悩んでいる人
C言語でマークル木とマークルパトリシア木を教えて！
こういった悩みにお答えします．
本記事の信頼性
- リアルタイムシステムの研究歴12年．
- 東大教員の時に，英語でOSの授業．
- 2012年9月～2013年8月にアメリカのノースカロライナ大学チャペルヒル校コンピュータサイエンス学部（2021年の世界大学学術ランキングで20位）で客員研究員として勤務．C言語でリアルタイムLinuxの研究開発．
- プログラミング歴15年以上，習得している言語: C/C++，Solidity/Vyper，Java，Python，Ruby，Go，Rust，D，HTML/CSS/JS/PHP，MATLAB，Assembler (x64，ARM)．
- 東大教員の時に，C++言語で開発した「LLVMコンパイラの拡張」，C言語で開発した独自のリアルタイムOS「Mcube Kernel」をGitHubにオープンソースとして公開．
こういった私から学べます．
本記事では，ハッシュテーブルを理解していることを前提とします．
マークル木（マークルハッシュ木，ハッシュ木）【ビットコインで利用】
マークル木（マークルハッシュ木，ハッシュ木）とは，ハッシュリストとハッシュチェインを組み合わせたデータ構造です．
また，マークル木は仮想通貨ビットコインのブロックチェーンで利用するデータ構造でもあります．
ビットコインを知りたいあなたはこちらからどうぞ．
マークル木のコードは以下になります．
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/* * Author: Hiroyuki Chishiro * License: 2-Clause BSD */ #include <stdio.h> #include <stdlib.h> #include <string.h> #include <stdbool.h> #define HASH_TREE_SIZE 8 #define BUFSIZE 128 struct node { char key[BUFSIZE]; char val[BUFSIZE]; struct node *left; struct node *right; }; struct merkle_tree { struct node *head; }; struct node *find(struct node *tree, char *key) { if (tree == NULL) { return NULL; } if (strcmp(tree->key, key) == 0) { return tree; } else if (strcmp(key, tree->key) < 0) { return find(tree->left, key); } else { return find(tree->right, key); } } void insert_element(struct node *tree, struct node *item) { if (strcmp(item->key, tree->key) < 0) { if (tree->left == NULL) { tree->left = item; return; } else { insert_element(tree->left, item); return; } } else if (strcmp(item->key, tree->key) > 0) { if (tree->right == NULL) { tree->right = item; return; } else { insert_element(tree->right, item); return; } } } int get_hash_val(char *key) { int hash_val = 0; while (*key) { hash_val += *key++; } return hash_val % HASH_TREE_SIZE; } void insert(char *key, char *val, struct merkle_tree *mtree, int *nump) { int index = get_hash_val(key); struct node *tree = mtree[index].head; struct node *tmp; struct node *new_item; if ((new_item = malloc(sizeof(struct node))) == NULL) { fprintf(stderr, "Error: cannot allocate memory %zu bytes\n", sizeof(struct node)); exit(1); } strcpy(new_item->key, key); strcpy(new_item->val, val); new_item->left = NULL; new_item->right = NULL; if (tree == NULL) { mtree[index].head = new_item; (*nump)++; } else { if ((tmp = find(tree, key)) == NULL) { insert_element(tree, new_item); (*nump)++; } else { strcpy(tmp->val, val); } } } void print_node(struct node *p) { if (p == NULL) { return; } printf("pair(%s, %s) ", p->key, p->val); if (p->left != NULL) { print_node(p->left); } if (p->right != NULL) { print_node(p->right); } } void print_merkle_tree(struct merkle_tree *mtree) { int i; struct node *p; printf("print_merkle_tree()\n"); for (i = 0; i < HASH_TREE_SIZE; i++) { if ((p = mtree[i].head) != NULL) { printf("\t%d: ", i); print_node(p); printf("\n"); } } } struct node *erase_element(struct node *tree, char *key, int *nump) { struct node *left_one; if (tree == NULL) { return NULL; } if (strcmp(key, tree->key) < 0) { tree->left = erase_element(tree->left, key, nump); return tree; } else if (strcmp(key, tree->key) > 0) { tree->right = erase_element(tree->right, key, nump); return tree; } else { if (tree->left == NULL && tree->right == NULL) { (*nump)--; return tree->left; } else if (tree->left != NULL && tree->right == NULL) { (*nump)--; return tree->left; } else if (tree->left == NULL && tree->right != NULL) { (*nump)--; return tree->right; } else { left_one = tree->left; while (left_one->right != NULL) { left_one = left_one->right; } strcpy(tree->key, left_one->key); strcpy(tree->val, left_one->val); tree->left = erase_element(tree->left, tree->key, nump); return tree; } } } struct node *search(char *key, struct merkle_tree *mtree) { int index = get_hash_val(key); struct node *tree = (struct node *) mtree[index].head; struct node *tmp; if (tree == NULL) { return NULL; } else { if ((tmp = find(tree, key)) == NULL) { return NULL; } else { return tmp; } } } bool erase(char *key, struct merkle_tree *mtree, int *nump) { int index = get_hash_val(key); struct node *tree = mtree[index].head; struct node *tmp; if (tree == NULL) { return false; } else { if ((tmp = find(tree, key)) == NULL) { return false; } else { erase_element(tree, key, nump); free(tmp); return true; } } } void init_merkle_tree(struct merkle_tree *mtree) { int i; for (i = 0; i < HASH_TREE_SIZE; i++) { mtree[i].head = NULL; } } void exit_merkle_tree(struct merkle_tree *mtree) { int i; struct node *tree; for (i = 0; i < HASH_TREE_SIZE; i++) { if ((tree = mtree[i].head) != NULL) { free(tree); } } } int main(void) { struct merkle_tree mtree[HASH_TREE_SIZE]; int number_of_elements = 0; struct node *node; char *word = "two"; init_merkle_tree(mtree); insert("one", "val1", mtree, &number_of_elements); insert("two", "val2", mtree, &number_of_elements); insert("three", "val3", mtree, &number_of_elements); print_merkle_tree(mtree); if ((node = search(word, mtree)) != NULL) { printf("\"%s\" is found\n", word); } else { printf("\"%s\" is not found\n", word); } erase("two", mtree, &number_of_elements); print_merkle_tree(mtree); exit_merkle_tree(mtree); return 0; } |
実行結果は以下になります．
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$ gcc merkle_tree.c $ a.out print_merkle_tree() 0: pair(three, val3) 2: pair(one, val1) pair(two, val2) "two" is found print_merkle_tree() 0: pair(three, val3) 2: pair(one, val1) |
マークルパトリシア木（基数木，パトリシア木）【イーサリアムで利用】
マークルパトリシア木（基数木，パトリシア木）とは，文字列集合を格納するトライ木をベースとしたデータ構造です．
また，マークルパトリシア木は仮想通貨イーサリアムのブロックチェーンで利用するデータ構造でもあります．
イーサリアムを知りたいあなたはこちらからどうぞ．
また，Linuxカーネルでも基数木（Radix Tree）という名前で実装されています（詳細はこちら）．
Linuxカーネルを知りたいあなたはこちらからどうぞ．
マークルパトリシア木のコードは以下になります．
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/* * Author: Hiroyuki Chishiro * License: 2-Clause BSD */ #include <stdio.h> #include <stdlib.h> #include <string.h> #include <stdbool.h> #define BUFSIZE 128 /* HASH_TREE_SIZE is as same as ASCII code size. */ #define HASH_TREE_SIZE 128 #define MIN(x, y) ((x) < (y) ? (x) : (y)) #define INIT_TRANSITION_CHAR -1 #define NO_MISMATCH -1 struct mpedge { char label[BUFSIZE]; struct mpnode *next; }; struct hash_map { int transition_char; struct mpedge *edge; }; struct mpnode { bool is_leaf; struct hash_map edges[HASH_TREE_SIZE]; }; struct mptree { struct mpnode *root; }; void init_node(struct mpnode *node, bool is_leaf) { int i; node->is_leaf = is_leaf; for (i = 0; i < HASH_TREE_SIZE; i++) { node->edges[i].transition_char = INIT_TRANSITION_CHAR; node->edges[i].edge = NULL; } } void init_mptree(struct mptree *mtree) { if ((mtree->root = malloc(sizeof(struct mpnode))) == NULL) { fprintf(stderr, "Error: cannot allocate memory %zu bytes\n", sizeof(struct mpnode)); exit(1); } init_node(mtree->root, false); } void exit_node(struct mpnode *node) { size_t i; if (!node) { return; } for (i = 0; i < HASH_TREE_SIZE; i++) { if (node->edges[i].edge != NULL) { exit_node(node->edges[i].edge->next); free(node->edges[i].edge); } } free(node); } void exit_mptree(struct mptree *mtree) { exit_node(mtree->root); } int get_first_mismatch_letter(char *word, char *edge_word) { int length; size_t i; if (!word || !edge_word) { return NO_MISMATCH; } length = MIN(strlen(word), strlen(edge_word)); for (i = 1; i < length; i++) { if (word[i] != edge_word[i]) { return i; } } return NO_MISMATCH; } void print_all_words_rec(struct mpnode *current, char *result) { size_t i; char buf[BUFSIZE]; struct mpedge *edge; if (!current) { return; } if (current->is_leaf) { printf("\t%s\n", result); } for (i = 0; i < HASH_TREE_SIZE; i++) { if (current->edges[i].edge != NULL) { edge = current->edges[i].edge; strcpy(buf, result); strcat(buf, edge->label); print_all_words_rec(edge->next, buf); } } } void