Many useful algorithms are recursive in structure: to solve a given problem, they call themselves recursively one or more times to deal with closely related subproblems.
These algorithms typically follow a divide-and-conquer approach: they break the problem into several subproblems that are similar to the original problem but smaller in size, solve the subproblems recursively, and then combine these solutions to create a solution to the original problem.
The divide-and-conquer paradigm involves three steps at each level of the recursion:
- Divide the problem into a number of subproblems that are smaller instances of the same problem.
- Conquer the subproblems by solving them recursively. If the subproblem sizes are small enough, however, just solve the subproblems in a straightforward manner.
- Combine the solutions to the subproblems into the solution for the original problem.
The merge sort algorithm closely follows the divide-and-conquer paradigm. Intuitively, it operates as follows.
- Divide: Divide the n-element sequence to be sorted into two subsequences of n=2 elements each.
- Conquer: Sort the two subsequences recursively using merge sort.
- Combine: Merge the two sorted subsequences to produce the sorted answer.
here is a basic code in python
import sys SENTINEL = sys.maxint def merge(input\_array,first,middle,last): n1 = middle - first + 1 n2 = last - middle L = [None for t in range(n1+1)] R = [None for t in range(n2+1)] for i in range(n1): L[i] = input\_array[first + i - 1] for j in range(n2): R[j] =input\_array[middle + j] L[n1] = SENTINEL R[n2] = SENTINEL i = 0 j = 0 for k in range(first-1,last): if L[i] <= R[j]: input\_array[k] = L[i] i = i + 1 else: input\_array[k] = R[j] j = j + 1 def mergeSort(input\_array,first,last): if first < last: middle = int((first + last)/2) mergeSort(input\_array,first,middle) mergeSort(input\_array,middle + 1,last) merge(input\_array,first,middle,last) arr = [5,2,4,7,1,3,2,6] mergeSort(arr,1,len(arr)) print arr
Hope this helps ;)