PAT甲级1123 Is It a Complete AVL Tree【AVL树】
题目：https://pintia.cn/problem-sets/994805342720868352/problems/994805351302414336
题意：
给定n个树，依次插入一棵AVL树，按照层序遍历输出，最后判断这棵AVL树是不是完全二叉树。
思路：
这道题过段时间还要再来手搓一发。AVL模板要记住。
判断是不是完全二叉树的话只用看，如果有一个节点儿子是空，而他之后又出现了至少有一个儿子的节点的话，就不是完全二叉树。【蛮巧妙的】
1 #include<cstdio> 2 #include<cstdlib> 3 #include<map> 4 #include<set> 5 #include<iostream> 6 #include<cstring> 7 #include<algorithm> 8 #include<vector> 9 #include<cmath> 10 #include<stack> 11 #include<queue> 12 13 #define inf 0x7fffffff 14 using namespace std; 15 typedef long long LL; 16 typedef pair<string, string> pr; 17 18 int n; 19 const int maxn = 25; 20 vector<int>level[maxn]; 21 typedef struct AvlNode{ 22 int val; 23 AvlNode *left; 24 AvlNode *right; 25 int height; 26 }*AvlTree, AvlNode; 27 28 int Max(AvlTree a, AvlTree b) 29 { 30 int x = 0, y = 0; 31 if(a)x = a->height; 32 if(b)y = b->height; 33 if(x > y)return x; 34 else return y; 35 } 36 37 AvlTree singleRotateWithRight(AvlTree T) 38 { 39 AvlTree L = T->left; 40 T->left = L->right; 41 L->right = T; 42 T->height = Max(T->left, T->right) + 1; 43 L->height = Max(L->left, L->right) + 1; 44 return L; 45 } 46 47 AvlTree singleRotateWithLeft(AvlTree T) 48 { 49 AvlTree R = T->right; 50 T->right = R->left; 51 R->left = T; 52 T->height = Max(T->left, T->right) + 1; 53 R->height = Max(R->left, R->right) + 1; 54 return R; 55 } 56 57 AvlTree doubleRotateWithLeft(AvlTree T) 58 { 59 T->left = singleRotateWithLeft(T->left); 60 return singleRotateWithRight(T); 61 } 62 63 AvlTree doubleRotateWithRight(AvlTree T) 64 { 65 T->right = singleRotateWithRight(T->right); 66 return singleRotateWithLeft(T); 67 } 68 69 AvlTree Insert(AvlTree T, int val) 70 { 71 if(T == NULL){ 72 T = (AvlNode *)malloc(sizeof(struct AvlNode)); 73 if(T){ 74 T->val = val; 75 T->left = NULL; 76 T->right = NULL; 77 T->height = 0; 78 } 79 } 80 else if(val < T->val){ 81 T->left = Insert(T->left, val); 82 int l = 0, r = 0; 83 if(T->left){ 84 l = T->left->height; 85 } 86 if(T->right){ 87 r = T->right->height; 88 } 89 if(l - r == 2){ 90 if(val < T->left->val){ 91 T = singleRotateWithRight(T); 92 } 93 else{ 94 T = doubleRotateWithLeft(T); 95 } 96 } 97 } 98 else if(val > T->val){ 99 T->right = Insert(T->right, val); 100 int l = 0, r = 0; 101 if(T->left)l = T->left->height; 102 if(T->right)r = T->right->height; 103 if(r - l == 2){ 104 if(val > T->right->val){ 105 T = singleRotateWithLeft(T); 106 } 107 else{ 108 T = doubleRotateWithRight(T); 109 } 110 } 111 } 112 T->height = Max(T->left, T->right) + 1; 113 return T; 114 } 115 116 bool after = false, iscomplete = true; 117 bool first = false; 118 void levelOrder(AvlTree T) 119 { 120 queue<AvlTree>que; 121 que.push(T); 122 while(!que.empty()){ 123 AvlTree now = que.front();que.pop(); 124 if(first)printf(" "); 125 else first = true; 126 printf("%d", now->val); 127 level[now->height].push_back(now->val); 128 if(now->left){ 129 if(after)iscomplete = false; 130 que.push(now->left); 131 } 132 else{ 133 after = 1; 134 } 135 if(now->right){ 136 if(after)iscomplete = false; 137 que.push(now->right); 138 } 139 else{ 140 after = 1; 141 } 142 } 143 } 144 145 int main() 146 { 147 scanf("%d", &n); 148 AvlTree Tree = NULL; 149 for(int i = 0; i < n; i++){ 150 int x; 151 scanf("%d", &x); 152 Tree = Insert(Tree, x); 153 } 154 levelOrder(Tree); 155 printf("\n"); 156 if(iscomplete)printf("YES\n"); 157 else printf("NO\n"); 158 return 0; 159 }
