7-31 笛卡尔树 (25分)--判断二叉搜索树，小顶堆

先初步判断是否满足二叉搜索树和小顶堆（针对每一颗最小的子树），如果都满足，进一步判断整棵树是否满足。

  1 #include <iostream>
  2 #include <string>
  3 #include <cstring>
  4 using namespace std;
  5 typedef struct node
  6 {
  7     int K1;
  8     int K2;
  9     int L;
 10     int R;
 11 }node_arr[1001];
 12 node_arr s;
 13 int n;
 14 int f[1001];//存放前驱结点，判断是否为小顶堆的时候用到
 15 int f_is_BST1 = 0;
 16 int f_greater1 = 0;
 17 int f_greater2 = 0;
 18 void is_BST1(int i)//二叉搜索树的初步判断
 19 {
 20     if (s[i].L != -1)
 21     {
 22         if (s[i].K1 > s[s[i].L].K1)
 23         {
 24             is_BST1(s[i].L);
 25         }
 26         else
 27         {
 28             f_is_BST1 = 1;
 29             return;
 30         }
 31     }
 32     if (s[i].R != -1)
 33     {
 34         if (s[i].K1 <= s[s[i].R].K1)
 35         {
 36             is_BST1(s[i].R);
 37         }
 38         else
 39         {
 40             f_is_BST1 = 1;
 41             return;
 42         }
 43     }
 44 }
 45 void is_greater1(int i)//小顶堆的初步判断
 46 {
 47     if (s[i].L != -1)
 48     {
 49         if (s[i].K2 <= s[s[i].L].K2)
 50         {
 51             is_greater1(s[i].L);
 52         }
 53         else
 54         {
 55             f_greater1 = 1;
 56             return;
 57         }
 58     }
 59     if (s[i].R != -1)
 60     {
 61         if (s[i].K2 <= s[s[i].R].K2)
 62         {
 63             is_greater1(s[i].R);
 64         }
 65         else
 66         {
 67             f_greater1 = 1;
 68             return;
 69         }
 70     }
 71 }
 72 void is_greater2()//小顶堆进一步判断（整棵树）
 73 {
 74     for (int i = 0; i < n; i++)
 75     {
 76         int j = i;
 77         while (f[j] != -1)
 78         {
 79             if (s[f[j]].K2 > s[j].K2)
 80                 f_greater2 = 1;
 81             j = f[j];
 82         }
 83     }
 84 }
 85 bool is_BST2(int x, int min, int max)//搜索树进一步判断（整棵树）
 86 {
 87     if (x == -1)return true;
 88     if (s[x].K1 > max || s[x].K1 < min) return false;
 89     return (is_BST2(s[x].L, min, s[x].K1 - 1) && is_BST2(s[x].R, s[x].K1, max));
 90 }
 91 int main()
 92 {
 93     int r[1001] = { 0 };
 94     cin >> n;
 95     for (int i = 0; i < n; i++)f[i] = -1;
 96     for (int i = 0; i < n; i++)
 97     {
 98         struct node temp;
 99         cin >> temp.K1 >> temp.K2 >> temp.L >> temp.R;
100         if (temp.L != -1)
101         {
102             f[temp.L] = i;
103             r[temp.L] = 1;
104         }
105         if (temp.R != -1)
106         {
107             f[temp.R] = i;
108             r[temp.R] = 1;
109         }
110         s[i] = temp;
111     }
112     int root;
113     for (int i = 0; i < n; i++)
114     {
115         if (r[i] == 0)root = i;
116     }
117     for (int i = 0; i < n; i++)
118         is_BST1(i);
119     is_greater1(0);
120     is_greater2();
121     if (f_is_BST1 == 0 && f_greater1 == 0)
122         if (f_greater2 == 1 || is_BST2(root, -32767, 32767) == false)
123             cout << "NO";
124         else
125             cout << "YES";
126     else
127     {
128         cout << "NO";
129     }
130     return 0;
131 }

原文地址：https://www.cnblogs.com/2020R/p/12590987.html