二叉树的深度优先遍历与广度优先遍历
2014年11月22日
二叉树的深度优先遍历就是二叉树地前序遍历．二叉树的广度遍历就是层序遍历.（最后面有完整的代码）．
一．深度优先遍历(DFS)
深度优先遍历与前序遍历的结果是一样的．那么递归实现应该是
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void dfs_r(T) { if (T == NULL) { return ; } print(T.k); dfs_r(T.left); dfs_r(T.right); } |
与之对应的非递归算法是，使用栈的先进后出的特性．
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void dfs(T) { push(q,T); while (!is_empty(q)) { n = pop(q); print(n.k); if (n.right) { push(q,n.right); } if (n.left) { push(q,n.left); } } } |
二.广度优先遍历(BFS)
二叉树的广度优先遍历其实很简单，大概的思路是访问一个结点时，将它的子结点放入队列后面，当本层访问结束后，队列中就剩下下一层的所有结点，直到队列中没有结点为止．
可以看到队列的前部是当前层剩下的结点，队列的后部是当前层已经访问过的结点的子结点．
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void bfs(T) { push(s,T); while (!is_empty(s)) { n = pop(s); print(n.k); if (n.left) { push(s,n.left); } if (n.right) { push(s,n.right); } } return ; } |
完整代码
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#include <stdio.h> #include <stdlib.h> /*implement list*/ typedef struct link_s link_t; typedef struct link_s list_t; struct link_s { link_t *next; link_t *prev; }; /*list init*/ static void list_init(list_t *l) { l->next = l->prev = l; } /*list insert tail*/ static void list_insert_t(list_t *l,link_t *n) { n->prev = l->prev; n->next = l; n->prev->next = n; n->next->prev = n; } /*list insert head*/ static void list_insert_h(list_t *l,link_t *n) { n->prev = l; n->next = l->next; n->prev->next = n; n->next->prev = n; } static link_t* list_remove(link_t *n) { n->next->prev = n->prev; n->prev->next = n->next; return n; } static int list_is_empty(list_t *l) { return l->prev == l; } /*binary tree*/ typedef struct bnode_s btree_t; typedef struct bnode_s bnode_t; struct bnode_s { int k; bnode_t *l; bnode_t *r; }; btree_t *btree_create(int *k,int *n,int m); void btree_bfs(btree_t *T); void btree_dfs(btree_t *T); btree_t *btree_create(int *k,int *n,int m) { btree_t *T; int i; i = *n; *n = i + 1; if (i > m || k[i] == -1) { return NULL; } T = malloc(sizeof(btree_t)); if (T == NULL) { exit(-2); } T->k = k[i]; T->l = btree_create(k,n,m); T->r = btree_create(k,n,m); return T; } /************** 1 / \ 2 5 / \ 3 4 (1). create a binary tree (2). BFS: 1 2 5 3 4 (3). DFS: 1 2 3 4 5 **************/ int main(int argc,char **argv) { btree_t *T; int k[] = {1,2,3,-1,-1,4,-1,-1,5,-1,-1}; /*-1: NULL*/ int p,n; n = sizeof(k) / sizeof(k[0]); p = 0; T = btree_create(k,&p,n); if (T == NULL) { fprintf(stderr,"create a binary tree failed!"); exit(-2); } btree_bfs(T); btree_dfs(T); return 0; } typedef struct node_s node_t; struct node_s{ link_t link; /*MUST be FIRST*/ bnode_t *node; }; static node_t *alloc_node(bnode_t *nd) { node_t *b; b = (node_t *)malloc(sizeof(node_t)); if (b == NULL) { return NULL; } b->node = nd; return b; } void free_node(node_t *bfs) { free(bfs); } /*BFS*/ void btree_bfs(btree_t *T) { node_t *n,*top; link_t q; list_init(&q); printf("BFS: "); /*push root*/ n = alloc_node(T); list_insert_t(&q,&n->link); while (!list_is_empty(&q)) { /*remove front*/ top = (node_t*)list_remove(q.next); printf("%d ",top->node->k); /*push left child*/ if (top->node->l) { n = alloc_node(top->node->l); list_insert_t(&q,&n->link); } /*push right child*/ if (top->node->r) { n = alloc_node(top->node->r); list_insert_t(&q,&n->link); } free_node(top); } printf("\n"); return ; } /*DFS*/ void btree_dfs(btree_t *T) { node_t *n,*top; link_t s; list_init(&s); printf("DFS: "); /*push root*/ n = alloc_node(T); list_insert_h(&s,&n->link); while (!list_is_empty(&s)) { top = (node_t*)list_remove(s.next); printf("%d ",top->node->k); /*push right*/ if (top->node->r) { n = alloc_node(top->node->r); list_insert_h(&s,&n->link); } /*push left*/ if (top->node->l) { n = alloc_node(top->node->l); list_insert_h(&s,&n->link); } free_node(top); } printf("\n"); return ; } |
分类: 算法导论