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Standard merging procedure for merging two sorted arrays array_1: [10] and array_2: [1,2,3,4,6,9,14] goes as below: Standard merging procedure for merging two sorted arrays array_1: [10] and array_2: [1,2,3,4,6,9,14] goes as below:
CREATE GIF CREATE GIF
![enter image description here](https://lh3.googleusercontent.com/fGNXjeqWRQEtqN3ZjxR55HsZv61YSpxgT98dpXaCe2YMmBNaJz9O5jrMFRamL1GV3DkAuWhUVuOV) ![enter image description here](https://github.com/KingsGambitLab/Lecture_Notes/blob/master/articles/Akash%20Articles/md/Images/Tim_Sort/11.jpg)
![enter image description here](https://lh3.googleusercontent.com/pDUhaOlftbV2L3ITwk18SVkVG5NXuGoMJ1XDC3q50IjgYAn-c-DJmP6l2nILbwe32ulWNnW0FkbC) ![enter image description here](https://github.com/KingsGambitLab/Lecture_Notes/blob/master/articles/Akash%20Articles/md/Images/Tim_Sort/12.jpg)
![enter image description here](https://lh3.googleusercontent.com/MQw924q3lie_KKdFj1AaAWnMghDVP7TCcugsp71Uk4Z8VdvvJ-I5IaMknrBG7N0T-XCmZqAB4wtB) ![enter image description here](https://github.com/KingsGambitLab/Lecture_Notes/blob/master/articles/Akash%20Articles/md/Images/Tim_Sort/13.jpg)
![enter image description here](https://lh3.googleusercontent.com/jUk_Vzny2Ro0bRttqEEsd8627CbHZ7jVkdjZzeLbpBCic5oNhCDhEy8naQA68xKmkO9ucDH7A933) ![enter image description here](https://github.com/KingsGambitLab/Lecture_Notes/blob/master/articles/Akash%20Articles/md/Images/Tim_Sort/14.jpg)
![enter image description here](https://lh3.googleusercontent.com/RDQTt974n5uox1D9LtQhMpgyf9v3_aqc8fL4q9jwYmbJo1nrlGgUPUZNSf63DGPoJ2U54oTcEjp6) ![enter image description here](https://github.com/KingsGambitLab/Lecture_Notes/blob/master/articles/Akash%20Articles/md/Images/Tim_Sort/15.jpg)
![enter image description here](https://lh3.googleusercontent.com/9Ma4pKJQPO866e8PdytQZnZ3ljcuO-A38mNT9QNU6qsn7ZvgCAiU4dLbyyfBkAiBa9WdRMef8o1Z) ![enter image description here](https://github.com/KingsGambitLab/Lecture_Notes/blob/master/articles/Akash%20Articles/md/Images/Tim_Sort/16.jpg)
![enter image description here](https://lh3.googleusercontent.com/2ilz_WMDaNbLNdQ5xop1vwHjMkufbNt8KH93pAE6JIDIPUl9Ub0JH6YdZZJIK9e_jkJu3oKpLG6j) ![enter image description here](https://github.com/KingsGambitLab/Lecture_Notes/blob/master/articles/Akash%20Articles/md/Images/Tim_Sort/17.jpg)
![enter image description here](https://lh3.googleusercontent.com/ZY8fNtYIR3ZbWESgVeUm20GuFpz-34X7YqHvSxKmmwtsFIwWmDfDuJiNSX1UpccRkz2ap3I7oN5v) ![enter image description here](https://github.com/KingsGambitLab/Lecture_Notes/blob/master/articles/Akash%20Articles/md/Images/Tim_Sort/18.jpg)
As you can see we are consistently taking elements from array_2 until we reach $14$. But can we do better? Yes, use galloping. As you can see we are consistently taking elements from array_2 until we reach $14$. But can we do better? Yes, use galloping.
@ -48,7 +48,7 @@ Note that we can do galloping(exponential search) from any side of the array, ei
The starting position for the search is called a "$hint$". Sometimes it is better to search from the left and sometimes from the right. For the given array below, The starting position for the search is called a "$hint$". Sometimes it is better to search from the left and sometimes from the right. For the given array below,
![enter image description here](https://lh3.googleusercontent.com/jkr4R3v4liODaPlf3MzaGwXpTg83InKn6lOxX3XwdilDeDkZZO6RegRb8ZaFyHxRddkz7BdOPXFH) ![enter image description here](https://github.com/KingsGambitLab/Lecture_Notes/blob/master/articles/Akash%20Articles/md/Images/Tim_Sort/19.jpg)
If we want to find position for $3$, then starting from index 0($hint = 0$) is efficient, but if we are looking for position of $13$ then starting from index $len-1$($hint = len-1$) is more efficient. **It is particularly efficient for big arrays.** If we want to find position for $3$, then starting from index 0($hint = 0$) is efficient, but if we are looking for position of $13$ then starting from index $len-1$($hint = len-1$) is more efficient. **It is particularly efficient for big arrays.**
@ -63,13 +63,13 @@ We have two types of galloping function `gallopRight` and `gallopLeft`, the main
For example, for the array given below, For example, for the array given below,
![enter image description here](https://lh3.googleusercontent.com/FxAq82p754Q1Zkpdzca65jujMzeCx-9ho_rBWF2mUWJo5fu7-q8siSlVVgsJ4_Obln-B6i-AKJ5Y) ![enter image description here](https://github.com/KingsGambitLab/Lecture_Notes/blob/master/articles/Akash%20Articles/md/Images/Tim_Sort/110.jpg)
If you find a position of 13 by using galloping, then `gallopLeft` will return 6, but `gallopRight` will return 9. If you find a position of 13 by using galloping, then `gallopLeft` will return 6, but `gallopRight` will return 9.
In simple mode, it is trivial to maintain stability, but to maintain stability while merging in galloping mode, we sometimes use `gallopRight` and sometimes `gallopLeft`. Just to get the basic idea, see the below example, it will be more clear when we will the merge procedure. In simple mode, it is trivial to maintain stability, but to maintain stability while merging in galloping mode, we sometimes use `gallopRight` and sometimes `gallopLeft`. Just to get the basic idea, see the below example, it will be more clear when we will the merge procedure.
![enter image description here](https://lh3.googleusercontent.com/s-xqdPcSotlep3yl-xYqiFNzcEhbfBih0ZqLFS_uNXJN_pGoTGsXKcu9VJTRcYykYb4tqyLt_4XJ) ![enter image description here](https://github.com/KingsGambitLab/Lecture_Notes/blob/master/articles/Akash%20Articles/md/Images/Tim_Sort/111.jpg)
Now, if we are finding a position of run2[0] in run1, then we will use `gallopRight`, but if we are finding a position for run1[3] in run2, then we will use `gallopLeft`. Now, if we are finding a position of run2[0] in run1, then we will use `gallopRight`, but if we are finding a position for run1[3] in run2, then we will use `gallopLeft`.