===== Run-Length Encoding (RLE) =====

Run-Length Encoding (RLE) is one of the simplest **lossless data compression** techniques.  
It works by replacing sequences of **repeated elements** (called "runs") with a single value and a repetition count.

Run-Length Encoding cannot be attributed to a single inventor; rather, it is based on one of the earliest and simplest general principles of data compression, developed and first used in the 1950s for computer image processing.

----

==== Basic Idea ====
When a sequence contains the same value multiple times in a row, instead of storing it multiple times, we store only the value and the number of times it repeats.

For example:
<code>
AAAAABBBCCDAA → 5A3B2C1D2A
</code>

Here:
  * 'A' repeats 5 times → 5A  
  * 'B' repeats 3 times → 3B  
  * 'C' repeats 2 times → 2C  
  * 'D' repeats 1 time → 1D  
  * 'A' repeats again 2 times → 2A

The original message had 12 characters, but the encoded version has only 10, so there is some compression (especially for longer runs).

----

==== Binary Example ====
RLE is especially effective for **binary data**, such as black-and-white images.

Example (0 = white pixel, 1 = black pixel):

<code>
Original: 000000001111100000011111111000000000
Encoded : 8 0s, 5 1s, 6 0s, 8 1s, 7 0s → (8,0)(5,1)(6,0)(8,1)(7,0)
</code>

This binary form is what early image formats (like **PCX**, **TGA**) and **FAX machines** used.

----

==== Decoding ====
To reconstruct (decode) the original message, we simply repeat each symbol as many times as its count indicates.

For example:
<code>
Encoded: 12W1B12W3B24W1B14W
Decoded: WWWWWWWWWWWWBWWWWWWWWWWWWBBBWWWWWWWWWWWWWWWWWWWWWWWWBWWWWWWWWWWWWWWW
</code>

----

==== Advantages ====
  * Very simple to implement
  * Works well for data containing **long runs of identical values** (e.g., simple images, icons, masks)
  * Low computational cost (fast encoding/decoding)

----

==== Disadvantages ====
  * Inefficient when the data changes frequently (e.g., photographs, text files)
  * May increase file size if no long runs exist (e.g,. `ABCD` → `1A1B1C1D`, which is longer)
  * Usually combined with other compression algorithms in practical applications

----

==== Applications ====
  * Image compression (TGA, PCX, BMP with RLE)
  * FAX transmission (CCITT Group 3/4 standard)
  * Simple bitmap fonts
  * Storing masks and binary patterns
  * Used as a sub-step in complex formats (e.g., TIFF, PDF internal compression)

----
A C program that implements this algorithm:

<sxh c>
#include <stdio.h>
#include <string.h>

void runLengthEncoding(const char *input) {
    int length = strlen(input);
    
    for (int i = 0; i < length; i++) {
        // Count occurrences of the current character
        int count = 1;
        while (i < length - 1 && input[i] == input[i + 1]) {
            count++;
            i++;
        }
        
        // Print the count followed by the character
        printf("%d%c", count, input[i]);
    }
    
    printf("\n"); // New line after encoding
}

int main() {
    // Example string to encode
    char input[] = "WWWWWWWWWWWWBWWWWWWWWWWWWBBBWWWWWWWWWWWWWWWWWWWWWWWWBWWWWWWWWWWWWWWW";
    
    printf("Original String: %s\n", input);
    printf("Run-Length Encoded: ");
    runLengthEncoding(input);
    
    return 0;
}
</sxh>