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).

  1 #include <iostream>

  2 #include <fstream>

  3 #include <cstdio>

  4 

  5 using namespace std;

  6 

  7 class treap_node 

  8 {

  9     public:

 10         int label;

 11         float p;

 12         treap_node *left;

 13         treap_node *right;

 14         treap_node()

 15         {

 16             left = NULL;

 17             right = NULL;

 18         }

 19 };

 20 

 21 class treap:treap_node

 22 {

 23     public:

 24         treap_node *root;

 25         treap()

 26         {

 27             root = NULL;

 28         }

 29         void treap_left_rotate(treap_node* &a)

 30         {

 31             treap_node *b = a->right;

 32             a->right = b->left;

 33             b->left = a;

 34             a = b;

 35         }

 36         void treap_right_rotate(treap_node* &a)

 37         {

 38             treap_node *b = a->left;

 39             a->left = b->right;

 40             b->right = a;

 41             a = b;

 42         }

 43         void treap_insert(treap_node* &a, int &label, float &p)

 44         {

 45             if (!a)

 46             {

 47                 a = new treap_node;

 48                 a->label = label;

 49                 a->p = p;

 50             }

 51             else if (label > a->label)

 52             {

 53                 treap_insert(a->right, label, p);

 54                 if (a->right->p > a->p)

 55                     treap_left_rotate(a);

 56             }

 57             else

 58             {

 59                 treap_insert(a->left, label, p);

 60                 if (a->left->p < a->p)

 61                     treap_right_rotate(a);

 62             }

 63         }

 64         void treap_delete_smallestP(treap_node* &a)

 65         {

 66             treap_node *p = a;

 67             treap_node *pre = NULL;

 68             while (p->left != NULL)

 69             {

 70                 pre = p;

 71                 p = p->left;

 72             }

 73             if (pre != NULL)

 74             {

 75                 pre->left = p->right;

 76             }

 77             else

 78                 a = p->right;

 79             return;

 80         }

 81         void plist(treap_node *a) 

 82         {

 83             if (a != NULL)

 84             {

 85                 cout << "(";

 86                 plist(a->left);

 87                 cout << a->label << "/" << a->p;

 88                 plist(a->right);

 89                 cout << ")";

 90             }

 91         }

 92 };

 93 

 94 int atoi(char *s) 

 95 {

 96     int ret = 0;

 97     while (*s != '\0') {

 98         ret = ret * 10 + (int)(*s - '0');

 99         s++;

100     }

101     return ret;

102 }

103 

104 int main(int argc, char **argv) 

105 {

106  if (argc != 3) {

107      cout << "invalid input" << endl;

108    return 1;

109  }

110  //cout << argv[1] << " " << argv[2] << endl;

111  ifstream fin(argv[2]);

112  if (!fin) {

113      cout << "unable to open the file" << endl;

114      return 1;

115  }

116  int n = atoi(argv[1]);

117  int count = 0;

118  treap *p = new treap;

119  float s;

120  while (fin >> s) {

121      cout << s << " ";

122      if (count >= n) 

123      {

124          p->treap_delete_smallestP(p->root);

125      }

126      p->treap_insert(p->root, count, s);

127      p->plist(p->root); 

128      cout << p->root->p << endl;

129      count++;

130  }

131  return 0;

132 }