| b | e | k | o | p | r |
|---|---|---|---|---|---|
| 1 | 3 | 2 | 2 | 1 | 1 |
Ben Tanen · COMP-150
This is a visual explanation and exploration of adaptive Huffman coding and how it compares to traditional static Huffman coding. Specifically, we will focus on how our encoding trees might differ when using adaptive vs. static Huffman.
First, we will explore how traditional Huffman coding builds its encoding tree for a specific string, in this case "bookkeeper". We will then do the same for adaptive Huffman coding using the FGK algorithm and compare these two trees. At the end, you can further explore how static vs. Huffman coding trees compare through other strings.
Want to skip ahead? Click here for the explanation of the adaptive FGK algorithm and click here to explore other words.
Before we get started, let's quickly discuss what exactly Huffman coding is. When we transmit information, we generally need to convert some sort of data (text, pictures, etc.) into binary. To do this, we assign codes to help us distinguish between different pieces of data.
For example, if we had the string "abca", we might assign codes like: $a$ = 00, $b$ = 01, $c$ = 10. This would make it so that our binary encoding of "abca" is "00 01 10 00".
But what if we wanted to encode "aabaacaa"? If we used our original encoding where we use two bits for each character, we would be treating $a$ and $c$ with equal importance, even though $a$ appears much more.
Wouldn't it be more efficient if we used fewer bits for $a$ and more bits for $c$? This is where Huffman coding comes in.
Huffman coding is a lossless data compression algorithm that assigns variable-length codes based on the frequencies of our input characters.
In order to determine what code to assign to each character, we will first build a binary tree that will organize our characters based on frequency.
As an example, let's encode the string "bookkeeper". Before we can start encoding, we will build our Huffman tree for this string, which will in turn show us what binary encoding we will use for each character.
To start, we need to count the frequency for each character in our string and store these frequencies in a table.
We will use this table to add nodes and edges that will build up our tree.
First, we start by adding leaf nodes for the two characters that occur the least. In this case, we have a tie between $b$, $p$, and $r$, so we'll just arbitrarily choose $p$ and $r$.
When we add in our leaves for $p$ and $r$, we will attach them to a parent node for a new pseudo-character "pr". This pseudo-character represents occurrences of $p$ or $r$ so it's frequency is equal to the frequency of $p$ plus the frequency of $r$.
We will also update our table to include our new pseudo-character. We can get this by simply merging the columns of $p$ and $r$.
With a now reduced table, we can repeat this process again for our updated values.
As we can see, $b$ has the lowest frequency in our table so we'll use that. For the second lowest frequency, there is a tie between $k$, $o$, and "pr", so we can again pick arbitrarily. Let's use our pseudo-character "pr".
Since we don't have a leaf node for $b$ yet, we will have to add that into our tree.
Then, as we did before, we'll attach our $b$ node and our "pr" node to a parent node for a new pseudo-character "bpr".
Finally, we'll update our table to reflect our new pseudo-character.
It looks like our tree is coming along, but it doesn't quite have everything yet.
To keep going, we can repeat this process again...
...and again
...and again
...until our table is only left with one value, a pseudo-character containing all of our original characters. This means we're done building our Huffman tree!
So how do we use this tree to assign codes?
As we walk from root to leaf, we will denote a left traversal with "0" and a right traversal with a "1".
In our walk from root to the $p$ leaf, we go left, right, right, and left again. This means we will use four bits to encode $p$ as "0110".
For our walk to $k$, we traverse right then left. This means we will only use two bits to encode $k$ as "10".
It seems like our tree works - hooray for efficiency!
If we do this for all of our characters, we get our full binary encoding scheme. Let's compare this new Huffman scheme against a naive encoding scheme where we just arbitrarily assign binary codes.
| char | $b$ | $e$ | $k$ | $o$ | $p$ | $r$ |
|---|---|---|---|---|---|---|
| freq | 1 | 3 | 2 | 2 | 1 | 1 |
| old code | 000 | 001 | 010 | 011 | 100 | 101 |
| new code | 010 | 11 | 10 | 11 | 0110 | 0111 |
Using the naive scheme, encoding "bookkeeper" would take 30 bits. Using our Huffman scheme, we only use 25 bits to encode, which is a roughly a 17% improvement!
A small thing to note: as we were building our tree, when choosing our two least frequent characters in our table, we repeatedly had ties between three or more characters. When this happened, we would choose two of our tied elements arbitrarily.
By doing this, we can see that our arbitrary choice will change our tree. This means we can actually get multiple different trees from the same input string. For example, we could have initially chosen to start with $b$ and $r$ instead of $p$ and $r$. If we had done this, we would get a very similar tree but the $b$ and $p$ nodes would have been swapped.
While these trees might differ in their arrangement and shape, they are all valid Huffman trees. Since the algorithm is based on frequencies, this means that it doesn't matter if we assign a three-bit code to $b$ and a four-bit code to $p$ or vice versa. The tree and resulting encoding scheme will still result in the same efficiency improvement.
So how does this tree and this encoding compare to the one produced using adaptive Huffman coding? Keep scrolling to find out!
Want to skip around? Click here to head back to the beginning and click here to explore other words.
A favorite of romantic comedies. Two protagonists pretend to date for a pragmatic reason (inheritance, a family wedding, jealousy) and—surprise—catch real feelings. The joy here is the dramatic irony: the audience sees the truth long before the characters admit it.
