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![Now as most of you must be knowing a major drawback of
the linear search that it is extremely time consuming for large
data sets .
Consider for Example we have an array with only five numbers
[1,3,0,8,5] and we want to search the number 5 in the array.
Then the maximum time taken to search the array would be
basically five iterations.](https://image.slidesharecdn.com/binarysearch-160914144503/85/Binary-search-2-320.jpg)
![However , consider a case where you have say 10,000
numbers in an array [i.e. numbers from 1 to 10000 in any
random fashion] and we want to search an element which is
the last number in the array.
Now as you can see here this is extremely time consuming as
it would take 10000 iterations to search the number.
This Is where we use binary search to speed up the operation
significantly.](https://image.slidesharecdn.com/binarysearch-160914144503/85/Binary-search-3-320.jpg)
![Now as most of you must be knowing a major drawback of
the linear search that it is extremely time consuming for large
data sets .
Consider for Example we have an array with only five numbers
[1,3,0,8,5] and we want to search the number 5 in the array.
Then the maximum time taken to search the array would be
basically five iterations.](https://image.slidesharecdn.com/binarysearch-160914144503/75/Binary-search-2-2048.jpg)
![However , consider a case where you have say 10,000
numbers in an array [i.e. numbers from 1 to 10000 in any
random fashion] and we want to search an element which is
the last number in the array.
Now as you can see here this is extremely time consuming as
it would take 10000 iterations to search the number.
This Is where we use binary search to speed up the operation
significantly.](https://image.slidesharecdn.com/binarysearch-160914144503/75/Binary-search-3-2048.jpg)
Uploaded byronit gaikwad
Binary search
The document discusses the drawbacks of linear search in large datasets, illustrating its inefficiency through examples. It introduces binary search as a more efficient algorithm that significantly reduces the number of iterations required for finding an element in a sorted array. However, it emphasizes that binary search can only be applied to sorted arrays, which is its main limitation.
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Binary search
- 1.
- 2. Now as mostof you must be knowing a major drawback of the linear search that it is extremely time consuming for large data sets . Consider for Example we have an array with only five numbers [1,3,0,8,5] and we want to search the number 5 in the array. Then the maximum time taken to search the array would be basically five iterations.
- 3. However , considera case where you have say 10,000 numbers in an array [i.e. numbers from 1 to 10000 in any random fashion] and we want to search an element which is the last number in the array. Now as you can see here this is extremely time consuming as it would take 10000 iterations to search the number. This Is where we use binary search to speed up the operation significantly.
- 4. The pre requirementfor binary search is that the array should be in a sorted order. The following example will give you a better understanding of the working of the binary search algorithm.
- 5. 1 2 34 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Suppose the user wants to find the number 7 in the array of 20 numbers given below. To find 7, the number would be initially compared with middle element of the array say 10. Iteration no - 01
- 6. 1 2 34 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Now as we see the array is sorted and the number 7 is less than 10 the array after the number 10 is totally discarded thus reducing the array to be searched by half.
- 7. 1 2 34 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Now similar process is done on the rest of the array. Now the array to be searched is between the numbers 1 to 10. Again in a similar fashion the middle element of the array is searched and compared with the number 7. Again since 5 is the middle element it is not the number to be searched. Iteration no - 02
- 8. 1 2 34 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Now here as we see the number 7 is greater than 5 the array numbers 1 to 4 are discarded and the array to be searched is now from 5 to 10.
- 9. 1 2 34 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Again the same thing is done . The middle element of the array is found out i.e. the middle element of the array between 5 to 10 which turns out to be 7 the number to be found out. Iteration no - 03
- 10. 1 2 34 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Thus using binary search we found out the number 7 from an array of 20 numbers in 3 iterations which would have taken 7 iterations using linear search thus reducing the work by half.
- 11. Thus we seethat binary search is a much more efficient algorithm for searching in a large list then the linear search algorithm. The only drawback of the algorithm being the array on which the search is being performed should be COMPULSORILY in the sorted order.