### B-Tree Usage Example in Go

Source: https://github.com/arthur-zhang/letsddia-go/blob/main/btree/b-tree-on-disk/README.md

Demonstrates how to use the persistent B-Tree implementation in Go. It covers creating a new B-tree, inserting items with fixed-size keys and values, and searching for existing and non-existing keys.

```go
btree := NewBtree("/tmp/btree.db", 2)
arr := []byte{'F', 'S', 'Q', 'K', 'C', 'L', 'H', 'T', 'V', 'W', 'M', 'R', 'N', 'P', 'A', 'B', 'X', 'Y', 'D', 'Z', 'E'}
for _, v := range arr {
item := &Item{
key:   [N]byte{v},
value: [N]byte{v, byte('0'), byte('1')},
}
bTree.Insert(item)
}
key := Item{key: [N]byte{'A'}}
item := btree.Search(&key)
assert.True(t, item != nil)
assert.Equal(t, "A", decodeString(item.key))
assert.Equal(t, "A01", decodeString(item.value))

key = Item{key: [N]byte{'a'}}
item = btree.Search(&key)
assert.True(t, item == nil)
```

--------------------------------

### Bloom Filter Go Usage Example

Source: https://github.com/arthur-zhang/letsddia-go/blob/main/bloom-filter/README.md

Demonstrates how to create, insert into, and look up elements in a Bloom Filter implemented in Go. It initializes a Bloom Filter with a specified capacity and false-positive rate, inserts an item, and verifies its presence.

```go
func TestSingleElement(t *testing.T) {
	bf := NewBloomFilter[Key](10000, 0.10)
	item := Key("Hello")
	bf.Insert(item)
	if !bf.LookUp(item) {
		t.Errorf("Expected item to exist in the bloom filter")
	}
}
```

--------------------------------

### Test Rabin-Karp Algorithm Implementation in Go

Source: https://github.com/arthur-zhang/letsddia-go/blob/main/algorithms/rabin-karp/README.md

This Go code snippet demonstrates how to test the RabinKarpSearch function. It includes various test cases covering different scenarios such as finding patterns, patterns not present, empty strings, and partial matches. The tests use the standard Go testing package and the assert library for assertions.

```go
func TestRabinKarp(t *testing.T) {
	tests := []struct {
		s       string
		pattern string
		wantIdx int
		wantOk  bool
	}{
		{"hello world", "world", 6, true},
		{"hello world", "world!", 0, false},
		{"hello world", "o", 4, true},
		{"hello world", "hello world", 0, true},
		{"hello world", "hello world!", 0, false},
		{"", "", 0, true},
		{"", "a", 0, false},
		{"a", "", 0, true},
		{"abc", "abc", 0, true},
		{"abcabc", "abc", 0, true},
		{"abcabc", "acb", 0, false},
	}

	for _, test := range tests {
		gotIdx, gotOk := RabinKarpSearch(test.s, test.pattern)
		assert.Equal(t, test.wantIdx, gotIdx)
		assert.Equal(t, test.wantOk, gotOk)
	}
}
```

--------------------------------

### Cuckoo Hashing Usage and Test Cases in Go

Source: https://github.com/arthur-zhang/letsddia-go/blob/main/algorithms/cuckoo-hashing/README.md

