Merge and Count Merge and count step Given

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. n n i=6 3 7 10 14 18 19 2 11 16 17 23 25 two sorted halves auxiliary array Total: 1

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. n n i=6 3 7 10 14 18 19 2 11 16 17 23 25 two sorted halves 6 2 auxiliary array Total: 6 2

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. n n i=6 3 7 10 14 18 19 2 11 16 17 23 25 two sorted halves 6 2 auxiliary array Total: 6 3

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. n n i=6 3 7 10 14 18 19 2 11 16 17 23 25 two sorted halves 6 2 3 auxiliary array Total: 6 4

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. n n i=5 3 7 10 14 18 19 2 11 16 17 23 25 two sorted halves 6 2 3 auxiliary array Total: 6 5

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. n n i=5 3 7 10 14 18 19 2 11 16 17 23 25 two sorted halves 6 2 3 7 auxiliary array Total: 6 6

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. n n i=4 3 7 10 14 18 19 2 11 16 17 23 25 two sorted halves 6 2 3 7 auxiliary array Total: 6 7

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. n n i=4 3 7 10 14 18 19 2 11 16 17 23 25 two sorted halves 6 2 3 7 10 auxiliary array Total: 6 8

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. n n i=3 3 7 10 14 18 19 2 11 16 17 23 25 two sorted halves 6 2 3 7 10 auxiliary array Total: 6 9

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. n n i=3 3 7 2 10 3 14 7 18 10 19 2 11 6 3 11 16 17 23 25 two sorted halves auxiliary array Total: 6 + 3 10

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. n n i=3 3 7 2 10 3 14 7 18 10 19 2 11 6 3 11 16 17 23 25 two sorted halves auxiliary array Total: 6 + 3 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. n n i=3 3 7 2 10 3 14 7 18 10 19 11 2 11 6 3 14 16 17 23 25 two sorted halves auxiliary array Total: 6 + 3 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. n n i=2 3 7 2 10 3 14 7 18 10 19 11 2 11 6 3 14 16 17 23 25 two sorted halves auxiliary array Total: 6 + 3 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. n n i=2 3 7 2 10 3 14 7 18 10 19 11 14 2 11 16 6 3 2 16 17 23 25 two sorted halves auxiliary array Total: 6 + 3 + 2 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. n n i=2 3 7 2 10 3 14 7 18 10 19 11 14 2 11 16 6 3 2 16 17 23 25 two sorted halves auxiliary array Total: 6 + 3 + 2 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. n n i=2 3 7 2 10 3 14 7 18 10 19 11 14 16 2 11 16 17 6 3 2 2 17 23 25 two sorted halves auxiliary array Total: 6 + 3 + 2 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. n n i=2 3 7 2 10 3 14 7 18 10 19 11 14 16 2 11 16 17 6 3 2 2 17 23 25 two sorted halves auxiliary array Total: 6 + 3 + 2 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. n n i=2 3 7 2 10 3 14 7 18 10 19 11 14 16 2 11 16 17 6 3 2 2 17 18 23 25 two sorted halves auxiliary array Total: 6 + 3 + 2 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. n n i=1 3 7 2 10 3 14 7 18 10 19 11 14 16 2 11 16 17 6 3 2 2 17 18 23 25 two sorted halves auxiliary array Total: 6 + 3 + 2 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. n n i=1 3 7 2 10 3 14 7 18 10 19 11 14 16 2 11 16 17 6 3 2 2 17 18 19 23 25 two sorted halves auxiliary array Total: 6 + 3 + 2 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. n n first half exhausted 3 7 2 10 3 14 7 18 10 i=0 19 11 14 16 2 11 16 17 6 3 2 2 17 18 19 23 25 two sorted halves auxiliary array Total: 6 + 3 + 2 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. n n i=0 3 7 2 10 3 14 7 18 10 19 11 14 16 2 11 16 17 23 6 3 2 2 0 17 18 19 23 25 two sorted halves auxiliary array Total: 6 + 3 + 2 + 0 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. n n i=0 3 7 2 10 3 14 7 18 10 19 11 14 16 2 11 16 17 23 6 3 2 2 0 17 18 19 23 25 two sorted halves auxiliary array Total: 6 + 3 + 2 + 0 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. n n i=0 3 7 2 10 3 14 7 18 10 19 11 14 16 2 11 16 17 23 25 6 3 2 2 0 0 17 18 19 23 25 two sorted halves auxiliary array Total: 6 + 3 + 2 + 0 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. n n i=0 3 7 2 10 3 14 7 18 10 19 11 14 16 2 11 16 17 23 25 6 3 2 2 0 0 17 18 19 23 25 two sorted halves auxiliary array Total: 6 + 3 + 2 + 0 = 13 25