04-树7. Search in a Binary Search Tree (25)
时间限制
100 ms
内存限制
65536 kB
代码长度限制
8000 B
判题程序
Standard
作者
CHEN, Yue
To search a key in a binary search tree, we start from the root and move all the way down, choosing branches according to the comparison results of the keys. The searching path corresponds to a sequence of keys. For example, following {1, 4, 2, 3} we can find 3 from a binary search tree with 1 as its root. But {2, 4, 1, 3} is not such a path since 1 is in the right subtree of the root 2, which breaks the rule for a binary search tree. Now given a sequence of keys, you are supposed to tell whether or not it indeed correspnds to a searching path in a binary search tree.
Input Specification:
Each input file contains one test case. For each case, the first line gives two positive integers N and M (<=100) which are the total number of sequences, and the size of each sequence, respectively. Then N lines follow, each gives a sequence of keys. It is assumed that the keys are numbered from 1 to M.
Output Specification:
For each sequence, print in a line "YES" if the sequence does correspnd to a searching path in a binary search tree, or "NO" if not.
Sample Input:
3 4 1 4 2 3 2 4 1 3 3 2 4 1
Sample Output:
YES NO NO
提交代码
法一：
如果是二叉查找树，树上除了叶结点，每个节点的左右子树必有一棵空，另一棵不空。
1 #include<cstdio>
2 #include<algorithm>
3 #include<iostream>
4 #include<cstring>
5 #include<queue>
6 #include<vector>
7 using namespace std;
8 struct node{
9 int v;
10 node *l,*r;
11 node(){
12 l=r=NULL;
13 }
14 };
15 int main(){
16 //freopen("D:\\INPUT.txt","r",stdin);
17 int n,m;
18 scanf("%d %d",&n,&m);
19 while(n--){
20 queue<int> q;
21 int i,num;
22 node *p,*pp,*h=NULL;
23 for(i=0;i<m;i++){
24 scanf("%d",&num);
25 q.push(num);
26 }
27 h=new node();
28 h->v=q.front();
29 q.pop();
30 for(i=1;i<m;i++){
31 num=q.front();
32 q.pop();
33 p=h;
34 while(p){
35 pp=p;//pp point to the father of p
36 if(num>p->v&&p->l==NULL){
37 p=p->r;
38 }
39 else{
40 if(num<p->v&&p->r==NULL){
41 p=p->l;
42 }
43 else
44 break;//防止元素相等
45 }
46 }
47 if(p==NULL){
48 p=new node();
49 p->v=num;
50 if(num>pp->v){
51 pp->r=p;
52 }
53 else{
54 pp->l=p;
55 }
56 }
57 else{
58 break;
59 }
60 }
61 if(i==m){
62 printf("YES\n");
63 }
64 else{
65 printf("NO\n");
66 }
67 }
68 return 0;
69 }
法二：
先按题意建树，得到树后，用最后输入的数进行树的遍历，如果最后经过m次找到匹配的叶结点，说明序列正确；否则，序列错误。
1 #include<cstdio>
2 #include<algorithm>
3 #include<iostream>
4 #include<cstring>
5 #include<queue>
6 #include<vector>
7 using namespace std;
8 struct node{
9 int v;
10 node *l,*r;
11 node(){
12 l=r=NULL;
13 }
14 };
15 int main(){
16 //freopen("D:\\INPUT.txt","r",stdin);
17 int n,m;
18 scanf("%d %d",&n,&m);
19 while(n--){
20 queue<int> q;
21 int i,num,wantfind;
22 node *p,*pp,*h;
23 for(i=0;i<m;i++){
24 scanf("%d",&num);
25 q.push(num);
26 }
27 wantfind=num; //最后一个
28 h=new node();
29 h->v=q.front();
30 q.pop();
31 for(i=1;i<m;i++){ //建树
32 num=q.front();
33 q.pop();
34 p=h;
35 while(p){
36 pp=p;//pp point to the father of p
37 if(num>p->v){
38 p=p->r;
39 }
40 else{
41 p=p->l;
42 }
43 }
44 p=new node();
45 p->v=num;
46 if(num>pp->v){
47 pp->r=p;
48 }
49 else{
50 pp->l=p;
51 }
52 }
53 int count=0;
54 p=h;
55 while(p){
56 if(wantfind>p->v){
57 p=p->r;
58 }
59 else{
60 p=p->l;
61 }
62 count++;
63 }
64 if(count==m){
65 printf("YES\n");
66 }
67 else{
68 printf("NO\n");
69 }
70 }
71 return 0;
72 }