Insertion Sort Example

The two sorting algorithms we now have looked from to date are helpful whenever all the data has already been contained in array, and we wish to rearrange it into sorted order. Even so, if we arereading the data into an array one element at any given time, we areable to consider an additional approach - insert each element into its sorted position in the array as we read it. In this way, we areable to keep the array in sorted form all the time. This particular algorithm is known as insertion sort.

Algorithm:

    INSERTION-SORT(A)
    for j ← 2 to n   
    do key ← A[ j ]
    Insert A[ j ] into the sorted sequence A[1 . . j -1]
    i ← j - 1 
    while i  0 and A[i]  key
    do A[i + 1] ← A[i]
    i ← i – 1
    A[i + 1] ← key
    Insertion sort – sorts the elements in place
    
    

Loop Invariant for Insertion Sort:

    INSERTION-SORT(A)
    for j ← 2 to n
    do key ← A[ j ]
    Insert A[ j ] into the sorted sequence A[1 . . j -1] 
    i ← j – 1
    while i  0 and A[i]  key
    do A[i + 1] ← A[i]
    i ← i – 1
    A[i + 1] ← key
    Invariant: at the start of the for loop the elements in A[1 . . j-1] are in sorted order
     
    

Insertion Sort example:

Input array:

5 2 4 6 1 3

From each iteration, the actual array is divided in two sub-arrays:

Advantages:

Good running time for almost sorted arrays

Disadvantages:

running time in worst as well as average case

≈ n2/2 comparisons as well as exchanges

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