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Merge and Count

Merge and Count. current. Merge and count step. Given two sorted halves, count number of inversions where a i and a j are in different halves. Combine two sorted halves into sorted whole. smallest i = 6. smallest j = 6. 3. 7. 10. 14. 18. 19. 2. 11. 16. 17. 23. 25. N/2 = 6.

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Merge and Count

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  1. Merge and Count current • Merge and count step. • Given two sorted halves, count number of inversions where ai and aj are in different halves. • Combine two sorted halves into sorted whole. smallesti = 6 smallestj = 6 3 7 10 14 18 19 2 11 16 17 23 25 N/2 = 6 auxiliary array Inversions: Total: 0

  2. Merge and Count current • Merge and count step. • Given two sorted halves, count number of inversions where ai and aj are in different halves. • Combine two sorted halves into sorted whole. smallesti = 6 smallestj = 6 3 7 10 14 18 19 2 11 16 17 23 25 N/2 = 6 auxiliary array Inversions: Total: 0

  3. Merge and Count current • Merge and count step. • Given two sorted halves, count number of inversions where ai and aj are in different halves. • Combine two sorted halves into sorted whole. smallesti = 6 smallestj = 5 3 7 10 14 18 19 2 11 16 17 23 25 N/2 = 6 2 auxiliary array Inversions: 6 Total: 6

  4. Merge and Count current • Merge and count step. • Given two sorted halves, count number of inversions where ai and aj are in different halves. • Combine two sorted halves into sorted whole. smallesti = 6 smallestj = 5 3 7 10 14 18 19 2 11 16 17 23 25 N/2 = 6 2 auxiliary array Inversions: 6 Total: 6

  5. Merge and Count current • Merge and count step. • Given two sorted halves, count number of inversions where ai and aj are in different halves. • Combine two sorted halves into sorted whole. smallesti = 5 smallestj = 5 3 7 10 14 18 19 2 11 16 17 23 25 N/2 = 6 2 3 auxiliary array Inversions: 6 Total: 6

  6. Merge and Count current • Merge and count step. • Given two sorted halves, count number of inversions where ai and aj are in different halves. • Combine two sorted halves into sorted whole. smallesti = 5 smallestj = 5 3 7 10 14 18 19 2 11 16 17 23 25 N/2 = 6 2 3 auxiliary array Inversions: 6 Total: 6

  7. Merge and Count current • Merge and count step. • Given two sorted halves, count number of inversions where ai and aj are in different halves. • Combine two sorted halves into sorted whole. smallesti = 4 smallestj = 5 3 7 10 14 18 19 2 11 16 17 23 25 N/2 = 6 2 3 7 auxiliary array Inversions: 6 Total: 6

  8. Merge and Count current • Merge and count step. • Given two sorted halves, count number of inversions where ai and aj are in different halves. • Combine two sorted halves into sorted whole. smallesti = 4 smallestj = 5 3 7 10 14 18 19 2 11 16 17 23 25 N/2 = 6 2 3 7 auxiliary array Inversions: 6 Total: 6

  9. Merge and Count current • Merge and count step. • Given two sorted halves, count number of inversions where ai and aj are in different halves. • Combine two sorted halves into sorted whole. smallesti = 3 smallestj = 5 3 7 10 14 18 19 2 11 16 17 23 25 N/2 = 6 2 3 7 10 auxiliary array Inversions: 6 Total: 6

  10. Merge and Count current • Merge and count step. • Given two sorted halves, count number of inversions where ai and aj are in different halves. • Combine two sorted halves into sorted whole. smallesti = 3 smallestj = 5 3 7 10 14 18 19 2 11 16 17 23 25 N/2 = 6 2 3 7 10 auxiliary array Inversions: 6 Total: 6

  11. Merge and Count • Merge and count step. • Given two sorted halves, count number of inversions where ai and aj are in different halves. • Combine two sorted halves into sorted whole. smallesti = 3 smallestj = 4 3 7 10 14 18 19 2 11 16 17 23 25 N/2 = 6 2 3 7 10 11 auxiliary array Inversions: 6 + 3 Total: 9

  12. Merge and Count • Merge and count step. • Given two sorted halves, count number of inversions where ai and aj are in different halves. • Combine two sorted halves into sorted whole. smallesti = 3 smallestj = 4 3 7 10 14 18 19 2 11 16 17 23 25 N/2 = 6 2 3 7 10 11 auxiliary array Inversions: 6 + 3 Total: 9

  13. Merge and Count • Merge and count step. • Given two sorted halves, count number of inversions where ai and aj are in different halves. • Combine two sorted halves into sorted whole. smallesti = 2 smallestj = 4 3 7 10 14 18 19 2 11 16 17 23 25 N/2 = 6 2 3 7 10 11 14 auxiliary array Inversions: 6 + 3 Total: 9

