1119 Pre- and Post-order Traversals(30 分)(cj)

1119 Pre- and Post-order Traversals(30 分)

Suppose that all the keys in a binary tree are distinct positive integers. A unique binary tree can be determined by a given pair of postorder and inorder traversal sequences, or preorder and inorder traversal sequences. However, if only the postorder and preorder traversal sequences are given, the corresponding tree may no longer be unique.

Now given a pair of postorder and preorder traversal sequences, you are supposed to output the corresponding inorder traversal sequence of the tree. If the tree is not unique, simply output any one of them.

Input Specification:

Each input file contains one test case. 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 sequence and the third line gives the postorder sequence. All the numbers in a line are separated by a space.

Output Specification:

For each test case, first printf in a line Yes if the tree is unique, or No if not. Then print in the next line the inorder traversal sequence of the corresponding binary tree. If the solution is not unique, any answer would do. It is guaranteed that at least one solution exists. All the numbers in a line must be separated by exactly one space, and there must be no extra space at the end of the line.

Sample Input 1:

7
1 2 3 4 6 7 5
2 6 7 4 5 3 1

Sample Output 1:

Yes
2 1 6 4 7 3 5

Sample Input 2:

4
1 2 3 4
2 4 3 1

Sample Output 2:

No
2 1 3 4

就是通過 dps 來找中序遍歷的結果。

重點就是 如果 一個點只有一個子節點 先後序遍歷都無法確定這個子節點是左節點還是右節點。

如果一個點有左右子節點,他的先後序遍歷是可以確定左右的。

所以以此爲突破口解題,注意就是不要少了任何一個點。還有輸出末尾要加回車,不然會格式錯誤。。

code

#pragma warning(disable:4996)
#include <iostream>
#include <vector>
using namespace std;
int postarr[35], prearr[35];
bool f = 1;
vector<int> varr;
void dfs(int q, int e, int l, int r) {
	if (q > e) {
		f = 0;
		return;
	}
	if (q == e) {
		varr.push_back(prearr[q]);
		return;
	}
	int x = prearr[q + 1];
	int y = postarr[r - 1];
	int xx, yy;
	for (int i = q; i <= e; ++i) {
		if (prearr[i] == y) {
			yy = i;
			break;
		}
	}
	for (int i = l; i <= r; ++i) {
		if (postarr[i] == x) {
			xx = i;
			break;
		}
	}
	dfs(q + 1, yy - 1, l, xx);
	varr.push_back(prearr[q]);
	dfs(yy, e, xx + 1, r - 1);
}
int main() {
	int n;
	cin >> n;
	for (int i = 0; i < n; ++i) {
		cin >> prearr[i];
	}
	for (int i = 0; i < n; ++i) {
		cin >> postarr[i];
	}
	dfs(0, n - 1, 0, n - 1);
	if (f) cout << "Yes" << endl;
	else cout << "No" << endl;
	for (int i = 0; i < varr.size(); ++i) {
		if (i != 0) cout << ' ';
		cout << varr[i];
	}
	cout << endl;
	system("pause");
	return 0;
}

 

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