Merge branch 'master' of https://github.com/xtaci/algorithms

Author: xtaci

README.md

@@ -48,6 +48,7 @@
  Interval tree
  Prefix Tree(Trie)
  *Suffix Tree(未实现)*
+B-Tree
 
  Hash by multiplication
  Hash table

include/btree.h

@@ -48,6 +48,12 @@ namespace alg {
 } __attribute__ ((packed));
 typedef struct node_t *node;
 
+public:
+// node and index
+struct nr {
+uint32_t offset;
+int32_t idx;
+};
 private:
 node m_root;
 int fd;
@@ -72,7 +78,7 @@ namespace alg {
 close(fd);
 }
 
-int32_t Search(int32_t x) {
+nr Search(int32_t x) {
 return search(m_root, x);
 }
 
@@ -87,6 +93,7 @@ namespace alg {
 s->flag &= ~LEAF;
 s->flag |= ONDISK;// write to offset 0
 s->offset = 0;
+s->n = 0;
 s->c[0] = m_root->offset;
 // free old & set new
 free(m_root);
@@ -98,20 +105,30 @@ namespace alg {
 }
 }
 
+void DeleteKey(int32_t k) {
+node x = m_root;
+delete_op(m_root, k);
+}
+
 private:
 /**
  * search a key, returns node and index
  */
-int32_t search(node x, int32_t k) {
+nr search(node x, int32_t k) {
 int32_t i = 0;
+nr ret;
 while (i<x->n && k > x->key[i]) i++;
 
-if (i<x->n && k == x->key[i]) {
-return i;
-} else if (x->flag & LEAF) {
-return -1;
+if (i<x->n && k == x->key[i]) {// search in [0,n-1]
+ret.offset = x->offset;
+ret.idx = i;
+return ret;
+} else if (x->flag & LEAF) {// leaf, no more childs
+ret.offset = 0;
+ret.idx = -1;
+return ret;
 } else {
-std::auto_ptr<node_t> xi(READ(x, i));
+std::auto_ptr<node_t> xi(READ(x, i));// in last child
 return search(xi.get(), k);
 }
 }
@@ -121,8 +138,8 @@ namespace alg {
  */
 void insert_nonfull(node x, int32_t k) {
 int32_t i = x->n-1;
-if (x->flag & LEAF) {
-while (i>=0 && k <x->key[i]) {
+if (x->flag & LEAF) {// insert into leaf
+while (i>=0 && k < x->key[i]) {// shift from right to left, when k < key[i]
 x->key[i+1] = x->key[i];
 i = i - 1;
 }
@@ -140,6 +157,8 @@ namespace alg {
 if (k > x->key[i]) {
 i = i+1;
 }
+// reload x[i] after split_child(will modify child x[i])
+xi = READ(x, i);
 }
 insert_nonfull(xi, k);
 free(xi);
@@ -167,41 +186,87 @@ namespace alg {
 std::auto_ptr<node_t> y(READ(x, i));
 z->flag &= ~LEAF;
 z->flag |= (y->flag & LEAF);
-printf("leafz:%x\n", z->flag);
-printf("leafy:%x\n", y->flag);
-printf("leafx:%x offset:%x\n", x->flag, x->offset);
 z->n = T - 1;
 
 int32_t j;
-for (j=0;j<T-1;j++) {// init z
+for (j=0;j<T-1;j++) {// init z, t-1 keys
 z->key[j] = y->key[j+T];
 }
 
-if (!(y->flag & LEAF)) {
+if (!(y->flag & LEAF)) {// if not leaf, copy childs too.
 for (j=0;j<T;j++) {
 z->c[j] = y->c[j+T];
 }
 }
 
-y->n = T-1;// splited y
+y->n = T-1;// shrink y to t-1 elements
 WRITE(y.get());
 WRITE(z.get());
 
-for (j=x->n;j>=i+1;j--) {
-x->c[j+1] = x->c[j];// shift
+for (j=x->n;j>=i+1;j--) { // make place for the new child in x
+x->c[j+1] = x->c[j];
 }
 
-// save z
-x->c[i+1] = z->offset;
-
-for (j=x->n-1;j>=i;j--) {
+x->c[i+1] = z->offset; // make z the child of x
+for (j=x->n-1;j>=i;j--) { // move keys in x
 x->key[j+1] = x->key[j];
 }
-x->key[i] = y->key[T-1];
+x->key[i] = y->key[T-1];// copy the middle element of y into x
 x->n = x->n+1;
 WRITE(x);
 }
 
+/**
+ * recursion deletion
+ */
+void delete_op(node x, int32_t k) {
+int32_t i;
+for (i=0;i<x->n;i++) {
+if (x->key[i] == k) {// leaf node, case1
+break;
+}
+}
+
+if (i<x->n && (x->flag & LEAF)) {
+int j;
+for (j = i;j<x->n-1;j++) {// shift copy
+x->key[j] = x->key[j+1];
+}
+WRITE(x);
+} else if (x->key[i] == k) {// non-leaf
+if (i = x->n-1 || i == 0) {// outside, case 2c
+delete_case3(x);
+} else {
+node y= READ(x, i-1);
+if (y->n >= T) {// case 2a
+x->key[i] = y->key[y->n-1];// subsitute the key with predecessor
+delete_op(y, x->key[i]);
+free(y);
+return;
+}
+
+node z = READ(x, i+1);
+if (z->n >= T) {// case 2b
+x->key[i] = z->key[0];
+delete_op(z, x->key[i]);
+return;
+}
+
+// case 2c:
+if (y->n == T-1 && z->n == T-1) {
+
+}
+delete_case3(x);
+}
+}
+}
+
+/**
+ * delete case3
+ */
+void delete_case3(node x) {
+}
+
 /**
  * Read a 4K-block from disk, and returns the node struct.
  */
@@ -211,7 +276,7 @@ namespace alg {
 read(fd, xi, BLOCKSIZE);
 return (node)xi;
 }
-
+
 /**
  *	update a node struct to file, create if offset is -1.
  */

src/btree_demo.cpp

@@ -6,14 +6,9 @@ int main(void) {
 BTree x("./btree.dat");
 int32_t i;
 
-/*
-for (i=0;i<1024;i++) {
+for (i=0;i<100000;i++) {
 x.Insert(i);
-}
-*/
-
-for(i=0;i<1024;i++) {
-int32_t r = x.Search(i);
-printf("idx[%d]\n", r);
+BTree::nr r = x.Search(i);
+printf("offset[%x] idx[%d]\n", r.offset, r.idx);
 }
 }