Exponential Search
Another alternative to variable size decrease-and-conquer search is known as exponential search. This algorithm begins searching at the beginning of the list. It then progressively tests at larger intervals (A[2],A[4],A[8], . . .) until a straddling range is found which may contain the search value. A binary search is then performed on only the suspect range to ?nd the ?nal index position.
ALGORITHM ExponentialSearch (A[0 . . . n - 1], k)
// A variable-size 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: set pos ← 2
2: while pos < n and A[pos] < k do
3: prev ← pos
4: pos ← pos 2
5: if pos > n - 1 then
6: pos ← n - 1
7: result ← BinarySearch(A[prev . . . pos], k)
8: if result = -1 then
9: return -1
10: else
11: return result + prev
Algorithm ExponentialSearch shows the pseudocode for this solution. Implement the algorithm.