Here we need to notice that array underlying data structure of ArrayList stores all values in a continuous memory location, but DoublyLinkedList store each node at a random memory location. Iterating through continuous memory location is more performance efficient than random memory location, that is why we prefer ArrayList over LinkedList when searching by value. ArrayList can give you any element in O 1 complexity as the array has random access property.
You can access any index directly without iterating through the whole array. LinkedList has a sequential access property. It needs to iterate through each element to reach a given index, so time complexity to get a value by index from LinkedList is O N. It is similar to adding value at a given index. To remove an element by value in ArrayList and LinkedList we need to iterate through each element to reach that index and then remove that value.
This operation is of O N complexity. The difference is that to remove an element from LinkedList, we just need to modify pointers, which is O 1 complexity, but In ArrayList, we need to shift all elements after the index of the removed value to fill the gap created. As shifting is costly operation then modifying pointers, so even after the same overall complexity O N , we prefer LinkedList where more delete by value operation is required.
To remove by index, ArrayList find that index using random access in O 1 complexity, but after removing the element, shifting the rest of the elements causes overall O N time complexity.
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