Question

Show the correctness of insertion sort. (Proof by induction)

Answer 1

Insertion sort:
proof by induction:
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Base case:n=1//means only one element
since there is only one element, it is already sorted
hence true for base case
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Induction step:
assume that the first n-1 elements are sorted in array after n-1 iterations(outer loop)
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show that for nth element
now, to insert last nth element z into array, we will find it position to insert in between n-1 elements
by moving the bigger elements back one position, to place it in correct
which creates again sorted list of n elements
Hence insertion sort correctly sorts the data
hence proved by induction