calculate the running time of algorithm in mathematical steps

Step $1/4$

low $=1$; high $=$ n;

Explanation

Set two Pointers, low and high, to the start and end of the array, respectively. These Pointers will help us find the Peak using a binary search approach.

Step $2/4$

while $($low high$)\{$ mid $=($low $+$ high$)\backslash 2$; $\}$

Explanation

Perform a while loop where you will keep halving the array to find the Peak. The condition low $<$ high ensures that the loop continues until the Peak is found.

Step $3/4$

If $($A$[$mid$]$ A$[$mid $+1])\{$ low $=$ mid $+1$; $\}$ else $[$ high $=$ mid; $\}$

Explanation

If the middle element is less than its next element, then the Peak lies to the right of $17.$ Otherwise, the Peak is at m or to the left.

Step $4/4$

return Allow$]$;

Explanation

Once the loop exits, low will be equal to high, and this will be the Peak of the unimodal array. The value at A$[$low$]$ is the Peak entry.

Final answer

The Peak entry is at index low in the array, and its value is A$[$low$].$