PAT 甲级 1135 Is It A Red-Black Tree
https://pintia.cn/problem-sets/994805342720868352/problems/994805346063728640
There is a kind of balanced binary search tree named red-black tree in the data structure. It has the following 5 properties:
- (1) Every node is either red or black.
- (2) The root is black.
- (3) Every leaf (NULL) is black.
- (4) If a node is red, then both its children are black.
- (5) For each node, all simple paths from the node to descendant leaves contain the same number of black nodes.
For example, the tree in Figure 1 is a red-black tree, while the ones in Figure 2 and 3 are not.
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Figure 1 | Figure 2 | Figure 3 |
For each given binary search tree, you are supposed to tell if it is a legal red-black tree.
Input Specification:
Each input file contains several test cases. The first line gives a positive integer K (≤30) which is the total number of cases. For each case, the first line gives a positive integer N (≤30), the total number of nodes in the binary tree. The second line gives the preorder traversal sequence of the tree. While all the keys in a tree are positive integers, we use negative signs to represent red nodes. All the numbers in a line are separated by a space. The sample input cases correspond to the trees shown in Figure 1, 2 and 3.
Output Specification:
For each test case, print in a line "Yes" if the given tree is a red-black tree, or "No" if not.
Sample Input:
3
9
7 -2 1 5 -4 -11 8 14 -15
9
11 -2 1 -7 5 -4 8 14 -15
8
10 -7 5 -6 8 15 -11 17
Sample Output:
Yes
No
No
代码:
- #include <bits/stdc++.h>
- using namespace std;
- const int maxn = 500;
- int T, n;
- int preorder[maxn];
- struct Node {
- int child[2];
- int blackCnt;
- int value;
- int color;
- }s[maxn];
- int root, sz, ans;
- int AddNode(int valAndcol) {
- sz ++;
- s[sz].value = abs(valAndcol);
- s[sz].color = valAndcol >= 0;
- return sz;
- }
- void Build(int L, int R, int father, bool direction) {
- int l1 = -1, r1 = -1;
- int l2 = -1, r2 = -1;
- for(int i = L + 1; i <= R; i ++) {
- if(abs(preorder[i]) < abs(preorder[L])) {
- l1 = L + 1, r1 = i;
- } else if(abs(preorder[i]) == abs(preorder[L])) {
- ans = 0;
- return;
- } else {
- if(l2 == -1) l2 = i, r2 = R;
- }
- }
- if(l1 != -1) {
- for(int i = l1; i <= r1; i ++) {
- if(abs(preorder[i]) >= abs(preorder[L])) {
- ans = 0;
- return;
- }
- }
- }
- if(l2 != -1) {
- for(int i = l2; i <= r2; i ++) {
- if(abs(preorder[i]) <= abs(preorder[L])) {
- ans = 0;
- return;
- }
- }
- }
- // left: [l1, r1], right: [l2, r2]
- int currentNode = AddNode(preorder[L]);
- father != -1 ? s[father].child[direction] = currentNode : root = currentNode;
- if(l1 != -1) Build(l1, r1, currentNode, 0);
- if(ans == 0) return;
- if(l2 != -1) Build(l2, r2, currentNode, 1);
- }
- void Initialize() {
- ans = 1;
- root = -1;
- sz = 0;
- for(int i = 0; i < maxn; i ++) {
- s[i].child[0] = s[i].child[1] = s[i].color = -1;
- s[i].blackCnt = s[i].value = 0;
- }
- }
- void dfs(int x) {
- for(int i = 0; i < 2; i ++) {
- if(s[x].child[i] != -1) {
- dfs(s[x].child[i]);
- if(ans == 0) return;
- }
- }
- if(s[x].child[0] != -1 &&
- s[x].child[1] != -1 &&
- s[s[x].child[0]].blackCnt != s[s[x].child[1]].blackCnt) {
- ans = 0;
- return;
- }
- if(s[x].child[0] != -1) s[x].blackCnt = s[s[x].child[0]].blackCnt;
- if(s[x].child[1] != -1) s[x].blackCnt = s[s[x].child[1]].blackCnt;
- s[x].blackCnt += s[x].color;
- }
- int main() {
- scanf("%d", &T);
- while(T --) {
- scanf("%d", &n);
- for(int i = 1; i <= n; i ++) {
- scanf("%d", &preorder[i]);
- }
- Initialize();
- Build(1, n, -1, -1);
- /*
- // Debug Information:
- for(int i = 1; i <= sz; i ++) {
- printf("Id: %d, L: %d, R: %d, val: %d, col: %d\n", i, s[i].child[0], s[i].child[1], s[i].value, s[i].color);
- }
- */
- // (1) Every node is either red or black.
- // (2) The root is black.
- if(!s[root].color) ans = 0;
- // (3) Every leaf (NULL) is black.
- // (4) If a node is red, then both its children are black.
- for(int i = 1; i <= sz; i ++) {
- if(!s[i].color) {
- if(s[i].child[0] != -1 && !s[s[i].child[0]].color) ans = 0;
- if(s[i].child[1] != -1 && !s[s[i].child[1]].color) ans = 0;
- }
- }
- for(int i = 1; i <= n; i ++) {
- for(int j = 0; j < 2; j ++) {
- if(s[i].child[j] == -1) {
- s[i].child[j] = AddNode(0);
- }
- }
- }
- // (5) For each node, all simple paths from the node to descendant leaves contain the same number of black nodes.
- dfs(root);
- printf("%s\n", ans ? "Yes" : "No");
- }
- return 0;
- }
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