# Problem 5 Suppose you are given an array A[1…nl of distinct numbers that you are told satisfies A…

Problem 5 Suppose you are given an array A[1…nl of distinct numbers that you are told satisfies A 2 for some unknown i Such an array is known as unimodal (with the mode being a minimum). Give an O(log n) time algorithm for finding the min- imum item Ali] in such an array. As an example, in the array below, the minimum item is 4. 9 5 4 6 8 12 14 To get full marks you must fully describe your algorithm (pseudocode is fine), explain why it returns a correct answer and show why it runs in O(log n) time.

Suppose you are given an array Al1…n] of distinct numbers that you are told satisfies for some unknown. Such an array is known as unimodal (with the mode being a minimum). Give an O(log n) time algorithm for finding the min imum item Ali] in such an array. As an example, in the array below, the minimum item is 4. 9 5 4 6 8 12 14 To get full marks you must fully describe your algorithm (pseudocode is fine), explain why it returns a correct answer and show why it runs in O(logn ) time.

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int minimum(int array1[], int low, int n)
{
int min = array1[low];
int i;
for (i = low; i <= n; i++)
{
if (array1[i] < MIN)
min = array1[i];
}
return min;
}
The above code will return minimum value in Olog(n) time.
Description:
1) start from first value
2) loop n times
3) if value at position i is less then previous value then update minimum variable
4) end loop
return minimum

example
for array : 10 8 6 4 5 7 9
start loop
compare 10 with next variable and update min if min < array[i]

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