04-树7. Search in a Binary Search Tree (25)
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
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。
#include<cstdio>
#include<algorithm>
#include<iostream>
#include<cstring>
#include<queue>
#include<vector>
using namespace std;
struct node{
int v;
node *l,*r;
node(){
l=r=NULL;
}
};
int main(){
//freopen("D:\\INPUT.txt","r",stdin);
int n,m;
scanf("%d %d",&n,&m);
while(n--){
queue<int> q;
int i,num;
node *p,*pp,*h=NULL;
for(i=;i<m;i++){
scanf("%d",&num);
q.push(num);
}
h=new node();
h->v=q.front();
q.pop();
for(i=;i<m;i++){
num=q.front();
q.pop();
p=h;
while(p){
pp=p;//pp point to the father of p
if(num>p->v&&p->l==NULL){
p=p->r;
}
else{
if(num<p->v&&p->r==NULL){
p=p->l;
}
else
break;//防止元素相等
}
}
if(p==NULL){
p=new node();
p->v=num;
if(num>pp->v){
pp->r=p;
}
else{
pp->l=p;
}
}
else{
break;
}
}
if(i==m){
printf("YES\n");
}
else{
printf("NO\n");
}
}
return ;
}
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。
#include<cstdio>
#include<algorithm>
#include<iostream>
#include<cstring>
#include<queue>
#include<vector>
using namespace std;
struct node{
int v;
node *l,*r;
node(){
l=r=NULL;
}
};
int main(){
//freopen("D:\\INPUT.txt","r",stdin);
int n,m;
scanf("%d %d",&n,&m);
while(n--){
queue<int> q;
int i,num,wantfind;
node *p,*pp,*h;
for(i=;i<m;i++){
scanf("%d",&num);
q.push(num);
}
wantfind=num; //最后一个
h=new node();
h->v=q.front();
q.pop();
for(i=;i<m;i++){ //建树
num=q.front();
q.pop();
p=h;
while(p){
pp=p;//pp point to the father of p
if(num>p->v){
p=p->r;
}
else{
p=p->l;
}
}
p=new node();
p->v=num;
if(num>pp->v){
pp->r=p;
}
else{
pp->l=p;
}
}
int count=;
p=h;
while(p){
if(wantfind>p->v){
p=p->r;
}
else{
p=p->l;
}
count++;
}
if(count==m){
printf("YES\n");
}
else{
printf("NO\n");
}
}
return ;
}