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1115 Counting Nodes in a BST

Statement

Metadata

  • 作者: CHEN, Yue
  • 单位: 浙江大学
  • 代码长度限制: 16 KB
  • 时间限制: 400 ms
  • 内存限制: 64 MB

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 (\le 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

Solution

#include <bits/stdc++.h>
using namespace std;
const int N = 1e4 + 10;
int n, a[N], Max, ans[N];

struct BST {
    struct node {
        int v, son[2];
        node() {
            v = 0, son[0] = son[1] = 0;
        }
    } t[N];
    int rt, tot;
    void init() {
        rt = 0;
        tot = 0;
    }
    int newnode() {
        ++tot;
        t[tot] = node();
        return tot;
    }
    void insert(int &rt, int v, int dep) {
        Max = max(Max, dep);
        if (rt == 0) {
            rt = newnode();
            ++ans[dep];
            t[rt].v = v;
            return;
        }
        if (v <= t[rt].v)
            insert(t[rt].son[0], v, dep + 1);
        else
            insert(t[rt].son[1], v, dep + 1);
    }
} bst;

int main() {
    while (scanf("%d", &n) != EOF) {
        Max = 0;
        memset(ans, 0, sizeof ans);
        bst.init();
        for (int i = 1, x; i <= n; ++i) {
            scanf("%d", &x);
            bst.insert(bst.rt, x, 0);
        }
        assert(Max >= 0);
        if (Max == 0) {
            printf("%d + %d = %d\n", ans[Max], 0, ans[Max]);
        } else {
            printf("%d + %d = %d\n", ans[Max], ans[Max - 1], ans[Max] + ans[Max - 1]);
        }
    }
    return 0;
}
Last update: May 4, 2022
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