Merge Sort is a Divide and Conquer algorithm which sorts given set of elements recursively.
Pseudocode of merge sort can be written as follows:
//A->array, l->left most index, r->right most indexMERGE-SORT(A, l, r)//function named “MERGE-SORT” to sort the array “A”, with the lower bound “l” and upper bound “r” and splits the array later into two parts. if l < r mid = (l+(r-l)/2) MERGE-SORT(A, l, mid)// Function call keeps on splitting the left part of the array till single element is achieved. MERGE-SORT (A, mid+1, r)// Function call keeps on splitting the right part of the array till single element is achieved.. MERGE(A, l, mid ,r)end funcMERGE(A, l, mid, r) nL = mid-l+1 //nL tells the max number of elements in the array L nR = r-mid //nR tells the max number of elements in the array R Create arrays L[1..nL+1] and R[1..nR+1] for i=0 to nL-1 L[i] = A[l+i] end for for j=0 to nR-1 // adds elements to the initial array A R[j] = A[m+l+j] end for i=0; j=0; k=l; while i < nL and j < nR // adds elements to the initial array A if L[i] <= R[j] A[k]=L[i]; i=i+1; k=k+1; else A[k]=R[j]; j=j+1; k=k+1; end while while i < nL // adds elements to the initial array A A[k]=L[i]; i=i+1; k=k+1; end while while j < nR // adds elements to the initial array A A[k]=R[j]; j=j+1; k=k+1; end whileend func
Merge Sort Explained:
C program for Merge Sort
#include<stdlib.h> #include<stdio.h> // Merges two subarrays of arr[ ]. // First subarray is arr[l..m] // Second subarray is arr[m+1..r] void merge(int arr[ ], int l, int m, int r) { int i, j, k; int n1 = m - l + 1; int n2 = r - m; /* create temp arrays */ int L[n1], R[n2]; /* Copy data to temp arrays L[ ] and R[ ] */ for (i = 0; i < n1; i++) L[i] = arr[l + i]; for (j = 0; j < n2; j++) R[j] = arr[m + 1+ j]; /* Merge the temp arrays back into arr[l..r]*/ i = 0; // Initial index of first subarray j = 0; // Initial index of second subarray k = l; // Initial index of merged subarray while (i < n1 && j < n2) { if (L[i] <= R[j]) { arr[k] = L[i]; i++; } else { arr[k] = R[j]; j++; } k++; } /* Copy the remaining elements of L[], if there are any */ while (i < n1) { arr[k] = L[i]; i++; k++; } /* Copy the remaining elements of R[], if there are any */ while (j < n2) { arr[k] = R[j]; j++; k++; } } /* l is for left index and r is right index of the sub-array of arr to be sorted */void mergeSort(int arr[], int l, int r) { if (l < r) { // Same as (l+r)/2, but avoids overflow for // large l and h int m = l+(r-l)/2; // Sort first and second halves mergeSort(arr, l, m); mergeSort(arr, m+1, r); merge(arr, l, m, r); } } /* UTILITY FUNCTIONS *//* Function to print an array */void printArray(int A[ ], int size) { int i; for (i=0; i < size; i++) printf("%d ", A[i]); printf("\n"); } /* Driver program to test above functions */int main() { int arr[] = {12, 11, 13, 5, 6, 7}; // or you can take input direct from the user itself using scanf function int arr_size = sizeof(arr)/sizeof(arr[0]); printf("Given array is \n"); printArray(arr, arr_size); mergeSort(arr, 0, arr_size - 1); printf("\nSorted array is \n"); printArray(arr, arr_size); return 0; }
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