数据结构实验之查找二：平衡二叉树

Time Limit: 400 ms Memory Limit: 65536 KiB

Submit Statistic

Problem Description

根据给定的输入序列建立一棵平衡二叉树，求出建立的平衡二叉树的树根。

Input

输入一组测试数据。数据的第1行给出一个正整数N(n <= 20)，N表示输入序列的元素个数；第2行给出N个正整数，按数据给定顺序建立平衡二叉树。

Output

输出平衡二叉树的树根。

Sample Input

5
88 70 61 96 120

Sample Output

70

C语言实现，代码如下：

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
struct tree
{
    int data, h;
    struct tree *l, *r;
} *root;
int height(struct tree *root)
{
    if(!root) return 0;
    else return root->h;
}
struct tree *RR(struct tree *root)
{
    struct tree *a = root, *b = root->r;
    a->r = b->l;
    b->l = a;
    a->h = height(a->l) > height(a->r) ? height(a->l) + 1 : height(a->r) + 1;
    b->h = height(b->l) > height(b->r) ? height(b->l) + 1 : height(b->r) + 1;
    return b;
};
struct tree *LL(struct tree *root)
{
    struct tree *a = root, *b = root->l;
    a->l = b->r;
    b->r = a;
    a->h = height(a->l) > height(a->r) ? height(a->l) + 1 : height(a->r) + 1;
    b->h = height(b->l) > height(b->r) ? height(b->l) + 1 : height(b->r) + 1;
    return b;
};
struct tree *LR(struct tree *root)
{
    root->l = RR(root->l); // 先左
    return LL(root); // 后右
};
struct tree *RL(struct tree *root)
{
    root->r = LL(root->r); // 先右
    return RR(root); // 后左
};
struct tree *Insert(struct tree *root, int x)
{
    if(!root)
    {
        root = (struct tree *)malloc(sizeof(struct tree));
        root->data = x;
        root->h = 0;
        root->l = NULL;
        root->r = NULL;
    }
    else
    {
        if(x < root->data)
        {
            root->l = Insert(root->l, x);
            if(height(root->l) - height(root->r) == 2)
            {
                if(x < root->l->data)
                    root = LL(root);
                else
                    root = LR(root);
            }
        }
        else
        {
            root->r = Insert(root->r, x);
            if(height(root->l) - height(root->r) == -2)
            {
                if(x > root->r->data)
                    root = RR(root);
                else
                    root = RL(root);
            }
        }
    }
    root->h = height(root->l) > height(root->r) ? height(root->l) + 1: height(root->r) + 1;
    return root;
};
int main()
{
    int n;
    struct tree *root;
    root = NULL;
    scanf("%d", &n);
    while(n--)
    {
        int x;
        scanf("%d", &x);
        root = Insert(root, x);
    }
    printf("%d\n", root->data);
    return 0;
}