1110 Complete Binary Tree (25 分)

Given a tree, you are supposed to tell if it is a complete binary tree.

Input Specification:

Each input file contains one test case. For each case, the first line gives a positive integer N (≤) which is the total number of nodes in the tree -- and hence the nodes are numbered from 0 to N−1. Then N lines follow, each corresponds to a node, and gives the indices of the left and right children of the node. If the child does not exist, a - will be put at the position. Any pair of children are separated by a space.

Output Specification:

For each case, print in one line YES and the index of the last node if the tree is a complete binary tree, or NO and the index of the root if not. There must be exactly one space separating the word and the number.

Sample Input 1:

9
7 8
- -
- -
- -
0 1
2 3
4 5
- -
- -

Sample Output 1:

YES 8

Sample Input 2:

8
- -
4 5
0 6
- -
2 3
- 7
- -
- -

Sample Output 2:

NO 1

/*
思路是先建树，找根节点，先序遍历找到最大节点，如果等于n表示完全二叉树 
*/
#include<iostream>
#include<cstdlib>
using namespace std;
const int maxn = 21;

bool isRoot[maxn] = {0};
int max_index = -1,last_v;
int root = 0;

struct Node
{
    int left,right;
}node[maxn];

int getNum(string s)
{
    int iRet = -1;
    if(s != "-")
    {
        iRet = atoi(s.c_str());
        isRoot[iRet] = 1;
    }
    return iRet;
}

void FindRoot(int n)
{
    for(int i = 0; i < n; i++)
    {
        if(0 == isRoot[i])
        {
            root = i;
            break;
        }
    }
}

void preOrder(int v,int index)
{
    if(-1 == v)
    {
        return;
    }
    if(index > max_index)
    {
        max_index = index;
        last_v = v;    
    }
    preOrder(node[v].left,index*2);
    preOrder(node[v].right,index*2+1);
}

int main()
{
    int n;
    cin >> n;
    string s1,s2;
    for(int i = 0; i < n; i++)
    {
        cin >> s1 >> s2;
        node[i].left = getNum(s1);
        node[i].right = getNum(s2);
    }
    FindRoot(n);
    preOrder(root,1);
    if(max_index == n)
    {
        printf("YES %d",last_v);
    }
    else
    {
        printf("NO %d",root);
    }
    return 0;
}

下面版本三个点段错误，待查

三个点错误是因为转换子树编号时错误，子树编号可以是两位数

#include<cstdio>

const int maxn = 30;
struct Node
{
    int left,right;    
}node[maxn];

int max_index = -1,last_v;
bool isRoot[maxn] = {0};
int root;

int changeNum(char c)
{
    int iRet = -1;
    if(c != '-')
    {
        iRet = c - '0';
        isRoot[iRet] = 1;
    }
    return iRet;
}

void FindRoot(int n)
{
    for(int i = 0; i < n; i++)
    {
        if(0 == isRoot[i])
        {
            root = i;
            break;
        }
    }
}

void preOrder(int v,int index)
{
    if(-1 == v)
    {
        return;
    }
    if(index > max_index)
    {
        max_index = index;
        last_v = v;    
    }
    preOrder(node[v].left,index*2);
    preOrder(node[v].right,index*2+1);
}

int main()
{
    int n;
    scanf("%d",&n);
    char c1,c2;
    for(int i = 0; i < n; i++)
    {
        getchar();
         scanf("%c%*c%c",&c1,&c2);
        node[i].left = changeNum(c1);
        node[i].right = changeNum(c2);
    }
    FindRoot(n);
    preOrder(root,1);
    if(max_index == n)
    {
        printf("YES %d",last_v);
    }
    else
    {
        printf("NO %d",root);
    }
    return 0;
}