Question

Illustrate the operation of PARTITION on the array ? = < 15, 1,9, 5, 13,6, 8, 4, 21, 2, 6, 11 >

Following is the algorithm we used in class:

PARTITION(A, p, r)

1 x = A[r]

2 i = p -1

3 for j = p to r -1

4 if A[j] ≤ x

5 i = i +1

6 exchange A[i] with A[j]

7 exchange A[i+1] with A[r]

8 return i + 1

**Please use p,j,i, and r on the array so I can clearly see the steps to better understand. Any help is appreciated. Thank you!

Answer 1

? = < 15, 1,9, 5, 13,6, 8, 4, 21, 2, 6, 11 >

Initially p = 1 and r = 12 [I.e size]
Line 1. x = A[r] i.e x = A[12] = 11 i.e last value in array
Line 2. i = p-1 i.e i = 0
Line 3. Loop starts from j = 1 to 11 (r-1) [ Last element is omitted]
----------------if A[1] i.e 15 < 11 false , i remains as 0
----------------if A[2] i.e 1 < 11 true , i is incremented by 1 i.e its 1 now
------------------------------------Swap A[1] and A[2] i.e [ 1, 15,9, 5, 13,6, 8, 4, 21, 2, 6, 11 ]
----------------if A[3] i.e 9 < 11 true , i is incremented by 1 i.e its 2 now
------------------------------------Swap A[2] and A[3] i.e [ 1, 9,15, 5, 13,6, 8, 4, 21, 2, 6, 11 ]
----------------if A[4] i.e 5 < 11 true , i is incremented by 1 i.e its 3 now
------------------------------------Swap A[3] and A[4] i.e [ 1, 9,5, 15, 13,6, 8, 4, 21, 2, 6, 11 ]
----------------if A[5] i.e 13 < 11 false , i remains as 3
----------------if A[6] i.e 6 < 11 true , i is incremented by 1 i.e its 4 now
------------------------------------Swap A[4] and A[6] i.e [ 1, 9,5, 6, 13,15, 8, 4, 21, 2, 6, 11 ]
----------------if A[7] i.e 8 < 11 true , i is incremented by 1 i.e its 5 now
------------------------------------Swap A[5] and A[7] i.e [ 1, 9,5, 6, 8,15, 13, 4, 21, 2, 6, 11 ]
----------------if A[8] i.e 4 < 11 true , i is incremented by 1 i.e its 6 now
------------------------------------Swap A[6] and A[8] i.e [ 1, 9,5, 6, 8,4, 13, 15, 21, 2, 6, 11 ]
----------------if A[9] i.e 21 < 11 false , i remains as 6
----------------if A[10] i.e 2 < 11 true , i is incremented by 1 i.e its 7 now
------------------------------------Swap A[7] and A[10] i.e [ 1, 9,5, 6, 8,4, 2, 15, 21, 13, 6, 11 ]
----------------if A[11] i.e 6 < 11 true , i is incremented by 1 i.e its 8 now
------------------------------------Swap A[8] and A[11] i.e [ 1, 9,5, 6, 8,4, 2, 6, 21, 13, 15, 11 ]


Now Since the LOOP IS COMPLETE IT WILL EXCHANGE [i+1] with 11

[ 1, 9,5, 6, 8,4, 2, 6, 11, 21, 13, 15, 21 ]

Now we can see that elements to left of 11 are less and elements to right of 11 are greater ..Hence it partitions the Array.

PLEASE UPVOTE, Thanks, PLEASE COMMENT if there is any concern.