Suppose we have two arrays A[1:n] and B[1:m] which are both in sorted order and are consisting of distinct numbers. Design an algorithm that given an integer 1≤r≤m+n, find the element with rank in the union of arrays A and B. Your algorithm should run in only O(log (n+m)) time. Example. Suppose A= [1,5,7,9] and B= [2,4,6,12] and so n=m= 4. Then, the answer to r= 3 is 4 and the answer to r= 7 is 9 because the union of arrays A and B in the sorted order is [1,2,4,5,6,7,9,12]. The answers should not be code/program. Rather, it should be some pseudocode and/or English explanation with proof of correctness that leads to the run time it asks for.

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
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Suppose we have two arrays A[1:n] and B[1:m] which are both in sorted order and are consisting of distinct numbers. Design an algorithm that given an integer 1≤r≤m+n, find the element with rank in the union of arrays A and B. Your algorithm should run in only O(log (n+m)) time.

Example. Suppose A= [1,5,7,9] and B= [2,4,6,12] and so n=m= 4. Then, the answer to r= 3 is 4 and the answer to r= 7 is 9 because the union of arrays A and B in the sorted order is [1,2,4,5,6,7,9,12].

The answers should not be code/program. Rather, it should be some pseudocode and/or English explanation with proof of correctness that leads to the run time it asks for.

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