Lecture 348:- Merging

Merging is a fundamental operation in various algorithms, especially in sorting and divide-and-conquer algorithms. It involves combining two or more sorted sequences (arrays, lists, or other data structures) into a single sorted sequence.

The process of merging is usually straightforward and efficient because both input sequences are already sorted. Merging can be performed in linear time, making it a key operation in several sorting algorithms like Merge Sort.

Let's explore the merging process using two sorted arrays as an example:

Suppose we have two sorted arrays:

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Array 1: [3, 6, 9, 12] Array 2: [4, 7, 8, 10, 11]

The task is to merge these two arrays into a single sorted array.

Merging Algorithm:

1. Initialize three variables: i for Array 1, j for Array 2, and an empty array result to store the merged elements.
2. Compare the elements at indices i and j in Array 1 and Array 2, respectively.
3. Select the smaller element among the two and add it to the result array.
4. Increment the corresponding index (i or j) of the selected element in the original array from which it was chosen.
5. Repeat steps 2 to 4 until all elements of either Array 1 or Array 2 are added to the result array.
6. Once one of the arrays is completely processed, add the remaining elements of the other array (if any) to the result array.

Using the example arrays above, the merged array will be:

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Merged Array: [3, 4, 6, 7, 8, 9, 10, 11, 12]

Merging is a crucial operation in Merge Sort, where it combines the sorted sub-arrays during the merging step to achieve the overall sorted array. The time complexity of merging is O(n), where n is the total number of elements in the input arrays.

Many other algorithms and data structures also utilize merging, making it a fundamental and efficient operation in computer science.