Before we discuss plot points, we must understand why we care. In fandom culture, audiences "ship" characters (short for relationship). Whether it is Aragorn and Arwen or Lorelai and Luke, the act of investing in a romantic storyline activates the brain’s reward system.
The Dopamine Loop: Romantic storylines are structured around proximity, uncertainty, and resolution. When two characters almost kiss but are interrupted, your brain releases dopamine—the anticipation drug. When they finally confess their love, you get an oxytocin hit (the bonding chemical). Writers exploit this biological reality. A great romantic storyline is not just a narrative; it is a neurological roller coaster.
Why Conflict is Sexier Than Compatibility: In real life, we seek low-conflict partners. In fiction, we crave friction. Enemies-to-lovers, forbidden love, and second-chance romances thrive because conflict creates tension. Tension creates emotional investment. As the screenwriter Robert McKee famously said, "True character is revealed in the choices a human being makes under pressure." Nothing applies more pressure than love.
Romantic storylines are a cornerstone of human storytelling, appearing across literature, film, television, and digital media. This paper examines the structural and psychological functions of romantic relationships in narratives. It argues that effective romantic storylines serve not merely as subplots but as engines of character development, thematic exploration, and audience engagement. Drawing on narrative theory, attachment psychology, and genre analysis, the paper analyzes common tropes (e.g., enemies-to-lovers, slow burn, love triangles), their emotional impact, and their evolution in contemporary media. The conclusion addresses criticisms of romantic clichés and proposes a framework for writing authentic, compelling romantic arcs.
Relationships and romantic storylines endure because they are never merely about love—they are about vulnerability, choice, timing, and growth. Effective romantic arcs balance emotional authenticity with narrative structure, avoid reductive tropes, and treat both partners as full characters. As media diversifies, the most memorable romantic storylines will be those that honor the complexity of real human attachment while still delivering the catharsis audiences crave.
Whether you are a writer crafting the next great romance or a person navigating a real-life "situationship," the rules of a great romantic storyline offer wisdom.
Lesson 1: The "Relationship Resume" is boring. In fiction, a list of compatible hobbies (we both like hiking and sushi) does not make a story. Tension comes from difference. In real life, don't be afraid of friction. Growth happens when you date someone who challenges your worldview, not just validates it.
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We will never stop consuming relationships and romantic storylines because they are the map by which we navigate the most powerful force in human life. We watch fictional characters fall in love to remind ourselves why it is worth the risk. We read about heartbreak to validate our own pain. We ship unlikely couples because we want to believe that connection can bloom in the most barren soil.
The best romantic storylines do not give us answers; they give us a mirror. They ask: What are you willing to risk for connection? How do you change for love without losing yourself? And what happens after the kiss?
Whether you are writing a novel, pitching a screenplay, or just trying to survive dating in a digital world, remember the golden rule of the romantic storyline: Love is not the destination. Love is the vehicle. The story is the road.
And the road, thank goodness, is infinitely long.
The following story explores themes of serendipity and second chances, common in romantic narratives. The Unfinished Letter
For five years, Clara’s most prized possession was a creative writing notebook that didn’t belong to her. It had been accidentally packed in a box of her things after a messy breakup with Elias, her high school sweetheart. The pages were filled with his messy handwriting—character sketches, half-baked plots, and, on the final page, an unfinished letter addressed to her. It stopped mid-sentence: "I know we said it wasn’t the right time, but Clara, I never stopped—"
Clara had moved across the country to escape the memory of that ending. She built a successful career, but her relationships always felt like placeholder chapters. Then, on a drizzly Tuesday, she walked into a bookstore in her new city and saw a face that made the air feel like it was buzzing with electricity.
It was Elias. He was there for a reading of his debut novel.
Their reunion wasn't a cinematic slow-motion run. It was awkward and quiet, filled with the "shaky voices" of people who had once known each other's every secret. They went for coffee—just like old times—and realized that while they were different people now, the "sparks" were still there.
Over the next few weeks, they followed the "3-3-3 rule," navigating three dates to confirm their feelings, three weeks to build trust, and three months to realize this wasn't just nostalgia. Elias admitted he had spent years "waiting" for the right timing, choosing integrity over fleeting passion until he found his way back to her. A favorite of romantic comedies
One evening, Clara finally showed him the notebook. Elias looked at the unfinished letter and picked up a pen. He didn’t cross anything out; he just finished the sentence he had started half a decade ago:
"—I never stopped believing that fate would bring us back together." Popular Romantic Story Tropes & Resources
If you are interested in exploring more about relationship dynamics or romantic storylines, consider these common themes and guides:
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The most dangerous trope in modern storytelling isn't the love triangle or the love-at-first-sight. It is the "Meet-Cute."
The Meet-Cute tells us that love happens in a single, perfect moment. Bumping into a stranger at a bookstore. Spilling coffee on a handsome CEO. This is a lovely fantasy. But it creates a silent poison. When our real relationships start with a clumsy Hinge date or a mediocre Tinder match, we feel cheated. We think, "This isn't how the story starts."
We become addicted to the beginning. The chase. The dopamine of the unknown. Romantic storylines often end at the peak of commitment—the wedding, the first "I love you." They rarely show the ten-thousandth Tuesday. They cut to credits before the mortgage is due. Safety and Security When visiting adult websites, safety
FGK Tree
Huffman Tree