CS 5302 Data Structures and Algorithm
Tutorial 2 Recursion (Suggested Solution)
Programming Exercise
1. Suppose you are given an n-element array A containing distinct integers that are
listed in increasing order. Given a number k, describe a recursive algorithm to
find two integers in A that sum to k, if such a pair exists. What is the running
time of your algorithm?
Algorithm FindPair(A, i, j, k)
Input
An integer subarray A[i…j] and integer k
Output Return true if there are two elements of A[i..j] that sum to k
if i = j then
return false
else
if A[i] + A[j] < k then
return FindPair(A, i+1, j, k)
else
if A[i]+A[j] > k then
return FindPair(A, i, j-1, k)
else
return true
endif
endif
endif
For each call, the running time is O(1).
For each call, at most one recursive call is activated.
Since the input size decrease by 1 at each recursive call, we can represent the running
time as:
T(n) = T(n-1) + O(1)
Obviously, T(n) = O(n).