1043 Is It a Binary Search Tree

1. 这是二叉查找树BST那节的习题，要做出来这题，需要具备的基础知识有：BST的创建，涉及函数createBST，insertBST，newNode，二叉树的先序遍历、后序遍历。

2. 需要转过来的弯的有：

给定了序列，其实就可以创建出唯一的BST了。也就是一开始给定的那个序列，不要管他是什么序，反正就是个确定的序列。后面用来比对的时候再看他是不是先序，是不是镜像先序。

所谓镜像就是把检索左右子树的位置互换以下。

3. 一个非常使用的技巧：向量容器盛整数可以直接比对序列。详见妙用vector:根据第一个不等的元素比较两个序列大小的利器

4. 我犯了一个非常傻的错误，在遍历的时候第一句应该是root==NULL退出，写成了!=，导致我一直在纠结传进来的参数的引用写的对不对。也调试不出，后来猛然看见的。

AC代码

#include<cstdio>
#include<map>
#include<set>
#include<string>
#include<cstring>
#include<iostream>
#include<vector>
#include<stack>
#include<queue>
#include<algorithm>
#include<cmath>
typedef long long LL;using namespace std;const int maxn = 100010;struct Node{int data;Node *lchild,*rchild;
};Node* newNode(int v){Node* node = new Node;//申请变量的地址空间node->lchild = node->rchild = NULL;//新建的结点没有左右孩子node->data = v;//数据域为传进的参数值return node;
}void insertBST(Node* &root,int v){//由于要对二叉树的结构进行修改，所以传入根节点的引用if(root==NULL){//查找失败的位置，就是要插入的位置root = newNode(v);return;}if(v<root->data)insertBST(root->lchild,v);//根据BST的性质，此时往左子树搜索 else insertBST(root->rchild,v);
}Node* createBST(vector<int> data,int n){//data是待插入值域的数组，n是数组长度 Node* root = NULL;for(int i=0;i<n;i++){insertBST(root,data[i]);}return root;
}void preOrder(Node* root,vector<int>& preSeq){if(root==NULL)return;preSeq.push_back(root->data);preOrder(root->lchild,preSeq);preOrder(root->rchild,preSeq);
}void mirrorPreOrder(Node* root,vector<int>& mirrorPreSeq){if(root==NULL)return;mirrorPreSeq.push_back(root->data);mirrorPreOrder(root->rchild,mirrorPreSeq);mirrorPreOrder(root->lchild,mirrorPreSeq);}void postOrder(Node* root,vector<int>& postSeq){if(root==NULL)return;postOrder(root->lchild,postSeq);postOrder(root->rchild,postSeq);postSeq.push_back(root->data);
}void mirrorPostOrder(Node* root,vector<int>& mirrorPostSeq){if(root==NULL)return;mirrorPostOrder(root->rchild,mirrorPostSeq);mirrorPostOrder(root->lchild,mirrorPostSeq);mirrorPostSeq.push_back(root->data);
} int main(){int n,data;vector<int> initSeq,preSeq,mirrorPreSeq,postSeq,mirrorPostSeq;scanf("%d",&n);for(int i=0;i<n;i++){scanf("%d",&data);initSeq.push_back(data);}Node* root = createBST(initSeq,n);preOrder(root,preSeq);if(preSeq==initSeq){printf("YES\n");postOrder(root,postSeq);for(int i=0;i<postSeq.size();i++){printf("%d",postSeq[i]);if(i!=postSeq.size()-1)printf(" ");}return 0;}mirrorPreOrder(root,mirrorPreSeq);if(mirrorPreSeq==initSeq){printf("YES\n");mirrorPostOrder(root,mirrorPostSeq);for(int i=0;i<mirrorPostSeq.size();i++){printf("%d",mirrorPostSeq[i]);if(i!=mirrorPostSeq.size()-1)printf(" ");}return 0;}printf("NO"); return 0;
}

邪门，第二次做代码优化了，对于镜像居然检测不出

#include<cstdio>
#include<iostream>
#include<cmath>
#include<cstring>
#include<algorithm>
#include<bits/stdc++.h>
#include<stdlib.h>
#include<time.h>
#include<vector>
#include<set>
#include<string>
#include<tr1/unordered_map>using namespace std;
using namespace std::tr1;
typedef long long LL;const int maxn = 107;
const int MOD = 1000000007;
const int INF = 1000000000;//INF:下确界
const LL SUP = (1LL<<63)-1;//SUP:上确界
const double eps = 1e-5;struct Node{int v;Node *lchild,*rchild;
};void insert(int x,Node* &root){if(root==NULL){root = new Node;root->v = x;root->lchild = root->rchild = NULL;return;}if(x<root->v)insert(x,root->lchild);else insert(x,root->rchild);
}vector<int> initV,testV,testV2,postV;void preOrder(Node* root){if(root==NULL)return;testV.push_back(root->v);if(root->lchild!=NULL)preOrder(root->lchild);if(root->rchild!=NULL)preOrder(root->rchild);
}void preOrderMir(Node* root){if(root==NULL)return;testV2.push_back(root->v);if(root->rchild!=NULL)preOrder(root->rchild);if(root->lchild!=NULL)preOrder(root->lchild);
}void postOrder(Node* root){if(root==NULL)return;if(root->lchild!=NULL)postOrder(root->lchild);if(root->rchild!=NULL)postOrder(root->rchild);postV.push_back(root->v);
}void postOrderMir(Node* root){if(root==NULL)return;if(root->rchild!=NULL)postOrder(root->rchild);if(root->lchild!=NULL)postOrder(root->lchild);postV.push_back(root->v);
}int main(){int n,x;cin>>n;for(int i=0;i<n;i++){cin>>x;initV.push_back(x);}Node* root = NULL;for(int i=0;i<n;i++){insert(initV[i],root);}preOrder(root);if(testV==initV){printf("YES\n");postOrder(root);for(int i=0;i<postV.size();i++){printf("%d%s",postV[i],i==postV.size()-1?"\n":" ");}return 0;}preOrderMir(root);if(testV2==initV){printf("YES\n");postV.clear();postOrderMir(root);for(int i=0;i<postV.size();i++){printf("%d%s",postV[i],i==postV.size()-1?"\n":" ");}return 0;}printf("NO\n");return 0;
}

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