print_all_words(struct mptree *mtree) { printf("print_all_words()\n"); print_all_words_rec(mtree->root, ""); } struct mpedge *get_transition(struct mpnode *node, int transition_char) { size_t i; if (!node) { return NULL; } for (i = 0; i < HASH_TREE_SIZE; i++) { if (node->edges[i].transition_char == transition_char) { return node->edges[i].edge; } } return NULL; } void add_edge(struct mpnode *node, char *label, struct mpnode *next) { int transition_char = label[0]; struct mpedge *edge; if ((edge = malloc(sizeof(struct mpedge))) == NULL) { fprintf(stderr, "Error: cannote allocate memory %zu bytes\n", sizeof(struct mpedge)); exit(1); } strcpy(edge->label, label); edge->next = next; node->edges[transition_char].transition_char = transition_char; node->edges[transition_char].edge = edge; } struct mpedge *remove_edge(struct mpnode *node, int transition_char) { size_t i; struct mpedge *edge; for (i = 0; i < HASH_TREE_SIZE; i++) { if (node->edges[i].transition_char == transition_char) { edge = node->edges[i].edge; node->edges[i].transition_char = INIT_TRANSITION_CHAR; node->edges[i].edge = NULL; return edge; } } return NULL; } int get_total_edges(struct mpnode *node) { size_t i; int sum = 0; for (i = 0; i < HASH_TREE_SIZE; i++) { if (node->edges[i].edge != NULL) { sum++; } } return sum; } void insert_word(struct mptree *mtree, char *word) { struct mpnode *current = mtree->root; int current_index = 0; size_t word_length = strlen(word); size_t current_edge_label_length; int transition_char; char *current_str; struct mpedge *current_edge; struct mpedge *edge; size_t current_str_length; char suffix[BUFSIZE]; struct mpnode *after_new_next; struct mpnode *new_next; struct mpnode *prev_next; int split_index; while (current_index < word_length) { transition_char = word[current_index]; current_edge = get_transition(current, transition_char); current_str = &word[current_index]; current_str_length = strlen(current_str); if (current != NULL && current_edge == NULL) { if ((edge = malloc(sizeof(struct mpedge))) == NULL) { fprintf(stderr, "Error: cannote allocate memory %zu bytes\n", sizeof(struct mpedge)); exit(1); } strcpy(edge->label, current_str); if ((edge->next = malloc(sizeof(struct mpnode))) == NULL) { fprintf(stderr, "Error: cannot allocate memory %zu bytes\n", sizeof(struct mpnode)); exit(2); } init_node(edge->next, true); current->edges[transition_char].transition_char = transition_char; current->edges[transition_char].edge = edge; break; } split_index = get_first_mismatch_letter(current_str, current_edge->label); if (split_index == NO_MISMATCH) { current_edge_label_length = strlen(current_edge->label); if (current_str_length == current_edge_label_length) { current_edge->next->is_leaf = true; break; } else if (current_str_length < current_edge_label_length) { strcpy(suffix, ¤t_edge->label[current_str_length]); strcpy(current_edge->label, current_str); if ((new_next = malloc(sizeof(struct mpnode))) == NULL) { fprintf(stderr, "Error: cannot allocate memory %zu bytes\n", sizeof(struct mpnode)); exit(3); } init_node(new_next, true); after_new_next = current_edge->next; current_edge->next = new_next; add_edge(new_next, suffix, after_new_next); break; } else { split_index = current_edge_label_length; } } else { strcpy(suffix, ¤t_edge->label[split_index]); current_edge->label[split_index] = '\0'; prev_next = current_edge->next; if ((current_edge->next = malloc(sizeof(struct mpnode))) == NULL) { fprintf(stderr, "Error: cannot allocate memory %zu bytes\n", sizeof(struct mpnode)); exit(4); } init_node(current_edge->next, false); add_edge(current_edge->next, suffix, prev_next); } current = current_edge->next; current_index += split_index; } } struct mpnode *delete_word_from_root(struct mpnode *root, struct