Demonstrates the usage of the Cuckoo Hashing implementation in Go through unit tests. It covers inserting keys, looking up existing and non-existent keys, and erasing keys.

```go
func TestCuckooHashing(t *testing.T) {

	cht := New(4, hash0, hash1)

	// insert key
	t.Run("Insert", func(t *testing.T) {
		keys := []int{10, 20, 30, 40, 50}
		for _, key := range keys {
		cht.Insert(key)
		}

		// ensure all keys are present
		for _, key := range keys {
			if ok := cht.Lookup(key); !ok {
				t.Errorf("Expected key %d to be present, but it was not", key)
			}
		}
	})

	// lookup key
	t.Run("Lookup", func(t *testing.T) {
		if ok := cht.Lookup(10); !ok {
			t.Error("Expected key 10 to be present, but it was not")
		}

		if ok := cht.Lookup(100); ok {
			t.Error("Expected key 100 to be absent, but it was found")
		}
	})

	// delete key
	t.Run("Erase", func(t *testing.T) {
	cht.Erase(30)
		if ok := cht.Lookup(30); ok {
			t.Error("Expected key 30 to be absent after erasing, but it was found")
		}
	})

	// delete nonexistent key
	t.Run("Erase nonexistent key", func(t *testing.T) {
	cht.Erase(100)
		if ok := cht.Lookup(100); ok {
			t.Error("Expected key 100 to be absent, but it was found")
		}
	})
}
```

--------------------------------

### Implement HyperLogLog in Go

Source: https://context7.com/arthur-zhang/letsddia-go/llms.txt

A probabilistic cardinality estimator that approximates the count of distinct elements using minimal space. The implementation includes corrections for small and large ranges to improve accuracy.

```go
package main

import "hyperloglog"

func main() {
    // Create HyperLogLog with b bits for bucket indexing
    // m = 2^b buckets, standard error ~= 1.04/sqrt(m)
    hll := hyperloglog.New(14) // 16384 buckets, ~0.81% standard error

    // Add elements (strings)
    hll.Add("user:alice")
    hll.Add("user:bob")
    hll.Add("user:charlie")
    hll.Add("user:alice")  // duplicate, won't increase cardinality

    // Or add integers
    hll.AddInt(12345)
    hll.AddInt(67890)

    // Get cardinality estimate
    count := hll.Cardinality()  // ~3.0 for unique users
}
```

--------------------------------

### In-Memory B-Tree Implementation in Go

Source: https://context7.com/arthur-zhang/letsddia-go/llms.txt

An in-memory B-Tree implementation based on Introduction to Algorithms. Provides O(log n) search and insertion with automatic node splitting when full. Requires the 'b_tree' package.

```go
package main

import "b_tree"

func main() {
    // Create B-Tree with degree T=2 (max 3 keys per node)
    btree := b_tree.NewBtree()

    // Insert keys
    keys := []int{10, 20, 5, 6, 12, 30, 7, 17}
    for _, key := range keys {
        btree.Insert(key)
    }

    // Search for key
    node, idx := btree.Search(12)
    if node != nil {
        // Found at node.keys[idx]
    }

    // Search for non-existent key
    node, _ = btree.Search(100)
    // node == nil
}
```

--------------------------------

### B-Tree Disk Layout Description

Source: https://github.com/arthur-zhang/letsddia-go/blob/main/btree/b-tree-on-disk/README.md

Describes the on-disk layout of the persistent B-Tree, specifying the size and order of fields like 'isLeaf', 'numKeys', and key-value pairs.

```text
|isLeaf 1-byte|
|numKeys 8-bytes|
|Key#0 10-bytes |
|Value#0 10-bytes |
```

--------------------------------

### Rabin-Karp String Search in Go

Source: https://context7.com/arthur-zhang/letsddia-go/llms.txt

A rolling hash algorithm for efficient string pattern matching. Uses polynomial hashing to achieve O(n+m) average-case complexity for finding a pattern in text. Requires the 'rabin_karp' package.

```go
package main

import "rabin_karp"

func main() {
    text := "hello world, hello universe"
    pattern := "world"

    // Search for pattern in text
    idx, found := rabin_karp.RabinKarpSearch(text, pattern)
    if found {
        // idx = 6, pattern found at position 6
    }

    // Search for non-existent pattern
    idx, found = rabin_karp.RabinKarpSearch(text, "galaxy")
    // found = false, idx = 0
}
```

