interpolation_recurse.py

# Python program to implement
# interpolation search  with recursion
# If x is present in arr[0..n-1], then
# returns index of it, else returns -1.
# Time complexity is O(log(log(n)) in
# average case. O(n) in the worst case.


def interpolationSearch(arr, lo, hi, x):

	# Since array is sorted, an element present
	# in array must be in range defined by corner
	if (lo <= hi and x >= arr[lo] and x <= arr[hi]):

		# Probing the position while keeping
		# uniform distribution in mind.
		pos = lo + ((hi - lo) // (arr[hi] - arr[lo]) *
					(x - arr[lo]))

		# Condition of target found
		if arr[pos] == x:
			return pos

		# If x is larger, x is in right subarray
		if arr[pos] < x:
			return interpolationSearch(arr, pos + 1,hi, x)

		# If x is smaller, x is in left subarray
		if arr[pos] > x:
			return interpolationSearch(arr, lo,pos - 1, x)
	return -1

# Driver code


# Array of items in which
# search will be conducted
arr = [10, 12, 13, 16, 18, 19, 20,
	21, 22, 23, 24, 33, 35, 42, 47]
n = len(arr)

# Element to be searched
x = 18
index = interpolationSearch(arr, 0, n - 1, x)

if index != -1:
	print("Element found at index", index)
else:
	print("Element not found")