二叉树的确定

二叉树的遍历方式分为：先序遍历、中序遍历、后序遍历、层次遍历

其中，中序序列与先序序列、后序序列、层次序列，两两组合均能确立一个唯一的二叉树

1、中序序列和先序序列

事实上，如果递归过程中当前先序序列的区间为[preL, preR], 中序序列的区间为[inL, inR], 那么左子树的节点个数为：numLeft = k - inL。这样左子树的先序序列区间就是[preL+1, preL +numLeft]，左子树的中序序列区间是[inL， k-1]，右子树的先序序列区间就是[preL + numLeft+1, preR], 右子树的中序序列是[k + 1, inR]

注：递归边界：先序序列的长度小于0，即 preL > preR

#include <cstdio>
const int maxn = 50;
int n; //n个结点
stuct node{
	int data;
	node* lchild;
	node* rchild;
};
int pre[maxn], post[maxn], in[maxn];
node* create(int preL, int preR, int inL, int inR){
	if(preL > preR){
		return NULL;
	}
	node* root = new node;
	root->data = pre[preL];
	int k;
	for(k = inL; k <= inR; k++){
		if(in[k] == pre[preL]){
			break;
		}
	}

	int numLeft = k - inL;

	//左子树[preL+1, preL+numLeft, inL, k-1];
	root->lchild = create(preL+1, preL+numLeft, inL, k-1);
	root->rchild = create(preL+numLeft+1, preR, k+1, inR);

	return root;
}

int main(void){
	scanf("%d", &n);

	//init
	for(int i = 0; i < n; i++){
		scanf("%d", &pre[i]);
	}
	for(int i = 0; i < n; i++){
		scanf("%d", &in[i]);
	}
	node* root = create(0, n-1, 0, n-1);

	return 0;
}

2、中序序列和后序序列

#include <cstdio>
#include <cstring>
#include <queue>
#include <algorithm>
using namespace std;
const int maxn = 50;
struct node{
	int data;
	node* lchild;
	node* rchild;
};
int pre[maxn], post[maxn], in[maxn];
int n; //结点个数

node* create(int postL, int postR, int inL, int inR){
	if(postL > postR){
		return NULL;
	}
	node* root = new node;
	root->data = post[postR];
	
	int k;
	for(k = inL; k <= inR; k++){
		if(in[k] == post[postR]){
			break;
		}
	}
	int numLeft = k - inL; 

	root->lchild = create(postL, postL + numLeft -1, inL, k - 1);
	root->rchild = create(postL + numLeft, postR - 1, k + 1, inR);

	return root;
}

int num = 0; //已输出的结点个数
void bfs(node* root){
	queue<node*> q;
	q.push(root);
	while(!q.empty()){
		node* now = q.front();
		q.pop();
		printf("%d", now->data);
		num++;
		if(num < n)
			printf(" ");
		if(now->lchild != NULL)
			q.push(now->lchild);
		if(now->rchild != NULL)
			q.push(now->rchild);
	}

}

int main(void){
	scanf("%d", &n);
	//init
	for(int i = 0; i < n; i++){
		scanf("%d", &post[i]);
	}
	for(int i = 0; i < n; i++){
		scanf("%d", &in[i]);
	}

	node* root = create(0, n-1, 0, n-1);
	bfs(root);

	return 0;
}

3、已知层次序列和中序序列，求先序序列

#include<iostream>
#include<cstring>
#include<string>
using namespace std;
//因为层序是先输出根节点的，所以可以递归查找
string s1,s2; //s1：中序序列 s2：层次序列
void find(int inL, int inR, int levelL, int levelR)
{
    int i, j;
    for(i = levelL; i <= levelR; i++)//找层次遍历中优先输出根节点的位置 
    {
        int f = 0; //是否存在
        for(j = inL; j <= inR; j++)
        {
            if(s2[i] == s1[j])//输出根节点 
            {
                cout << s1[j];
                f = 1;
                break;
            }
        }
        if(f)
            break;
    }
    if(j > inL)
        find(inL, j - 1, 0, levelR);//遍历左子树 
    if(j < inR)
        find(j + 1, inR, 0, levelR);//遍历右子树 i
}
int main()
{
    cin >> s1 >> s2;
	//中序、层次i
    find(0, s1.length()-1, 0, s2.length());
    return 0;
}