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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💡 Go Basics & Examples You Can Try Above

1. Declaring Variables and Constants

Use var or := to declare variables. Use const for constants.

package main

var x int = 10
const Pi = 3.14

func main() {
    name := "Alice"
    isActive := true
    println(x, Pi, name, isActive)
}

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Go supports if-else and switch statements with clean syntax.

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var name string
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fmt.Scan(&name)
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func greet(name string) string {
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}

message := greet("Alice")
println(message)

8. Maps

Maps are key-value stores. Declare with make().

ages := map[string]int{"Alice": 30}
ages["Bob"] = 25
println(ages["Alice"])

9. Error Handling

Go uses multiple return values for errors instead of exceptions.

import "errors"

func fail() error {
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}

err := fail()
if err != nil {
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10. File I/O

Use os and io/ioutil packages to read/write files.

import (
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)

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data, _ := ioutil.ReadFile("file.txt")
fmt.Println(string(data))

11. String Manipulation

Use the strings package for string operations.

import "strings"

text := "  Hello World  "
println(strings.TrimSpace(text))
println(strings.ToUpper(text))
println(strings.ReplaceAll(text, "Hello", "Hi"))

words := strings.Split(text, " ")
fmt.Println(words)

12. Structs & Objects

Use structs to define custom types with methods.

type Person struct {
  Name string
}

func (p Person) Greet() string {
  return "Hi, I'm " + p.Name
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p := Person{Name: "Alice"}
println(p.Greet())

13. References (Pointers)

Go supports pointers using * and &.

x := 10
ptr := &x
*ptr = 20
println(x) // 20