University of California San Diego Greedy Programming Questions 25 Points Divide and Conquer question: You are given an array of bits, b[1..n], b[i]∈{0,1

University of California San Diego Greedy Programming Questions 25 Points

Divide and Conquer question:

You are given an array of bits, b[1..n], b[i]∈{0,1}, where n=2^k+1 is a power of 2 plus 1 and is at least 3, b1=0 and bn=1

Give an O(log n) time algorithm that finds two consecutive bits that are the same, i.e., finds 1 ≤ i ≤ n−1 with bi = bi+1

(Hint: what would happen if there were no consecutive equal bits?)

Give a time analysis for your algorithm, and brief explanation for correctness.

Points distribution:

-algorithm (10 points)

-brief explanation of correctness (5 points)

-recursion for time (5 points)

-correct solution for recursion (5 points)