Inverting the Move to Front Transform
Prerequisite:Move To Front Data Transform Algorithm
The main idea behind inverse of MTF Transform:
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1. To compute inverse of MTF Transform is to undo the MTF Transform and recover the original string. We have with us “input_arr” which is the MTF transform and “n” which is the number of elements in “input_arr”.
2. Our task is to maintain an ordered list of characters (a to z, in our example) and read in “ith”element from “input_arr” one at a time.
3.Then, taking that element as index j, print “jth” character in the list.
Illustration for "[15 1 14 1 14 1]" List initially contains English alphabets in order. We move characters at indexes depicted by input to front of the list one by one. input arr chars output str list 15 p abcdefghijklmnopqrstuvwxyz 1 pa pabcdefghijklmnoqrstuvwxyz 14 pan apbcdefghijklmnoqrstuvwxyz 1 pana napbcdefghijklmoqrstuvwxyz 14 panam anpbcdefghijklmoqrstuvwxyz 1 panama manpbcdefghijkloqrstuvwxyz
Examples:
Input : arr[] = {15, 1, 14, 1, 14, 1}
Output : panama
Input : arr[] = {6, 5, 0, 10, 18, 8, 15, 18,
6, 6, 0, 6, 6};
Output : geeksforgeeks
Following is the code for idea explained above:
// C program to find Inverse of Move to Front// Transform of a given string#include<stdio.h>#include<stdlib.h>#include<string.h> // Takes index of printed character as argument// to bring that character to the front of the listvoid moveToFront(int index, char *list){ char record[27]; strcpy(record, list); // Characters pushed one position right // in the list up until index strncpy(list+1, record, index); // Character at index stored at 0th position list[0] = record[index];} // Move to Front Decodingvoid mtfDecode(int arr[], int n){ // Maintains an ordered list of legal symbols char list[] = "abcdefghijklmnopqrstuvwxyz"; int i; printf("\nInverse of Move to Front Transform: "); for (i = 0; i < n; i++) { // Printing characters of Inverse MTF as output printf("%c", list[arr[i]]); // Moves the printed character to the front // of the list moveToFront(arr[i], list); }} // Driver program to test functions aboveint main(){ // MTF transform and number of elements in it. int arr[] = {15, 1, 14, 1, 14, 1}; int n = sizeof(arr)/sizeof(arr[0]); // Computes Inverse of Move to Front transform // of given text mtfDecode(arr, n); return 0;} |
Output:
Inverse of Move to Front Transform: panama
Time Complexity: O(n^2)
Exercise: Implement MTF encoding and decoding together in one program and check if the original message is recovered.
Source:
http://www.cs.princeton.edu/courses/archive/fall07/cos226/assignments/burrows.html
