Recursive traversal of a tree P57669

Statement

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Write a program that reads the description of a natural binary tree and prints its postorder and inorder traversals.

In this exercise as well as in the rest of exercises of this section, if the contrary is not said the description of a tree consists of the number of nodes n followed by the traversal in preorder, which includes the leaves marked with a -1. This traversal has 2n + 1 elements.

(To see an instance with the tree corresponding to the input-output instance, consult the pdf or ps version of this wording.)

To solve this exercixe as well as most of the exercises of this section, you will need to store the tree in a vector. Do it using this code (slightly modified if it is necessary):

struct Node { int value; int left, right; }; // Reads a tree and stores it in a piece of the vector v starting at the position j. // Modifies the variable j in order to indicate the next free position of v. // Returns the position inside of v of the root of the (sub)tree read (o -1). int tree(int& j, vector<Node>& v) { int x; cin >> x; if (x == -1) return -1; int a = j; ++j; v[a].value = x; v[a].left = tree(j, v); v[a].right tree(j, v); return a; } ... int main() { int n; cin >> n; vector<Node> v(n); int j = 0; int a = tree(j, v); ... }

With the tree of the instance, the final content of |v| would be

position	0	1	2	3	4	5	6	7	8	9
@v.value@	3	0	7	4	2	5	4	7	6	1
@v.left@	1	2	-1	-1	-1	6	-1	8	-1	-1
@v.right@	5	4	3	-1	-1	7	-1	-1	9	-1

Notice that each position of the vector stores the value of a node, the position of its left child and its right child. Value -1 is used to indicate empty trees. Variable |a| of the main program is the position of the root of the tree, and is -1 if the tree is empty, and 0 if it is not.

Input

Input consists of the description of a natural binary tree.

Output

Your program must print two lines, with the postorder and inorder traversals of the tree. Each element must be preceded by a space.

Public test cases

Input

10
3 0 7 -1 4 -1 -1 2 -1 -1 5
4 -1 -1 7 6 -1 1 -1 -1 -1

Output

 4 7 2 0 4 1 6 7 5 3
 7 4 0 2 3 4 5 6 1 7

Information

Author: Salvador Roura
Language: English
Translator: Carlos Molina
Original language: Catalan
Other languages: Catalan
Official solutions: C++
User solutions: C++ Python