Table of Contents
- 1 How many comparisons are needed for a binary search in a set of 10 elements?
- 2 What is the average number of comparisons required to search an element using binary search?
- 3 When using binary search What is the average number of comparisons needed to search an array of length?
- 4 What is the maximum number of comparisons in a binary search?
- 5 What many comparisons on average is required for the sequential search algorithm within a list of n items?
How many comparisons are needed for a binary search in a set of 10 elements?
Running time of binary search
| n | log 2 n \log_2 n log2n |
|---|---|
| 128 | 7 |
| 256 | 8 |
| 512 | 9 |
| 1024 | 10 |
How do you find the number of comparisons in a binary search?
- The time complexity or O(n) of Binary search is log n (base 2) as the “domain” halves after each comparison, so if you half a million 21 times you will reach 1 answer which will be the number you need.
- for 8 numbers in a binary search we will need at most 4 i.e. log 8 +1 =4.
What is the average number of comparisons required to search an element using binary search?
So average number of comparisons = 1+2∗3+4∗5+3∗710=4.8.
What is the minimum number of comparisons necessary when performing a linear and binary search on 1024 items?
Answer and Explanation: For a sorted list of 1024 elements, a binary search takes at most 11 comparisons.
When using binary search What is the average number of comparisons needed to search an array of length?
N/2 comparisons
In general, for a list of length N, the worst case is N comparisons and the average case is N/2 comparisons.
How many comparisons are needed for linear search array when elements are in order in best case?
one comparison
For a list with n items, the best case is when the value is equal to the first element of the list, in which case only one comparison is needed.
What is the maximum number of comparisons in a binary search?
8. Efficiency Comparison
| Size of List | Maximum Number of Comparisons | |
|---|---|---|
| Linear Search | Binary Search | |
| 100,000 | 100,000 | 16 |
| 200,000 | 200,000 | 17 |
| 400,000 | 400,000 | 18 |
How does binary search differ from linear search?
Linear search is a search that finds an element in the list by searching the element sequentially until the element is found in the list. On the other hand, a binary search is a search that finds the middle element in the list recursively until the middle element is matched with a searched element.
What many comparisons on average is required for the sequential search algorithm within a list of n items?
Thus, on average, successful sequential searches of an N item list require ½ N comparisons. So, given a list of 10,000 items, on average 5,000 comparisons are required to find an item that is in the list.