Question

Use a loop invariant to prove that the following algorithm correctly identifies the location of the minimum value in the array data.

Input: data: array of integers

Input: n: size of data

Output: index min such that data[min] <= data[i] for any i from 1 to n

Algorithm: FindMin

min = 1;

for i = 2 to n do

if data[i] < data[min] then

min = i;

end

end

return min

Answer 1

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Loop invariant :

before the loop, the array has only one element and it is the minimum value of the array till the 1st element so true.

Inside the for loop if the value of the element is less than the minimum element then we reassign the minimum value to the current element. At the end of each iteration, min has the correct index of the minimum value.

After the loop, min has the correct index of the minimum value of all the elements of the array.