├── README.md ├── go.mod ├── node.go ├── .gitignore ├── leaf.go ├── tree.go ├── interior.go ├── tree_test.go └── LICENSE /README.md: -------------------------------------------------------------------------------- 1 | bplustree 2 | ========= 3 | -------------------------------------------------------------------------------- /go.mod: -------------------------------------------------------------------------------- 1 | module github.com/heeeeeng/bplustree 2 | 3 | go 1.12 4 | -------------------------------------------------------------------------------- /node.go: -------------------------------------------------------------------------------- 1 | package bplustree 2 | 3 | const ( 4 | MaxKV = 255 5 | MaxKC = 511 6 | ) 7 | 8 | type node interface { 9 | find(key int) (int, bool) 10 | parent() *interiorNode 11 | setParent(*interiorNode) 12 | full() bool 13 | } 14 | -------------------------------------------------------------------------------- /.gitignore: -------------------------------------------------------------------------------- 1 | # Compiled Object files, Static and Dynamic libs (Shared Objects) 2 | *.o 3 | *.a 4 | *.so 5 | 6 | # Folders 7 | _obj 8 | _test 9 | 10 | # Architecture specific extensions/prefixes 11 | *.[568vq] 12 | [568vq].out 13 | 14 | *.cgo1.go 15 | *.cgo2.c 16 | _cgo_defun.c 17 | _cgo_gotypes.go 18 | _cgo_export.* 19 | 20 | _testmain.go 21 | 22 | *.exe 23 | *.test 24 | .idea/bplustree.iml 25 | .idea/misc.xml 26 | .idea/modules.xml 27 | .idea/vcs.xml 28 | .idea/watcherTasks.xml 29 | .idea/workspace.xml 30 | -------------------------------------------------------------------------------- /leaf.go: -------------------------------------------------------------------------------- 1 | package bplustree 2 | 3 | import ( 4 | //"log" 5 | "fmt" 6 | "sort" 7 | ) 8 | 9 | type kv struct { 10 | key int 11 | value string 12 | } 13 | 14 | type kvs [MaxKV]kv 15 | 16 | func (a *kvs) Len() int { return len(a) } 17 | func (a *kvs) Swap(i, j int) { a[i], a[j] = a[j], a[i] } 18 | func (a *kvs) Less(i, j int) bool { return a[i].key < a[j].key } 19 | 20 | func (a *kvs) String() string { 21 | var s string 22 | for _, kv := range a { 23 | s += fmt.Sprintf("%d\t", kv.key) 24 | } 25 | return s 26 | } 27 | 28 | type leafNode struct { 29 | kvs kvs 30 | count int 31 | next *leafNode 32 | p *interiorNode 33 | } 34 | 35 | func newLeafNode(p *interiorNode) *leafNode { 36 | return &leafNode{ 37 | p: p, 38 | } 39 | } 40 | 41 | // find finds the index of a key in the leaf node. 42 | // If the key exists in the node, it returns the index and true. 43 | // If the key does not exist in the node, it returns index to 44 | // insert the key (the index of the smallest key in the node that larger 45 | // than the given key) and false. 46 | func (l *leafNode) find(key int) (int, bool) { 47 | c := func(i int) bool { 48 | return l.kvs[i].key >= key 49 | } 50 | 51 | i := sort.Search(l.count, c) 52 | 53 | if i < l.count && l.kvs[i].key == key { 54 | return i, true 55 | } 56 | 57 | return i, false 58 | } 59 | 60 | // insert 61 | func (l *leafNode) insert(key int, value string) (int, bool) { 62 | i, ok := l.find(key) 63 | 64 | if ok { 65 | //log.Println("insert.replace", i) 66 | l.kvs[i].value = value 67 | return 0, false 68 | } 69 | 70 | if !l.full() { 71 | copy(l.kvs[i+1:], l.kvs[i:l.count]) 72 | l.kvs[i].key = key 73 | l.kvs[i].value = value 74 | l.count++ 75 | return 0, false 76 | } 77 | 78 | next := l.split() 79 | 80 | if key < next.kvs[0].key { 81 | l.insert(key, value) 82 | } else { 83 | next.insert(key, value) 84 | } 85 | 86 | return next.kvs[0].key, true 87 | } 88 | 89 | func (l *leafNode) split() *leafNode { 90 | next := newLeafNode(nil) 91 | 92 | copy(next.kvs[0:], l.kvs[l.count/2+1:]) 93 | 94 | next.count = MaxKV - l.count/2 - 1 95 | next.next = l.next 96 | 97 | l.count = l.count/2 + 1 98 | l.next = next 99 | 100 | return next 101 | } 102 | 103 | func (l *leafNode) full() bool { return l.count == MaxKV } 104 | 105 | func (l *leafNode) parent() *interiorNode { return l.p } 106 | 107 | func (l *leafNode) setParent(p *interiorNode) { l.p = p } 108 | -------------------------------------------------------------------------------- /tree.go: -------------------------------------------------------------------------------- 1 | package bplustree 2 | 3 | type BTree struct { 4 | root *interiorNode 5 | first *leafNode 6 | leaf int 7 | interior int 8 | height int 9 | } 10 | 11 | func newBTree() *BTree { 12 | leaf := newLeafNode(nil) 13 | r := newInteriorNode(nil, leaf) 14 | leaf.p = r 15 | return &BTree{ 16 | root: r, 17 | first: leaf, 18 | leaf: 1, 19 | interior: 1, 20 | height: 2, 21 | } 22 | } 23 | 24 | // first returns the first leafNode 25 | func (bt *BTree) First() *leafNode { 26 | return bt.first 27 | } 28 | 29 | // insert inserts a (key, value) into the B+ tree 30 | func (bt *BTree) Insert(key int, value string) { 31 | _, oldIndex, leaf := search(bt.root, key) 32 | p := leaf.parent() 33 | 34 | mid, bump := leaf.insert(key, value) 35 | if !bump { 36 | return 37 | } 38 | 39 | var midNode node 40 | midNode = leaf 41 | 42 | p.kcs[oldIndex].child = leaf.next 43 | leaf.next.setParent(p) 44 | 45 | interior, interiorP := p, p.parent() 46 | 47 | for { 48 | var oldIndex int 49 | var newNode *interiorNode 50 | 51 | isRoot := interiorP == nil 52 | 53 | if !isRoot { 54 | oldIndex, _ = interiorP.find(key) 55 | } 56 | 57 | mid, newNode, bump = interior.insert(mid, midNode) 58 | if !bump { 59 | return 60 | } 61 | 62 | if !isRoot { 63 | interiorP.kcs[oldIndex].child = newNode 64 | newNode.setParent(interiorP) 65 | 66 | midNode = interior 67 | } else { 68 | bt.root = newInteriorNode(nil, newNode) 69 | newNode.setParent(bt.root) 70 | 71 | bt.root.insert(mid, interior) 72 | return 73 | } 74 | 75 | interior, interiorP = interiorP, interiorP.parent() 76 | } 77 | } 78 | 79 | // Search searches the key in B+ tree 80 | // If the key exists, it returns the value of key and true 81 | // If the key does not exist, it returns an empty string and false 82 | func (bt *BTree) Search(key int) (string, bool) { 83 | kv, _, _ := search(bt.root, key) 84 | if kv == nil { 85 | return "", false 86 | } 87 | return kv.value, true 88 | } 89 | 90 | func search(n node, key int) (*kv, int, *leafNode) { 91 | curr := n 92 | oldIndex := -1 93 | 94 | for { 95 | switch t := curr.