  14. Merge and Count • Merge and count step. • Given two sorted halves, count number of inversions where ai and aj are in different halves. • Combine two sorted halves into sorted whole. smallesti = 2 smallestj = 4 3 7 10 14 18 19 2 11 16 17 23 25 N/2 = 6 2 3 7 10 11 14 auxiliary array Inversions: 6 + 3 Total: 9

  15. Merge and Count • Merge and count step. • Given two sorted halves, count number of inversions where ai and aj are in different halves. • Combine two sorted halves into sorted whole. smallesti = 2 smallestj = 3 3 7 10 14 18 19 2 11 16 17 23 25 N/2 = 6 2 3 7 10 11 14 16 auxiliary array Inversions: 6 + 3 + 2 Total: 11

  16. Merge and Count • Merge and count step. • Given two sorted halves, count number of inversions where ai and aj are in different halves. • Combine two sorted halves into sorted whole. smallesti = 2 smallestj = 3 3 7 10 14 18 19 2 11 16 17 23 25 N/2 = 6 2 3 7 10 11 14 16 auxiliary array Inversions: 6 + 3 + 2 Total: 11

  17. Merge and Count • Merge and count step. • Given two sorted halves, count number of inversions where ai and aj are in different halves. • Combine two sorted halves into sorted whole. smallesti = 2 smallestj = 2 3 7 10 14 18 19 2 11 16 17 23 25 N/2 = 6 2 3 7 10 11 14 16 17 auxiliary array Inversions: 6 + 3 + 2 + 2 Total: 13

  18. Merge and Count • Merge and count step. • Given two sorted halves, count number of inversions where ai and aj are in different halves. • Combine two sorted halves into sorted whole. smallesti = 2 smallestj = 2 3 7 10 14 18 19 2 11 16 17 23 25 N/2 = 6 2 3 7 10 11 14 16 17 auxiliary array Inversions: 6 + 3 + 2 + 2 Total: 13

  19. Merge and Count • Merge and count step. • Given two sorted halves, count number of inversions where ai and aj are in different halves. • Combine two sorted halves into sorted whole. smallesti = 1 smallestj = 2 3 7 10 14 18 19 2 11 16 17 23 25 N/2 = 6 2 3 7 10 11 14 16 17 18 auxiliary array Inversions: 6 + 3 + 2 + 2 Total: 13

  20. Merge and Count • Merge and count step. • Given two sorted halves, count number of inversions where ai and aj are in different halves. • Combine two sorted halves into sorted whole. smallesti = 1 smallestj = 2 3 7 10 14 18 19 2 11 16 17 23 25 N/2 = 6 2 3 7 10 11 14 16 17 18 auxiliary array Inversions: 6 + 3 + 2 + 2 Total: 13

  21. Merge and Count • Merge and count step. • Given two sorted halves, count number of inversions where ai and aj are in different halves. • Combine two sorted halves into sorted whole. smallesti = 0 smallestj = 2 first half exhausted 3 7 10 14 18 19 2 11 16 17 23 25 N/2 = 6 2 3 7 10 11 14 16 17 18 19 auxiliary array Inversions: 6 + 3 + 2 + 2 Total: 13

  22. Merge and Count • Merge and count step. • Given two sorted halves, count number of inversions where ai and aj are in different halves. • Combine two sorted halves into sorted whole. smallesti = 0 smallestj = 2 first half exhausted 3 7 10 14 18 19 2 11 16 17 23 25 N/2 = 6 2 3 7 10 11 14 16 17 18 19 auxiliary array Inversions: 6 + 3 + 2 + 2 Total: 13

  23. Merge and Count • Merge and count step. • Given two sorted halves, count number of inversions where ai and aj are in different halves. • Combine two sorted halves into sorted whole. smallesti = 0 smallestj = 2 first half exhausted 3 7 10 14 18 19 2 11 16 17 23 25 N/2 = 6 2 3 7 10 11 14 16 17 18 19 23 auxiliary array Inversions: 6 + 3 + 2 + 2 + 0 Total: 13

  24. Merge and Count • Merge and count step. • Given two sorted halves, count number of inversions where ai and aj are in different halves. • Combine two sorted halves into sorted whole. smallesti = 0 smallestj = 1 first half exhausted 3 7 10 14 18 19 2 11 16 17 23 25 N/2 = 6 2 3 7 10 11 14 16 17 18 19 23 auxiliary array Inversions: 6 + 3 + 2 + 2 + 0 Total: 13

  25. Merge and Count • Merge and count step. • Given two sorted halves, count number of inversions where ai and aj are in different halves. • Combine two sorted halves into sorted whole. smallesti = 0 smallestj = 0 second half exhausted first half exhausted 3 7 10 14 18 19 2 11 16 17 23 25 N/2 = 6 2 3 7 10 11 14 16 17 18 19 23 25 auxiliary array Inversions: 6 + 3 + 2 + 2 + 0 + 0 Total: 13

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