Byte Pair Encoding (BPE) Merges

GPT-style tokenizers use Byte Pair Encoding: start from single characters and repeatedly merge the most common pair of neighbors into a new symbol.

Split every word in words into characters. Repeated words count multiple times.
Count every pair of adjacent symbols across all words.
Pick the most frequent pair. If pairs tie, pick the one that is smallest when you compare (first symbol, second symbol) as strings.
Replace every occurrence of that pair, left to right, with the merged symbol, and record the merged symbol.
Repeat num_merges times, or stop early when no word has two symbols left.

Implement bpe_merges(words, num_merges).

Input

words: The training words (lowercase letters).

num_merges: How many merges to learn.

Output

Return the merged symbols in the order they were learned.

Constraints

1 ≤ number of words ≤ 1,000, 1 ≤ length of each word ≤ 30

0 ≤ num_merges ≤ 200

Examples

Example 1

Input:
words = ["low", "lower", "lowest"]
num_merges = 2

Expected output:
["lo", "low"]

Explanation

Pairs: "l o" and "o w" appear 3 times each; the tie goes to "l o" ("l" < "o"), giving "lo". Now "lo w" appears 3 times, giving "low". Result: ["lo", "low"].

Example 2

Input:
words = ["aaa"]
num_merges = 3

Expected output:
["aa", "aaa"]

Explanation

"aaa" has the pair "a a" twice. Merging left to right gives "aa" + "a". Then "aa a" merges into "aaa", and the word is a single symbol, so the third merge has nothing to do. Result: ["aa", "aaa"].

References

Run the sample tests to check your code without submitting.

Example 1 Not run

Input:

words = ["low", "lower", "lowest"]
num_merges = 2

Expected output:

["lo", "low"]

Your output

Example 2 Not run
Input:
```
words = ["aaa"]
num_merges = 3
```
Expected output:
```
["aa", "aaa"]
```
Your output

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💡 Kotlin Basics Guide for Beginners

1. Declaring Variables and Constants

Kotlin uses val for immutable variables and var for mutable ones.

val name: String = "Alice"
var age: Int = 30
val pi = 3.14  // type inferred

// Constants
const val MAX_USERS = 100

2. Conditionals (if / when)

Use if expressions or when for multiple branches.

val x = 2
if (x == 1) {
    println("One")
} else if (x == 2) {
    println("Two")
} else {
    println("Other")
}

when (x) {
    1 -> println("One")
    2 -> println("Two")
    else -> println("Other")
}

3. Loops

Use for, while, and do-while for iteration.

for (i in 0..2) {
    println(i)
}

var n = 3
while (n > 0) {
    println(n)
    n--
}

4. Arrays

Kotlin supports arrays using the arrayOf() function.

val numbers = arrayOf(10, 20, 30)
println(numbers[1])

5. List Manipulation

Use mutableListOf for dynamic lists.

val nums = mutableListOf(1, 2, 3)
nums.add(4)
nums.removeAt(0)

for (n in nums) {
    print("$n ")
}

6. Console Input/Output

Use readLine() for input and println() for output.

print("Enter your name: ")
val name = readLine()
println("Hello, $name")

7. Functions

Functions use fun keyword with optional return type.

fun add(a: Int, b: Int): Int {
    return a + b
}

println(add(3, 4))

8. Maps

mutableMapOf stores key-value pairs.

val ages = mutableMapOf("Alice" to 30)
println(ages["Alice"])

9. Exception Handling

Use try, catch, and finally to handle errors.

try {
    val result = 10 / 0
} catch (e: ArithmeticException) {
    println("Error: ${e.message}")
}

10. File I/O

Use File from java.io for file operations.

import java.io.File

File("file.txt").writeText("Hello File")
val text = File("file.txt").readText()
println(text)

11. String Manipulation

Kotlin strings support many methods and interpolation.

val text = "Hello World"
println(text.length)
println(text.substring(0, 5))
println(text.contains("World"))

12. Classes & Objects

Kotlin classes are concise and support default constructors.

class Person(val name: String) {
    fun greet() = println("Hi, I'm $name")
}

val p = Person("Alice")
p.greet()

13. Null Safety

Kotlin distinguishes nullable and non-nullable types. Use ? and ?: for safety.

val name: String? = null
println(name?.length ?: 0)