--------------------------------

### Implement LSM Tree Disk Store in Go

Source: https://context7.com/arthur-zhang/letsddia-go/llms.txt

A Log-Structured Merge Tree implementation using block-based disk files. It optimizes for efficient sequential writes with periodic compaction and provides iterator-based range scans.

```go
package main

import "lsm"

func main() {
    // Create disk store in specified directory
    store := lsm.NewDiskStore("/tmp/lsm_data")
    defer store.Close()

    // Iterate over all key-value pairs across multiple disk files
    iter := store.Iter()
    iter.SeekToFirst()

    for iter.Valid() {
        key := iter.Key()
        value := iter.Value()
        // Process key-value pair
        iter.Next()
    }
}
```

--------------------------------

### Implement Bitcask Storage Engine in Go

Source: https://context7.com/arthur-zhang/letsddia-go/llms.txt

A log-structured key-value store based on the Bitcask paper. It offers fast reads via an in-memory hash index and append-only writes for durability. Supports compaction to reclaim space.

```go
package main

import "bitcask"

func main() {
    // Open or create a Bitcask database
    opts := bitcask.Opts{} // Use defaults
    db := bitcask.Open("/tmp/mydb", opts)

    // Put key-value pairs (append-only writes)
    db.Put("user:1001", []byte(`{"name":"Alice","age":30}`))
    db.Put("user:1002", []byte(`{"name":"Bob","age":25}`))

    // Get value by key (O(1) via in-memory index)
    value, err := db.Get("user:1001")
    if err != nil {
        panic(err)
    }
    // value = []byte(`{"name":"Alice","age":30}`)

    // Delete key (writes tombstone marker)
    db.Delete("user:1002")

    // Merge/compact to reclaim space from old entries
    db.Merge()
}
```

--------------------------------

### Cuckoo Hashing for O(1) Worst-Case Lookup (Go)

Source: https://context7.com/arthur-zhang/letsddia-go/llms.txt

Demonstrates Cuckoo Hashing in Go, a hash table implementation with O(1) worst-case lookup time. It uses two hash functions and handles collisions via displacement chains. Requires the 'cuckoo_hashing' Go package.

```go
package main

import "cuckoo_hashing"

func main() {
    // Define two hash functions
    hash1 := func(key int) int { return key % 11 }
    hash2 := func(key int) int { return (key / 11) % 11 }

    // Create cuckoo hash table with size 11
    cht := cuckoo_hashing.New(11, hash1, hash2)

    // Insert keys (may trigger displacement chain)
    cht.Insert(20)
    cht.Insert(50)
    cht.Insert(53)
    cht.Insert(75)

    // O(1) lookup
    found := cht.Lookup(50)  // true
    found = cht.Lookup(99)   // false

    // Delete
    cht.Erase(50)
}
```

--------------------------------

### On-Disk B-Tree Implementation in Go

Source: https://context7.com/arthur-zhang/letsddia-go/llms.txt

A persistent B-Tree implementation that stores nodes on disk with fixed-size keys and values. Supports page-based I/O for durability. Requires the 'b_tree_on_disk' package.

```go
package main

import "b_tree_on_disk"

func main() {
    // Create persistent B-Tree with minimum degree t=2
    btree := b_tree_on_disk.NewBtree("/tmp/btree.db", 2)

    // Keys and values are fixed-size byte arrays (10 bytes each)
    const N = 10

    // Insert items
    item := &b_tree_on_disk.Item{
        key:   [N]byte{'U', 'S', 'E', 'R', '1'},
        value: [N]byte{'A', 'L', 'I', 'C', 'E'},
    }
    btree.Insert(item)

    // Search by key
    searchKey := &b_tree_on_disk.Item{key: [N]byte{'U', 'S', 'E', 'R', '1'}}
    result := btree.Search(searchKey)
    if result != nil {
        // Found: result.value contains the data
    }
}
```

