# What is the recurrence equation for the merge sort?

## What is the recurrence equation for the merge sort?

It is possible to come up with a formula for recurrences of the form T(n) = aT(n/b) + nc (T(1) = 1). This is called the master method. – Merge-sort ⇒ T(n)=2T(n/2) + n (a = 2,b = 2, and c = 1).

What is the solution of recurrence?

Linear Recurrence Relations

Recurrence relations Initial values Solutions
Fn = Fn-1 + Fn-2 a1 = a2 = 1 Fibonacci number
Fn = Fn-1 + Fn-2 a1 = 1, a2 = 3 Lucas Number
Fn = Fn-2 + Fn-3 a1 = a2 = a3 = 1 Padovan sequence
Fn = 2Fn-1 + Fn-2 a1 = 0, a2 = 1 Pell number

What is recurrence for worst case of Mergesort?

algorithm sorting time-complexity mergesort recurrence. This is the recurrence of the worst-case running time T(n) of the Merge-Sort procedure.

### What is the recurrence relation for the number of comparisons of the mergesort algorithm?

Eq. 2.1 is the recurrence relation for Merge Sort. T(N) refers to the total number of comparisons between array elements in Merge Sort when we are sorting the entire array of N elements. The divide stage performs Merge Sort on two halves of the array, which is what 2*T(N/2) refers to.

Is merge sort worse than heap sort?

Heap Sort is better :The Heap Sort sorting algorithm uses O(1) space for the sorting operation while Merge Sort which takes O(n) space Merge Sort is better * The merge sort is slightly faster than…

What does merge sort mean?

In computer science, merge sort (also commonly spelled mergesort) is an efficient, general-purpose, comparison-based sorting algorithm. Most implementations produce a stable sort, which means that the order of equal elements is the same in the input and output.

## Is merge sort a stable sorting algorithm?

Merge sort is an algorithm based on the divide and conquer paradigm which was invented by John von Neumann in the year 1945. It is a stable but not an in-place sorting algorithm. A stable sorting algorithm is the one where two keys having equal values appear in the same order in the sorted output array as it is present in the input unsorted array.

What is the base case of merge sort?

Merge sort is a recursive algorithm that continually splits a list in half. If the list is empty or has one item , it is sorted by definition (the base case). If the list has more than one item, we split the list and recursively invoke a merge sort on both halves.