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Merge Sort

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Merge sort is a divide and conquer algorithm that divides an array into halves, recursively sorts the halves, and then merges the sorted halves back together. The key steps are: 1. Divide the array into equal halves until reaching base cases of arrays with one element. 2. Recursively sort the left and right halves by repeating the divide step. 3. Merge the sorted halves back into a single sorted array by comparing elements pairwise and copying the smaller element into the output array. Merge sort has several advantages including running in O(n log n) time in all cases, accessing data sequentially with low random access needs, and being suitable for external sorting of large data sets that do not fit in memory

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Merge Sort
MERGE SORT Nikhil R S USN: 1BM15IS051 K. Sai Supreeth USN:1BM15IS034
Topics to be covered: ■ Introduction ■ Definition ■ Algorithm ■ Steps involved ■ Program ■ Applications
Introduction: ■ Merge Sort is a complex and fast sorting algorithm that repeatedly divides an un- sorted section into two equal sub- sections, sorts them separately and merges them correctly.
Definition: ■ Merge sort is a DIVIDE AND CONQUER algorithm. It divides input array in two halves, calls itself for the two halves and then merges the two sorted halves.The merge() function is used for merging two halves.
Steps involved: – Divide the problem into sub-problems that are similar to the original but smaller in size. – Conquer the sub-problems by solving them recursively. If they are small enough, just solve them in a straightforward manner. – Combine the solutions to create a solution to the original problem.
Algorithm: mergeSort(arr[], l, r) If l < r 1. Find the middle point to divide the array into two halves: middle m = (l+r)/2 2. Call mergeSort for first half: Call mergeSort(arr, l, m) 3. Call mergeSort for second half: Call mergeSort(arr, m+1, r) 4. Merge the two halves sorted in step 2 and 3: Call merge(arr, l, m, r)
Example:
Program:
Merge Sort
Merge Sort
Merge Sort
Output:
Why Merge Sort?? ■ Compared to insertion sort merge sort is faster. ■ On small inputs, insertion sort may be faster. But for large enough inputs, merge sort will always be faster, because its running time grows more slowly than insertion sorts.
■ Merge sort type algorithms allows large data sets to be sorted easily. ■ Merge sort accesses data sequentially and the need of random access is low. ■ Inversion count problem. ■ Used in External Sorting. Applications:
■ Organize an MP3 library.
■ Display Google PageRank results. ■ The e-commerce application.
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Merge Sort

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Merge Sort

  • 2. MERGE SORT Nikhil R S USN: 1BM15IS051 K. Sai Supreeth USN:1BM15IS034
  • 3. Topics to be covered: ■ Introduction ■ Definition ■ Algorithm ■ Steps involved ■ Program ■ Applications
  • 4. Introduction: ■ Merge Sort is a complex and fast sorting algorithm that repeatedly divides an un- sorted section into two equal sub- sections, sorts them separately and merges them correctly.
  • 5. Definition: ■ Merge sort is a DIVIDE AND CONQUER algorithm. It divides input array in two halves, calls itself for the two halves and then merges the two sorted halves.The merge() function is used for merging two halves.
  • 6. Steps involved: – Divide the problem into sub-problems that are similar to the original but smaller in size. – Conquer the sub-problems by solving them recursively. If they are small enough, just solve them in a straightforward manner. – Combine the solutions to create a solution to the original problem.
  • 7. Algorithm: mergeSort(arr[], l, r) If l < r 1. Find the middle point to divide the array into two halves: middle m = (l+r)/2 2. Call mergeSort for first half: Call mergeSort(arr, l, m) 3. Call mergeSort for second half: Call mergeSort(arr, m+1, r) 4. Merge the two halves sorted in step 2 and 3: Call merge(arr, l, m, r)
  • 14. Why Merge Sort?? ■ Compared to insertion sort merge sort is faster. ■ On small inputs, insertion sort may be faster. But for large enough inputs, merge sort will always be faster, because its running time grows more slowly than insertion sorts.
  • 15. ■ Merge sort type algorithms allows large data sets to be sorted easily. ■ Merge sort accesses data sequentially and the need of random access is low. ■ Inversion count problem. ■ Used in External Sorting. Applications:
  • 16. ■ Organize an MP3 library.
  • 17. ■ Display Google PageRank results. ■ The e-commerce application.