--------------------------------

### T-Digest for Streaming Quantile Estimation (Go)

Source: https://context7.com/arthur-zhang/letsddia-go/llms.txt

Shows how to use T-Digest, a streaming quantile estimation algorithm in Go, for accurate percentile calculations on streaming data. Useful for P50, P95, P99. Requires the 't_digest' Go package.

```go
package main

import "t_digest"

func main() {
    // Create T-Digest
    td := t_digest.NewTDigestV2()

    // Insert streaming values
    values := []float64{1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0}
    for _, v := range values {
        td.Insert(v)
    }

    // Query quantiles
    p50 := td.Quantile(0.5)   // Median ~5.5
    p90 := td.Quantile(0.9)   // 90th percentile ~9.0
    p99 := td.Quantile(0.99)  // 99th percentile ~10.0
}
```

--------------------------------

### SimHash for Near-Duplicate Document Detection (Go)

Source: https://context7.com/arthur-zhang/letsddia-go/llms.txt

Implements SimHash, a locality-sensitive hashing algorithm to detect near-duplicate documents. It generates similar hash values for similar input strings, enabling efficient similarity detection. Requires the 'simhash' Go package.

```go
package main

import "simhash"

func main() {
    // Generate SimHash for documents
    doc1 := "the quick brown fox jumps over the lazy dog"
    doc2 := "the quick brown fox jumps over the lazy cat"
    doc3 := "completely different text about programming"

    hash1 := simhash.SimHash(doc1)
    hash2 := simhash.SimHash(doc2)
    hash3 := simhash.SimHash(doc3)

    // Similar documents have similar hashes (low Hamming distance)
    // hash1 and hash2 will be similar
    // hash1 and hash3 will be very different
}
```

--------------------------------

### K-Way Merge Algorithm using Min-Heap (Go)

Source: https://context7.com/arthur-zhang/letsddia-go/llms.txt

Implements the K-Way Merge algorithm in Go using a min-heap. This algorithm is essential for external sorting, efficiently merging K sorted files with bounded memory usage, suitable for datasets larger than RAM. Uses Go's standard 'container/heap' package.

```go
package main

import (
    "container/heap"
)

// MinHeap implementation for merge entries
type Entry struct {
    value   int
    iterIdx int
}

type MinHeap []Entry

func (h MinHeap) Len() int           { return len(h) }
func (h MinHeap) Less(i, j int) bool { return h[i].value < h[j].value }
func (h MinHeap) Swap(i, j int)      { h[i], h[j] = h[j], h[i] }
func (h *MinHeap) Push(x interface{}) { *h = append(*h, x.(Entry)) }
func (h *MinHeap) Pop() interface{} {
    old := *h
    n := len(old)
    x := old[n-1]
    *h = old[0 : n-1]
    return x
}

func main() {
    // Create iterators for each sorted file
    iters := make([]Iterator, K) // K sorted file iterators

    // Initialize min-heap with first element from each iterator
    pq := &MinHeap{}
    heap.Init(pq)

    for i := 0; i < len(iters); i++ {
        if iters[i].Next() {
            heap.Push(pq, Entry{value: iters[i].Value(), iterIdx: i})
        }
    }

    // Merge: always extract minimum and replenish from same iterator
    for pq.Len() > 0 {
        item := heap.Pop(pq).(Entry)
        // Output item.value (next smallest element)

        // Replenish from the same iterator
        if iters[item.iterIdx].Next() {
            heap.Push(pq, Entry{
                value:   iters[item.iterIdx].Value(),
                iterIdx: item.iterIdx,
            })
        }
    }
}
```

--------------------------------

### Roaring Bitmap for Compressed Integer Sets (Go)

Source: https://context7.com/arthur-zhang/letsddia-go/llms.txt

Demonstrates the use of Roaring Bitmap, a compressed bitmap data structure in Go. It automatically selects optimal storage based on data density, making it efficient for storing large sets of integers. Requires the 'roaring_bitmap' Go package.

```go
package main

import "roaring_bitmap"

func main() {
    // Create roaring bitmap
    rb := roaring_bitmap.New()

    // Add 32-bit integers
    rb.Add(1)
    rb.Add(2)
    rb.Add(3)
    rb.Add(1000000)
    rb.Add(1000001)

    // Container type is chosen automatically:
    // - ArrayContainer for sparse data (<4096 elements)
    // - BitmapContainer for dense data
    // - RunContainer for sequential runs

    // Remove elements
    rb.Remove(2)

    // Get total count
    count := rb.Len() // 4
}
```