mpnode *current, char *word) { size_t i; struct mpnode *deleted; struct mpedge *deleted_edge; int transition_char; struct mpedge *edge; size_t edge_label_length; struct mpedge *after_deleted; char buf[BUFSIZE]; if (word == NULL || (word != NULL && strlen(word) == 0)) { if (get_total_edges(current) == 0 && current != root) { return NULL; } current->is_leaf = false; return current; } transition_char = word[0]; if ((edge = get_transition(current, transition_char)) == NULL) { return current; } edge_label_length = strlen(edge->label); if (strncmp(word, edge->label, edge_label_length) != 0) { return current; } deleted = delete_word_from_root(root, edge->next, &word[edge_label_length]); if (deleted == NULL) { deleted_edge = remove_edge(current, transition_char); if (deleted_edge) { free(deleted_edge->next); free(deleted_edge); } if (get_total_edges(current) == 0 && !current->is_leaf && current != root) { return NULL; } } else if (get_total_edges(deleted) == 1 && !deleted->is_leaf) { deleted_edge = remove_edge(current, transition_char); if (deleted_edge) { for (i = 0; i < HASH_TREE_SIZE; i++) { if (deleted->edges[i].edge != NULL) { after_deleted = deleted->edges[i].edge; strcpy(buf, edge->label); strcat(buf, after_deleted->label); add_edge(current, buf, after_deleted->next); free(after_deleted); } } free(deleted_edge->next); free(deleted_edge); } } return current; } void delete_word(struct mptree *mtree, char *word) { mtree->root = delete_word_from_root(mtree->root, mtree->root, word); } bool search_word(struct mptree *mtree, char *word) { struct mpnode *current = mtree->root; int current_index = 0; int transition_char; size_t word_length = strlen(word); char *current_substring; size_t edge_label_length; struct mpedge *edge; while (current_index < word_length) { transition_char = word[current_index]; if ((edge = get_transition(current, transition_char)) == NULL) { return false; } current_substring = &word[current_index]; edge_label_length = strlen(edge->label); if (strncmp(current_substring, edge->label, edge_label_length) != 0) { return false; } current_index += edge_label_length; current = edge->next; } return current->is_leaf; } int main(void) { struct mptree mtree; init_mptree(&mtree); insert_word(&mtree, "test"); insert_word(&mtree, "water"); insert_word(&mtree, "fast"); insert_word(&mtree, "faster"); insert_word(&mtree, "team"); insert_word(&mtree, "tester"); insert_word(&mtree, "t"); insert_word(&mtree, "toast"); print_all_words(&mtree); printf("%d\n", search_word(&mtree, "faster")); printf("%d\n", search_word(&mtree, "t")); printf("%d\n", search_word(&mtree, "te")); printf("%d\n", search_word(&mtree, "tes")); printf("%d\n", search_word(&mtree, "test")); printf("%d\n", search_word(&mtree, "toast")); printf("%d\n", search_word(&mtree, "tester")); delete_word(&mtree, "test"); delete_word(&mtree, "t"); delete_word(&mtree, "faster"); delete_word(&mtree, "wate"); printf("%d\n", search_word(&mtree, "faster")); printf("%d\n", search_word(&mtree, "t")); printf("%d\n", search_word(&mtree, "te")); printf("%d\n", search_word(&mtree, "tes")); printf("%d\n", search_word(&mtree, "test")); printf("%d\n", search_word(&mtree, "toast")); printf("%d\n", search_word(&mtree, "tester")); print_all_words(&mtree); exit_mptree(&mtree); return 0; } |
実行結果は以下になります．
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$ gcc merkle_patricia_tree.c $ a.out print_all_words() fast faster t team test tester toast water 1 1 0 0 1 1 1 0 0 0 0 0 1 1 print_all_words() fast team tester toast water |
まとめ
C言語でマークル木とマークルパトリシア木を紹介しました．
マークル木はビットコイン，マークルパトリシア木はイーサリアムで利用されていることがわかりました．
C言語を独学で習得することは難しいです．
私にC言語の無料相談をしたいあなたは，公式LINE「ChishiroのC言語」の友だち追加をお願い致します．
私のキャパシティもあり，一定数に達したら終了しますので，今すぐ追加しましょう！
独学が難しいあなたは，元東大教員がおすすめするC言語を学べるオンラインプログラミングスクール5社で自分に合うスクールを見つけましょう．後悔はさせません！
