Adnan Shahzada

• Input:• sequence a1, a2, …, an of numbers.

• Output:

…• permutation a'1, a'2, …, a'n such that a'1 a'2

… a'n .

• Example:

• Input: 8 2 4 9 3 6

• Output: 2 3 4 6 8 9

INSERTION-SORT (A, n) A[1 . . n]for j ← 2 to n

do key ← A[ j]i ← j – 1while i > 0 and A[i] > key

do A[i+1] ← A[i]do A[i+1] ← A[i]i ← i – 1

A[i+1] = key

i j

keysorted

1 n

8 2 4 9 3 6

8 2 4 9 3 6

8 2 4 9 3 6

2 8 4 9 3 6

8 2 4 9 3 6

2 8 4 9 3 6

8 2 4 9 3 6

2 8 4 9 3 6

2 4 8 9 3 6

8 2 4 9 3 6

2 8 4 9 3 6

2 4 8 9 3 6

8 2 4 9 3 6

2 8 4 9 3 6

2 4 8 9 3 6

2 4 8 9 3 6

8 2 4 9 3 6

2 8 4 9 3 6

2 4 8 9 3 6

2 4 8 9 3 6

8 2 4 9 3 6

2 8 4 9 3 6

2 4 8 9 3 6

2 4 8 9 3 6

2 3 4 8 9 6

8 2 4 9 3 6

2 8 4 9 3 6

2 4 8 9 3 6

2 4 8 9 3 6

2 3 4 8 9 6

8 2 4 9 3 6

2 8 4 9 3 6

2 4 8 9 3 6

2 4 8 9 3 6

2 3 4 8 9 6

2 3 4 6 8 9 done

T(n) = (n)T(n) = (n)

T(n)=(n2)

- Expected No of Key Comparisons to insert key j is:

- Total expected number of KC is:- Total expected number of KC is:

- T(n)= (n2)