PAT甲级1115

1115. Counting Nodes in a BST (30)

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

A Binary Search Tree (BST) is recursively defined as a binary tree which has the following properties:

• The left subtree of a node contains only nodes with keys less than or equal to the node's key.
• The right subtree of a node contains only nodes with keys greater than the node's key.
• Both the left and right subtrees must also be binary search trees.

Insert a sequence of numbers into an initially empty binary search tree. Then you are supposed to count the total number of nodes in the lowest 2 levels of the resulting tree.

Input Specification:

Each input file contains one test case. For each case, the first line gives a positive integer N (<=1000) which is the size of the input sequence. Then given in the next line are the N integers in [-1000 1000] which are supposed to be inserted into an initially empty binary search tree.

Output Specification:

For each case, print in one line the numbers of nodes in the lowest 2 levels of the resulting tree in the format:

n1 + n2 = n

where n1 is the number of nodes in the lowest level, n2 is that of the level above, and n is the sum.

Sample Input:

9 25 30 42 16 20 20 35 -5 28

Sample Output:

2 + 4 = 6

#include<cstdio>
#include<algorithm>
#include<queue>
using namespace std;
struct Node
{
  int data;
  int depth;
  Node *l, *r;
  Node(int x) :data(x), l(NULL), r(NULL) {}
}*root;
void insert(Node*&root, int x)//这个地方要用引用
{
  if (root == NULL)
  {
    root = new Node(x);
    return;
  }
  else if (x <= root->data)
  {
    insert(root->l, x);
  }
  else
    insert(root->r, x);
}
int maxdepth = -1;
void dfs(Node*root, int depth)
{
  if (!root)
  {
    maxdepth = max(maxdepth, depth);
    return;
  }
  dfs(root->l, depth + 1);
  dfs(root->r, depth + 1);
}
int sum1=0, sum2=0;
void levelorder(Node*root)
{
  queue<Node*> Q;
  Q.push(root);
  root->depth = 1;
  if (root->depth == maxdepth)
  {
    sum2++;
  }
  else if (root->depth == maxdepth - 1)
    sum1++;
  while (!Q.empty())
  {
    Node*f = Q.front();
    Q.pop();
    if (f->l)
    {
      Q.push(f->l);
      f->l->depth = f->depth + 1;
      if (f->l->depth == maxdepth - 1)
      {
        sum1++;
      }
      else if (f->l->depth == maxdepth)
      {
        sum2++;
      }
    }
    if (f->r)
    {
      Q.push(f->r);
      f->r->depth = f->depth + 1;
      if (f->r->depth == maxdepth - 1)
      {
        sum1++;
      }
      else if (f->r->depth == maxdepth)
      {
        sum2++;
      }
    }
  }
}
int main()
{
  int n;
  scanf("%d", &n);
  int x;
  for (int i = 0; i < n; i++)
  {
    scanf("%d", &x);
    insert(root, x);
  }
  dfs(root, 0);
  levelorder(root);
  printf("%d + %d = %d\n", sum2, sum1, sum1 + sum2);
  return 0;
}