Merge pull request #20 from juitelavane/sortalgo

Fix: #14 Add new sorting algo (merge sort)

algorithms/searching and sorting/merge sort/README.md

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+# Merge Sort
+
+## What is merge sort? 
+Merge sort is a sorting algorithm based on the Divide and conquer strategy. It works by recursively dividing the array into two equal halves, then sort them and combine them. 
+It takes a time of (n logn) in the worst case.
+
+## Features of binary search
+-Merge Sort is useful for sorting linked lists.
+-Merge Sort is a stable sort which means that the same element in an array maintain their original positions with respect to each other.
+-Overall time complexity of Merge sort is O(nLogn). It is more efficient as it is in worst case also the runtime is O(nlogn)
+-The space complexity of Merge sort is O(n). This means that this algorithm takes a lot of space and may slower down operations for the last data sets.

algorithms/searching and sorting/merge sort/merge sort.cpp

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+#include<iostream>
+using namespace std;
+void swapping(int &a, int &b) {     //swap the content of a and b
+   int temp;
+   temp = a;
+   a = b;
+   b = temp;
+}
+void display(int *array, int size) {
+   for(int i = 0; i<size; i++)
+      cout << array[i] << " ";
+   cout << endl;
+}
+void merge(int *array, int l, int m, int r) {
+   int i, j, k, nl, nr;
+   //size of left and right sub-arrays
+   nl = m-l+1; nr = r-m;
+   int larr[nl], rarr[nr];
+   //fill left and right sub-arrays
+   for(i = 0; i<nl; i++)
+      larr[i] = array[l+i];
+   for(j = 0; j<nr; j++)
+      rarr[j] = array[m+1+j];
+   i = 0; j = 0; k = l;
+   //marge temp arrays to real array
+   while(i < nl && j<nr) {
+      if(larr[i] <= rarr[j]) {
+         array[k] = larr[i];
+         i++;
+      }else{
+         array[k] = rarr[j];
+         j++;
+      }
+      k++;
+   }
+   while(i<nl) {       //extra element in left array
+      array[k] = larr[i];
+      i++; k++;
+   }
+   while(j<nr) {     //extra element in right array
+      array[k] = rarr[j];
+      j++; k++;
+   }
+}
+void mergeSort(int *array, int l, int r) {
+   int m;
+   if(l < r) {
+      int m = l+(r-l)/2;
+      // Sort first and second arrays
+      mergeSort(array, l, m);
+      mergeSort(array, m+1, r);
+      merge(array, l, m, r);
+   }
+}
+int main() {
+   int n;
+   cout << "Enter the number of elements: ";
+   cin >> n;
+   int arr[n];     //create an array with given number of elements
+   cout << "Enter elements:" << endl;
+   for(int i = 0; i<n; i++) {
+      cin >> arr[i];
+   }
+   cout << "Array before Sorting: ";
+   display(arr, n);
+   mergeSort(arr, 0, n-1);     //(n-1) for last index
+   cout << "Array after Sorting: ";
+   display(arr, n);
+}
+
+