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

 int main(int argc, char **argv)
 {
  if (argc != ) {
      cout << "invalid input" << endl;
    return ;
  }
  //cout << argv[1] << " " << argv[2] << endl;
  ifstream fin(argv[]);
  if (!fin) {
      cout << "unable to open the file" << endl;
      return ;
  }
  int n = atoi(argv[]);
  int count = ;
  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 ;
 }