Write the pseudocode of the binary search algorithm and generate the recurrence relation from it

Sure, here is the pseudocode for the binary search algorithm:

Algorithm BinarySearch(A, n, x)
   Input: An array A[0..n-1] sorted in ascending order, an integer x.
   Output: An index i such that A[i]=x or the special value NOT_FOUND.

   low ← 0
   high ← n - 1
   while low ≤ high do
      mid ← (low + high) / 2
      if A[mid] < x then
         low ← mid + 1
      else if A[mid] > x then
         high ← mid - 1
      else
         return mid
   return NOT_FOUND

Now, let's generate the recurrence relation from it.

The binary search algorithm divides the problem into two equal halves with each recursive call. Therefore, the recurrence relation for the binary search algorithm can be expressed as:

T(n) = T(n/2) + c

Here, T(n) is the time taken to search in an array of size 'n', T(n/2) is the time taken to search in the sub-array (which is half the size of the original array), and 'c' is the time taken for the comparison operations.