Interpolation Search

The next task is to implement a variable size decrease-and-conquer solution to search. See Levitin [2007] pp 190 for a detailed description of the interpolation search algorithm.

ALGORITHM InterpolationSearch (A[0 . . . n - 1], k)
// A variable-sized decrease and conquer search in an ordered list.
// INPUT : An array A[0 . . . n - 1] of ordered elements, and a search key k.
// OUTPUT : an index to the position of k in A if k is found or -1 otherwise.
1: l ← 0; r ← n - 1
2: while A[l] < k and A[r] ≥ k do
3: m ← l + (k-A[l])·(r-l)
A[r]-A[l]
4: if A[m] < k then
5: l ← m+ 1
6: else if A[m] > k then
7: r ← m- 1
8: else
9: return m
10: if A[l] = k then
11: return l
12: else
13: return -1

Algorithm InterpolationSearch shows the pseudocode for this solution. Implement the algorithm.