Suppose we are performing a binary search on a sorted vector initialized as follows: // index 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 vectornumbers {-5, -1, 0, 3, 9, 14, 19, 24, 33, 41, 56, 62, 70, 88, 99}; int index=binarySearch(numbers, 18);   Write the indexes of the elements that would be examined by the binary search (the mid values in our algorithm's code) and write the value that would be returned from the search.   please find  :                                      indexes examined                                                            and      value returned

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 are performing a binary search on a sorted vector initialized as follows:

// index 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
vector<int>numbers {-5, -1, 0, 3, 9, 14, 19, 24, 33, 41, 56, 62, 70, 88, 99};
int index=binarySearch(numbers, 18);
 

Write the indexes of the elements that would be examined by the binary search (the mid values in our algorithm's code) and write the value that would be returned from the search.

 

please find  :                                      indexes examined

                                                           and      value returned

Expert Solution
Explanation:

The binary search algorithm would work as follows:

  • Initialize start = 0, end = numbers.size()-1, and mid = (start + end) / 2 = 7
  • Compare numbers[mid] (24) with the target value (18), since 24 > 18, end = mid - 1 = 6
  • mid = (start + end) / 2 = 3, numbers[mid] (3) < 18, start = mid + 1 = 4
  • mid = (start + end) / 2 = 5, numbers[mid] (14) < 18, start = mid + 1 = 6
  • mid = (start + end) / 2 = 6, numbers[mid] (19) > 18, end = mid - 1 = 5
  • At this point, start > end, so the binary search terminates and returns -1, indicating that the target value was not found in the vector.

The elements examined by the binary search (in order) were: 24, 3, 14, 19.

The value returned by the search is -1.

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