(type) { 96 | case *leafNode: 97 | i, ok := t.find(key) 98 | if !ok { 99 | return nil, oldIndex, t 100 | } 101 | return &t.kvs[i], oldIndex, t 102 | case *interiorNode: 103 | i, _ := t.find(key) 104 | curr = t.kcs[i].child 105 | oldIndex = i 106 | default: 107 | panic("") 108 | } 109 | } 110 | } 111 | -------------------------------------------------------------------------------- /interior.go: -------------------------------------------------------------------------------- 1 | package bplustree 2 | 3 | import ( 4 | "fmt" 5 | "sort" 6 | ) 7 | 8 | type kc struct { 9 | key int 10 | child node 11 | } 12 | 13 | // one empty slot for split 14 | type kcs [MaxKC + 1]kc 15 | 16 | func (a *kcs) Len() int { return len(a) } 17 | 18 | func (a *kcs) Swap(i, j int) { a[i], a[j] = a[j], a[i] } 19 | 20 | func (a *kcs) Less(i, j int) bool { 21 | if a[i].key == 0 { 22 | return false 23 | } 24 | 25 | if a[j].key == 0 { 26 | return true 27 | } 28 | 29 | return a[i].key < a[j].key 30 | } 31 | 32 | func (a *kcs) String() string { 33 | var s string 34 | for _, kc := range a { 35 | s += fmt.Sprintf("%d\t", kc.key) 36 | } 37 | return s 38 | } 39 | 40 | type interiorNode struct { 41 | kcs kcs 42 | count int 43 | p *interiorNode 44 | } 45 | 46 | func newInteriorNode(p *interiorNode, largestChild node) *interiorNode { 47 | i := &interiorNode{ 48 | p: p, 49 | count: 1, 50 | } 51 | 52 | if largestChild != nil { 53 | i.kcs[0].child = largestChild 54 | } 55 | return i 56 | } 57 | 58 | func (in *interiorNode) find(key int) (int, bool) { 59 | c := func(i int) bool { return in.kcs[i].key > key } 60 | 61 | i := sort.Search(in.count-1, c) 62 | 63 | return i, true 64 | } 65 | 66 | func (in *interiorNode) full() bool { return in.count == MaxKC } 67 | 68 | func (in *interiorNode) parent() *interiorNode { return in.p } 69 | 70 | func (in *interiorNode) setParent(p *interiorNode) { in.p = p } 71 | 72 | func (in *interiorNode) insert(key int, child node) (int, *interiorNode, bool) { 73 | i, _ := in.find(key) 74 | 75 | if !in.full() { 76 | copy(in.kcs[i+1:], in.kcs[i:in.count]) 77 | 78 | in.kcs[i].key = key 79 | in.kcs[i].child = child 80 | child.setParent(in) 81 | 82 | in.count++ 83 | return 0, nil, false 84 | } 85 | 86 | // insert the new node into the empty slot 87 | in.kcs[MaxKC].key = key 88 | in.kcs[MaxKC].child = child 89 | child.setParent(in) 90 | 91 | next, midKey := in.split() 92 | 93 | return midKey, next, true 94 | } 95 | 96 | func (in *interiorNode) split() (*interiorNode, int) { 97 | sort.Sort(&in.kcs) 98 | 99 | // get the mid info 100 | midIndex := MaxKC / 2 101 | midChild := in.kcs[midIndex].child 102 | midKey := in.kcs[midIndex].key 103 | 104 | // create the split node with out a parent 105 | next := newInteriorNode(nil, nil) 106 | copy(next.kcs[0:], in.kcs[midIndex+1:]) 107 | next.count = MaxKC - midIndex 108 | // update parent 109 | for i := 0; i < next.count; i++ { 110 | next.kcs[i].child.setParent(next) 111 | } 112 | 113 | // modify the original node 114 | in.count = midIndex + 1 115 | midChild.setParent(in) 116 | 117 | return next, midKey 118 | } 119 | -------------------------------------------------------------------------------- /tree_test.go: -------------------------------------------------------------------------------- 1 | package bplustree 2 | 3 | import ( 4 | "fmt" 5 | "testing" 6 | "time" 7 | ) 8 | 9 | func TestInsert(t *testing.T) { 10 | testCount := 1000000 11 | bt := newBTree() 12 | 13 | start := time.Now() 14 | for i := testCount; i > 0; i-- { 15 | bt.Insert(i, "") 16 | } 17 | fmt.Println(time.Now().Sub(start)) 18 | 19 | verifyTree(bt, testCount, t) 20 | } 21 | 22 | func TestSearch(t *testing.T) { 23 | testCount := 1000000 24 | bt := newBTree() 25 | 26 | for i := testCount; i > 0; i-- { 27 | bt.Insert(i, fmt.Sprintf("%d", i)) 28 | } 29 | 30 | start := time.Now() 31 | for i := 1; i < testCount; i++ { 32 | v, ok := bt.Search(i) 33 | if !ok { 34 | t.Errorf("search: want = true, got = false") 35 | } 36 | if v != fmt.Sprintf("%d", i) { 37 | t.Errorf("search: want = %d, got = %s", i, v) 38 | } 39 | } 40 | fmt.Println(time.Now().Sub(start)) 41 | } 42 | 43 | func verifyTree(b *BTree, count int, t *testing.T) { 44 | verifyRoot(b, t) 45 | 46 | for i := 0; i < b.root.count; i++ { 47 | verifyNode(b.root.kcs[i].child, b.root, t) 48 | } 49 | 50 | leftMost := findLeftMost(b.root) 51 | 52 | if leftMost != b.first { 53 | t.Errorf("bt.first: want = %p, got = %p", b.first, leftMost) 54 | } 55 | 56 | verifyLeaf(leftMost, count, t) 57 | } 58 | 59 | // min child: 1 60 | // max child: MaxKC 61 | func verifyRoot(b *BTree, t *testing.T) { 62 | if b.root.parent() != nil { 63 | t.Errorf("root.parent: want = nil, got = %p", b.root.parent()) 64 | } 65 | 66 | if b.root.count < 1 { 67 | t.Errorf("root.min.child: want >=1, got = %d", b.root.count) 68 | } 69 | 70 | if b.root.count > MaxKC { 71 | t.Errorf("root.max.child: want <= %d, got = %d", MaxKC, b.root.count) 72 | } 73 | } 74 | 75 | func verifyNode(n node, parent *interiorNode, t *testing.T) { 76 | switch nn := n.(type) { 77 | case *interiorNode: 78 | if nn.count < MaxKC/2 { 79 | t.Errorf("interior.min.child: want >= %d, got = %d", MaxKC/2, nn.count) 80 | } 81 | 82 | if nn.count > MaxKC { 83 | t.Errorf("interior.max.child: want <= %d, got = %d", MaxKC, nn.count) 84 | } 85 | 86 | if nn.parent() != parent { 87 | t.Errorf("interior.parent: want = %p, got = %p", parent, nn.parent()) 88 | } 89 | 90 | var last int 91 | for i := 0; i < nn.count; i++ { 92 | key := nn.kcs[i].key 93 | if key != 0 && key < last { 94 | t.Errorf("interior.sort.key: want > %d, got = %d", last, key) 95 | } 96 | last = key 97 | 98 | verifyNode(nn.kcs[i].child, nn, t) 99 | } 100 | 101 | case *leafNode: 102 | if nn.parent() != parent { 103 | t.Errorf("leaf.parent: want = %p, got = %p", parent, nn.parent()) 104 | } 105 | 106 | if nn.count < MaxKV/2 { 107 | t.Errorf("leaf.min.child: want >= %d, got = %d", MaxKV/2, nn.count) 108 | } 109 | 110 | if nn.count > MaxKV { 111 | t.Errorf("leaf.max.child: want <= %d, got = %d", MaxKV, nn.count) 112 | } 113 | } 114 | } 115 | 116 | func verifyLeaf(leftMost *leafNode, count int, t *testing.T) { 117 | curr := leftMost 118 | last := 0 119 | c := 0 120 | 121 | for curr != nil { 122 | for i := 0; i < curr.count; i++ { 123 | key := curr.kvs[i].key 124 | 125 | if key <= last { 126 | t.Errorf("leaf.sort.key: want > %d, got = %d", last, key) 127 | } 128 | last = key 129 | c++ 130 | } 131 | curr = curr.next 132 | } 133 | 134 | if c != count { 135 | t.Errorf("leaf.count: want = %d, got = %d", count, c) 136 | } 137 | } 138 | 139 | func findLeftMost(n node) *leafNode { 140 | switch nn := n.(type) { 141 | case *interiorNode: 142 | return findLeftMost(nn.kcs[0].child) 143 | case *leafNode: 144 | return nn 145 | default: 146 | panic("") 147 | } 148 | } 149 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | Apache License 2 | Version 2.0, January 2004 3 | http://www.apache.org/licenses/ 4 | 5 | TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION 6 | 7 | 1. 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