左神算法进阶班5_1求二叉树中最大搜索子树大小

  1 #pragma once
  2 #include <iostream>
  3 #include <vector>
  4 #include <algorithm>
  5 
  6 using namespace std;
  7 
  8 struct Node
  9 {
 10     int val;
 11     Node* l;
 12     Node* r;
 13     Node(int a) :val(a), l(nullptr), r(nullptr) {}
 14 };
 15 
 16 //递归方式一
 17 struct returnType
 18 {
 19     int size;
 20     Node* head;
 21     int min;
 22     int max;
 23     returnType(int s, Node* h, int mi, int ma) :size(s), head(h), min(mi), max(ma) {}
 24 };
 25 
 26 returnType* findSTree1(Node* head)
 27 {
 28     if (head == nullptr)
 29         return new returnType(0, nullptr, INT_MAX, INT_MIN);
 30     returnType* lInfo = findSTree1(head->l);//得到左子树的最大搜索二叉树
 31     returnType* rInfo = findSTree1(head->r);//得到右子树的最大搜索二叉树
 32 
 33     int selfSize = 0;//判断包含该头节点的整棵树是否为搜索二次树
 34     if (lInfo->head == head->l &&
 35         rInfo->head == head->r &&
 36         lInfo->max < head->val &&
 37         rInfo->min > head->val
 38         )
 39         selfSize = lInfo->size + 1 + rInfo->size;
 40 
 41     int maxSize = max(max(lInfo->size, rInfo->size), selfSize);//求得最大的搜索二叉树的大小
 42     Node* maxHead = nullptr;//选择最大的子树的头结点
 43     if (maxSize == selfSize)
 44         maxHead = head;
 45     else if (maxSize == lInfo->size)
 46         maxHead = lInfo->head;
 47     else
 48         maxHead = rInfo->head;
 49 
 50     //这时返回的是包含head的整颗子树
 51     return new returnType(maxSize, maxHead,
 52         min(min(lInfo->min, rInfo->min), head->val),
 53         max(max(lInfo->max, rInfo->max), head->val));
 54 }
 55 
 56 
 57 //使用第二种递归
 58 
 59 Node* findSTree2(Node* head, vector<int>&info)
 60 {
 61     if (head == nullptr)
 62     {
 63         info[0] = 0;
 64         info[1] = INT_MIN;
 65         info[2] = INT_MAX;
 66         return nullptr;
 67     }
 68     vector<int>hv = info;
 69     //得到左右子树的信息
 70     Node* lNode = findSTree2(head->l, info);
 71     vector<int>lv = info;
 72     Node* rNode = findSTree2(head->r, info);
 73     vector<int>rv = info;
 74     //更新信息
 75     info[1] = max(max(lv[1], rv[1]), head->val);
 76     info[2] = min(min(lv[2], rv[2]), head->val);
 77     //判断
 78     if (lNode == head->l && rNode == head->r && lv[1] < head->val && rv[2] > head->val)
 79     {
 80         info[0] = lv[0] + rv[0] + 1;
 81         return head;
 82     }
 83     info[0] = max(lv[0], rv[0]);
 84     return lv[0] > rv[0] ? lNode : rNode;
 85 }
 86 
 87 
 88 int maxSTree(Node* head)
 89 {
 90     vector<int>info(3,0);//储存字数的大小、最大值、最小值
 91     findSTree2(head, info);
 92     return info[0];
 93 }
 94 
 95 
 96 
 97 
 98 void Test()
 99 {
100     Node* root = new Node(9);
101     root->l = new Node(8);
102     root->r = new Node(1);
103     root->l->l = new Node(5);
104     root->l->r = new Node(9);
105     root->l->l->l = new Node(4);
106     root->l->l->r = new Node(6);
107     root->r->l = new Node(5);
108     root->r->r = new Node(3);
109     returnType* p = findSTree1(root);
110     cout << p->size << endl;
111     
112     root = nullptr;
113     root = new Node(5);
114     root->l = new Node(2);
115     root->r = new Node(6);
116     root->l->l = new Node(1);
117     root->l->r = new Node(3);
118     p = findSTree1(root);
119     cout << p->size << endl;
120 
121     root = nullptr;
122     root = new Node(9);
123     root->l = new Node(8);
124     root->r = new Node(1);
125     root->l->l = new Node(5);
126     root->l->r = new Node(9);
127     root->l->l->l = new Node(4);
128     root->l->l->r = new Node(6);
129     root->r->l = new Node(5);
130     root->r->r = new Node(3);
131     cout << maxSTree(root) << endl;
132 
133     root = nullptr;
134     root = new Node(5);
135     root->l = new Node(2);
136     root->r = new Node(6);
137     root->l->l = new Node(1);
138     root->l->r = new Node(3);
139     cout << maxSTree(root) << endl;
140 
141 
142 
143 }