## Leaps-and-bounds algorithm :

The Leaps-and-Bounds algorithm is a search method that uses a combination of linear and binary search techniques to efficiently find a target value within a sorted array. This algorithm is particularly useful when searching for a specific value within a large dataset, as it can significantly reduce the number of steps required to locate the target value.

To understand how the Leaps-and-Bounds algorithm works, let’s consider the following example:

Suppose we have a sorted array of integers [1, 2, 4, 6, 7, 8, 9, 11, 13, 14, 15, 16, 17, 18, 19, 20]. We want to search for the value 8 within this array using the Leaps-and-Bounds algorithm.

The first step in the Leaps-and-Bounds algorithm is to use a linear search to find a rough estimate of the target value’s location within the array. In our example, we can use the linear search to quickly determine that the value 8 is likely to be located somewhere between the values 7 and 11.

Next, the Leaps-and-Bounds algorithm uses a binary search to refine the estimate of the target value’s location. In our example, we can use the binary search to quickly determine that the value 8 is located between the values 7 and 9.

Finally, the Leaps-and-Bounds algorithm uses a linear search to find the exact location of the target value within the refined search space. In our example, we can use the linear search to quickly locate the value 8 within the array.

The advantage of using the Leaps-and-Bounds algorithm is that it can significantly reduce the number of steps required to find a target value within a large dataset. In our example, using the Leaps-and-Bounds algorithm allowed us to quickly locate the value 8 within the array without having to search through every element in the array.

Another example of how the Leaps-and-Bounds algorithm can be useful is in the context of searching for a specific word within a large text document. Suppose we have a text document that contains a large number of words and we want to search for the word “apple” within this document.

Using the Leaps-and-Bounds algorithm, we can quickly locate the word “apple” within the text document without having to search through every word in the document. First, we can use a linear search to find a rough estimate of the word’s location within the document. This could involve searching through the first few hundred words in the document and looking for any words that start with the letter “a”.

Next, we can use a binary search to refine the estimate of the word’s location within the document. This could involve dividing the document into two halves and searching for the word “apple” within each half.

Finally, we can use a linear search to find the exact location of the word “apple” within the document. This could involve searching through the words in the refined search space and looking for the word “apple”.

Overall, the Leaps-and-Bounds algorithm is a powerful search method that can be used to efficiently locate a target value within a large dataset. By combining linear and binary search techniques, the Leaps-and-Bounds algorithm can significantly reduce the number of steps required to find a target value, making it a useful tool for solving many different types of search problems.