Algorithm: cartesian tree

http://baike.baidu.com/link?url=XUt5fXQ-jtFBM0UdKiGA41_NWFvdFSYwVsy4SVvCRRuEBvNkLfT9TgOtzsXvaOT9nuq_EzKJcO0gt6nyXRSLU_

这里有详细介绍

有一道coding test的题目给你一个int n， 一串float的数，要你实时打印出当前数到这个数前n个数这n个数里最大值，没有n个数就是前面那几个数的最大值。这里就可以用cartesian tree，label记录是数的下标，p表示数值。插入操作为lg(n), 删除操作也为lg(n)，总的复杂度为Nlg(n).

#include <iostream>
#include <fstream>
#include <cstdio>

using namespace std;

class treap_node 
{
    public:
        int label;
        float p;
        treap_node *left;
        treap_node *right;
        treap_node()
        {
            left = NULL;
            right = NULL;
        }
};

class treap:treap_node
{
    public:
        treap_node *root;
        treap()
        {
            root = NULL;
        }
        void treap_left_rotate(treap_node* &a)
        {
            treap_node *b = a->right;
            a->right = b->left;
            b->left = a;
            a = b;
        }
        void treap_right_rotate(treap_node* &a)
        {
            treap_node *b = a->left;
            a->left = b->right;
            b->right = a;
            a = b;
        }
        void treap_insert(treap_node* &a, int &label, float &p)
        {
            if (!a)
            {
                a = new treap_node;
                a->label = label;
                a->p = p;
            }
            else if (label > a->label)
            {
                treap_insert(a->right, label, p);
                if (a->right->p > a->p)
                    treap_left_rotate(a);
            }
            else
            {
                treap_insert(a->left, label, p);
                if (a->left->p < a->p)
                    treap_right_rotate(a);
            }
        }
        void treap_delete_smallestP(treap_node* &a)
        {
            treap_node *p = a;
            treap_node *pre = NULL;
            while (p->left != NULL)
            {
                pre = p;
                p = p->left;
            }
            if (pre != NULL)
            {
                pre->left = p->right;
            }
            else
                a = p->right;
            return;
        }
        void plist(treap_node *a) 
        {
            if (a != NULL)
            {
                cout << "(";
                plist(a->left);
                cout << a->label << "/" << a->p;
                plist(a->right);
                cout << ")";
            }
        }
};

int atoi(char *s) 
{
    int ret = 0;
    while (*s != '') {
        ret = ret * 10 + (int)(*s - '0');
        s++;
    }
    return ret;
}

int main(int argc, char **argv) 
{
 if (argc != 3) {
     cout << "invalid input" << endl;
   return 1;
 }
 //cout << argv[1] << " " << argv[2] << endl;
 ifstream fin(argv[2]);
 if (!fin) {
     cout << "unable to open the file" << endl;
     return 1;
 }
 int n = atoi(argv[1]);
 int count = 0;
 treap *p = new treap;
 float s;
 while (fin >> s) {
     cout << s << " ";
     if (count >= n) 
     {
         p->treap_delete_smallestP(p->root);
     }
     p->treap_insert(p->root, count, s);
     p->plist(p->root); 
     cout << p->root->p << endl;
     count++;
 }
 return 0;
}