How to solve a merge sort problem?

How it works:

  1. Divide the unsorted array into two sub-arrays, half the size of the original.
  2. Continue to divide the sub-arrays as long as the current piece of the array has more than one element.
  3. Merge two sub-arrays together by always putting the lowest value first.
  4. Keep merging until there are no sub-arrays left.

How to do merge sort step by step?

The instructions for executing a merge sort in full can be written as:

  1. Step 1: Take a list of data to be sorted.
  2. Step 2: Repeatedly split the list in half to give sublists, until each sublist only contains a single item.
  3. Step 3: Repeat steps 4–9 (a merge) until all sublists have been merged.

What is the formula for merge sort?

If the running time (number of comparisons) of merge sort for a list of length n is T(n), then the recurrence relation T(n) = 2T(n/2) + n follows from the definition of the algorithm (apply the algorithm to two lists of half the size of the original list, and add the n steps taken to merge the resulting two lists).

Why is merge sort O nlogn?

In Merge Sort, the best, average, and worst-case time complexities are all O(n log n). This consistency is due to the algorithm always dividing the array into two halves and merging them, regardless of the initial order of elements.

First, divide the list into the smallest unit (1 element), then compare each element with the adjacent list to sort and merge the two adjacent lists. Finally, …
Here’s how merge sort uses divide-and-conquer: Divide by finding the number q of the position midway between p and r.