--------------------------------

### Implement Count-Min Sketch in Go

Source: https://context7.com/arthur-zhang/letsddia-go/llms.txt

A probabilistic data structure for frequency estimation in data streams. It uses multiple hash functions and a 2D counter table to provide frequency estimates with bounded error. Estimates may overestimate but never underestimate.

```go
package main

import "count_min_sketch"

func main() {
    // Create Count-Min Sketch with d rows (hash functions) and w columns
    // Error bound: epsilon = e/w, probability: delta = 1/e^d
    cms := count_min_sketch.New(5, 1000) // 5 hash functions, 1000 columns

    // Update counts
    cms.Update("apple", 1)
    cms.Update("banana", 3)
    cms.Update("apple", 2)

    // Estimate frequency (may overestimate, never underestimate)
    appleCount := cms.Estimate("apple")   // ~3
    bananaCount := cms.Estimate("banana") // ~3
}
```

--------------------------------

### Hash Ring (Consistent Hashing) in Go

Source: https://context7.com/arthur-zhang/letsddia-go/llms.txt

A consistent hashing implementation for distributing resources across nodes with minimal redistribution when nodes are added or removed. Essential for distributed caching and load balancing. Requires the 'hash_ring' package.

```go
package main

import "hash_ring"

func main() {
    // Create hash ring with k bits (ring size = 2^k)
    ring := hash_ring.NewHashRing(10) // Ring size 0-1023

    // Add nodes (servers) at specific positions
    ring.AddNode(100)
    ring.AddNode(400)
    ring.AddNode(700)

    // Add resources (keys) - automatically assigned to closest node
    ring.AddResource(150)  // Goes to node at 400
    ring.AddResource(350)  // Goes to node at 400
    ring.AddResource(800)  // Goes to node at 100 (wraps around)

    // Remove a node - resources automatically migrate to next node
    ring.DeleteNode(400)

    // Debug output shows node assignments
    ring.DebugPrint()
}
```

--------------------------------

### Inverted Index Implementation in Go

Source: https://context7.com/arthur-zhang/letsddia-go/llms.txt

Implements a full-text search index that maps terms to document occurrences with frequency tracking. Useful for search engines and text retrieval systems. Requires the 'inverted_index' package.

```go
package main

import "inverted_index"

func main() {
    // Create inverted index
    idx := inverted_index.New()

    // Index documents
    idx.IndexDoc(&inverted_index.Doc{
        Id:      1,
        Content: "The quick brown fox jumps over the lazy dog",
    })
    idx.IndexDoc(&inverted_index.Doc{
        Id:      2,
        Content: "A quick brown dog runs in the park",
    })

    // Search for terms
    results := idx.Lookup("quick brown")
    // Returns map[string][]Appearance with document IDs and term frequencies
    // results["quick"] = [{DocId: 1, Freq: 1}, {DocId: 2, Freq: 1}]
    // results["brown"] = [{DocId: 1, Freq: 1}, {DocId: 2, Freq: 1}]
}
```

--------------------------------

### Implement Bloom Filter in Go

Source: https://context7.com/arthur-zhang/letsddia-go/llms.txt

A space-efficient probabilistic data structure for membership testing. It uses multiple hash functions to set bits in a bitmap, providing O(k) insertion and lookup. The implementation automatically calculates optimal bitmap size and hash function count.

```go
package main

import "bloom_filter"

// Key type must implement the Byteable interface
type Key string

func (k Key) Bytes() []byte {
    return []byte(k)
}

func main() {
    // Create bloom filter for 10000 items with 10% false positive rate
    // Optimal bitmap size (m) and hash function count (k) are calculated automatically
    bf := bloom_filter.NewBloomFilter[Key](10000, 0.10)

    // Insert items
    bf.Insert(Key("user:1001"))
    bf.Insert(Key("user:1002"))
    bf.Insert(Key("user:1003"))

    // Lookup - may return false positive but never false negative
    exists := bf.LookUp(Key("user:1001"))  // true
    exists = bf.LookUp(Key("user:9999"))   // false (or rarely true - false positive)
}
```

