PAT甲级 1130. Infix Expression (25)

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本文介绍了一种算法，该算法接收一个语法树（二叉树形式），并输出对应的带有括号表示运算符优先级的中缀表达式。文章详细解释了输入格式，包括节点数据、左右子树索引等，并提供了示例输入输出。此外，还分享了一个C++实现方案，通过递归深度优先搜索完成表达式的构建。

1130. Infix Expression (25)

时间限制

400 ms

内存限制

65536 kB

代码长度限制

16000 B

判题程序

Standard

作者

CHEN, Yue

Given a syntax tree (binary), you are supposed to output the corresponding infix expression, with parentheses reflecting the precedences of the operators.

Input Specification:

Each input file contains one test case. For each case, the first line gives a positive integer N ( <= 20 ) which is the total number of nodes in the syntax tree. Then N lines follow, each gives the information of a node (the i-th line corresponds to the i-th node) in the format:

data left_child right_child

where data is a string of no more than 10 characters, left_child and right_child are the indices of this node's left and right children, respectively. The nodes are indexed from 1 to N. The NULL link is represented by -1. The figures 1 and 2 correspond to the samples 1 and 2, respectively.


Figure 1	Figure 2

Output Specification:

For each case, print in a line the infix expression, with parentheses reflecting the precedences of the operators. Note that there must be no extra parentheses for the final expression, as is shown by the samples. There must be no space between any symbols.

Sample Input 1:

8
* 8 7
a -1 -1
* 4 1
+ 2 5
b -1 -1
d -1 -1
- -1 6
c -1 -1

Sample Output 1:

(a+b)*(c*(-d))

Sample Input 2:

8
2.35 -1 -1
* 6 1
- -1 4
% 7 8
+ 2 3
a -1 -1
str -1 -1
871 -1 -1

Sample Output 2:

(a*2.35)+(-(str%871))

——————————————————————————————

题目的意思是给出一棵树，每个节点都是将他的左孩子和右孩子进行运算，求表达式

思路：现根据题意建出二叉树，再中序遍历数输出，输出时除了根节点和叶子节点都要输出（）

#include<iostream>
#include<cstdio>
#include<cmath>
#include<cstring>
#include<algorithm>
#include<string>
#include<queue>
#include<stack>
#include<map>
#include<set>
using namespace std;
#define LL long long
const int inf=0x3f3f3f3f;

struct node
{
    string s;
    int pre,l,r;
} tree[105];

int findroot(int pos)
{
    if(tree[pos].pre==-1)
        return pos;
    return findroot(tree[pos].pre);
}

void dfs(int pos,int deep)
{
    if(pos==-1)
        return;
    if(deep!=0&&(tree[pos].l!=-1||tree[pos].r!=-1))
        printf("(");
    dfs(tree[pos].l,deep+1);
    cout<<tree[pos].s;
    dfs(tree[pos].r,deep+1);
    if(deep!=0&&(tree[pos].l!=-1||tree[pos].r!=-1))
        printf(")");
}
int main()
{
    string s;
    int l,r,n;
    scanf("%d",&n);
    for(int i=0; i<100; i++)
        tree[i].l=tree[i].r=tree[i].pre=-1;
    for(int i=1; i<=n; i++)
    {
        cin>>tree[i].s>>tree[i].l>>tree[i].r;
        tree[tree[i].l].pre=tree[tree[i].r].pre=i;
    }
    int root=findroot(1);
    dfs(root,0);
    return 0;
}