Inverting the Move to Front Transform

Prerequisite:Move To Front Data Transform Algorithm

The main idea behind inverse of MTF Transform:

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 list 
void 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 Decoding 
void 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 above 
int 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

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