--------------------------------

### Skip List Implementation in Go

Source: https://context7.com/arthur-zhang/letsddia-go/llms.txt

A probabilistic data structure providing O(log n) average-case search, insertion, and deletion. Implements a multi-level linked list with random level assignment. Requires the 'skiplist' package.

```go
package main

import "skiplist"

func main() {
    // Create generic skip list
    list := skiplist.NewSkipList[int, string]()

    // Insert key-value pairs
    key1, val1 := 10, "ten"
    key2, val2 := 5, "five"
    key3, val3 := 15, "fifteen"

    list.Insert(&key1, &val1)
    list.Insert(&key2, &val2)
    list.Insert(&key3, &val3)

    // Check membership
    searchKey := 10
    exists := list.Contains(&searchKey) // true

    // Find operations
    node := list.FindGreaterThanOrEqual(&searchKey)
    nodeLT := list.FindLessThan(&searchKey)
    lastNode := list.FindLast()

    // Delete
    list.Delete(&key1)

    // Iterator pattern
    iter := list.Iterator()
    iter.SeekToFirst()
    for iter.Valid() {
        key := iter.Key()
        value := iter.Value()
        // Process key-value
        iter.Next()
    }
    iter.Close()
}
```

--------------------------------

### Define Documents for Inverted Index (Go)

Source: https://github.com/arthur-zhang/letsddia-go/blob/main/inverted-index/README.md

This Go code snippet defines a slice of strings, where each string represents a document to be indexed. These documents serve as the input data for building the inverted index.

```go
var docs = []string{
    "new home sales top forecasts.",
    "home sales rise in july!",
    "increase in home sales in july...",
    "july new home sales rise,",
}
```

--------------------------------

### Calculate Cardinality - HyperLogLog Go

Source: https://github.com/arthur-zhang/letsddia-go/blob/main/algorithms/hyperloglog/README.md

Calculates the approximate number of distinct elements using the HyperLogLog algorithm. It applies different correction strategies based on the raw estimate and the number of zero registers. This function is essential for the count-distinct problem.

```go
func (hll *HyperLogLog) Cardinality() float64 {
	sum := 0.0
	zeros := 0
	for _, it := range hll.registers {
		sum += 1.0 / float64(int(1)<<it)
		if it == 0 {
			zeros++
		}
	}
	harmonicAvg := float64(hll.m) / sum
	E := hll.alphaM * float64(hll.m) * harmonicAvg // Raw estimate

	// Computes corrected estimate
	if E <= 2.5*float64(hll.m) { // Small range correction
		if zeros != 0 {
			return float64(hll.m) * math.Log(float64(hll.m)/float64(zeros))
		} else {
			return E
		}
	} else if E <= math.Pow(2, 32)/float64(30) { // Intermediate range, no correction
		return E
	} else { // E > 2^32/30, Large range correction
		return -math.Pow(2, 32) * math.Log(1-E/math.Pow(2, 32))
	}
}
```

--------------------------------

### Cuckoo Hashing Hash Functions in Go

Source: https://github.com/arthur-zhang/letsddia-go/blob/main/algorithms/cuckoo-hashing/README.md

Defines two hash functions, hash0 and hash1, used in the Cuckoo Hashing implementation. These functions are crucial for determining the potential locations of keys within the hash table.

```go
func hash0(key int) int {
	return key % 10
}
func hash1(key int) int {
	return key / 10
}
```

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