 3, 4) M ergeSort ( 7, 8)M ergeSort ( 5, 6) M erge Sort ( 1, 1) M erge Sort ( 2, 2) M erge Sort ( 3, 3) M erge Sort ( 4, 4) M erge Sort ( 5, 5) M erge Sort ( 6, 6) M erge Sort ( 7, 7) M erge Sort ( 8, 8)
- 8. Merge Sort Complexity Space 2n Time nlogn in all cases