已知先序序列，判斷對應的二叉排序樹是否為紅黑樹。序列中負數表示紅色結點，正數表示黑色結點。該序列負數取絕對值後再排序得到的是中序序列。根據紅黑樹的性質判斷它是否符合紅黑樹的要求。考察了根據先序序列和中序序列建樹和DFS。

  1 //#include "stdafx.h"
  2 #include <iostream>
  3 #include <algorithm>
  4 
  5 using namespace std;
  6 
  7 struct treeNode { // tree node struct
  8     int key, lchild, rchild, flag; //
 
 key, left child, right child, color flag
  9 }tree[31];
 10 
 11 struct intNode { // int node
 12     int key, flag; // key, color flag
 13 }pre[31]; // the array of the preorder traversal sequence
 14 
 15 int treeRoot, flag, blackNodeCount, in[31]; // the index of tree root node, whether it is a red-black tree, the number of black nodes, the array of the inorder traversal sequence
 

 16 
 17 void init(int m) { // initialize
 18     int i;
 19     for (i = 0; i < m; i++) { // every node has no child
 20         tree[i].lchild = tree[i].rchild = -1;
 21     }
 22     
 23     flag = 1; // at first, it is a red-black tree
 24     treeRoot = blackNodeCount = 0; // the initial index of tree root node is zero and the initial number of black nodes is zero
 

 25 
 26     sort(in, in + m); // sort in array to get the inorder traversal sequence
 27 }
 28 
 29 int buildTree(int a1, int a2, int b1, int b2) { // build a tree according to the preorder traversal sequence and inorder
 30     // initialize the current root node of the subtree
 31     int root = treeRoot++;
 32     int key = pre[a1].key;
 33     tree[root].key = key;
 34     tree[root].flag = pre[a1].flag;
 35 
 36     int i;
 37     for (i = b1; i <= b2; i++) { // seek the index of root node in the inorder traversal sequence
 38         if (in[i] == key) {
 39             break;
 40         }
 41     }
 42 
 43     if (i > b1) { // if left subtree exists
 44         tree[root].lchild = buildTree(a1 + 1, a1 + i - b1, b1, i - 1);
 45     }
 46     if (i < b2) { // if right subtree exists
 47         tree[root].rchild = buildTree(a1 + i - b1 + 1, a2, i + 1, b2);
 48     }
 49 
 50     return root; // return the current root node of the subtree
 51 }
 52 
 53 void dfs(int cur, int count) { // traverse all nodes based on depth first
 54     if (flag == 0) { // if it is not a red-black tree
 55         return;
 56     }
 57 
 58     if (cur == -1) { // if it is a leaf node
 59         if (count != blackNodeCount) { // judge whether black nodes is legal
 60             if (blackNodeCount == 0) {
 61                 blackNodeCount = count;
 62             } else {
 63                 flag = 0;
 64             }
 65         }
 66 
 67         return;
 68     }
 69 
 70     int l = tree[cur].lchild;
 71     int r = tree[cur].rchild;
 72 
 73     if (tree[cur].flag == 0) { // If a node is red, then both its children are black.
 74         if (l != -1 && tree[l].flag == 0) {
 75             flag = 0;
 76             return;
 77         } else if (r != -1 && tree[r].flag == 0) {
 78             flag = 0;
 79             return;
 80         }
 81     } else {
 82         count++;
 83     }
 84 
 85     // recursion
 86     dfs(l, count);
 87     dfs(r, count);
 88 }
 89 
 90 int judgeRBTree() {
 91     if (tree[0].flag == 0) { // The root is black.
 92         return 0;
 93     }
 94 
 95     // traverse
 96     dfs(0, 0); 
 97     return flag;
 98 }
 99 
100 int main() {
101     int n;
102     scanf("%d", &n);
103 
104     int m, i;
105     while (n--) {
106         scanf("%d", &m);
107         for (i = 0; i < m; i++) {
108             scanf("%d", &pre[i].key);
109 
110             // save the information of color
111             if (pre[i].key < 0) { 
112                 pre[i].key = - pre[i].key;
113                 pre[i].flag = 0;
114             } else {
115                 pre[i].flag = 1;
116             }
117 
118             in[i] = pre[i].key;
119         }
120 
121         init(m); // initialization
122         buildTree(0, m - 1, 0, m - 1); // build a tree
123 
124         if (judgeRBTree() == 1) {
125             printf("Yes\n");
126         } else {
127             printf("No\n");
128         }
129     }
130 
131     system("pause");
132     return 0;
133 }

PAT-A1135. Is It A Red-Black Tree (30)