03-树3 Tree Traversals Again
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An inorder binary tree traversal can be implemented in a non-recursive way with a stack. For example, suppose that when a 6-node binary tree (with the keys numbered from 1 to 6) is traversed, the stack operations are: push(1); push(2); push(3); pop(); pop(); push(4); pop(); pop(); push(5); push(6); pop(); pop(). Then a unique binary tree (shown in Figure 1) can be generated from this sequence of operations. Your task is to give the postorder traversal sequence of this tree.
Figure 1
Input Specification:
Each input file contains one test case. For each case, the first line contains a positive integer NN (\le 30≤30) which is the total number of nodes in a tree (and hence the nodes are numbered from 1 to NN). Then 2N2N lines follow, each describes a stack operation in the format: “Push X” where X is the index of the node being pushed onto the stack; or “Pop” meaning to pop one node from the stack.
Output Specification:
For each test case, print the postorder traversal sequence of the corresponding tree in one line. A solution is guaranteed to exist. All the numbers must be separated by exactly one space, and there must be no extra space at the end of the line.
Sample Input:
6
Push 1
Push 2
Push 3
Pop
Pop
Push 4
Pop
Pop
Push 5
Push 6
Pop
Pop
Sample Output:
3 4 2 6 5 1
题目大意:从push进去顺序可以看出是先序遍历,从pop进去的顺序可以看出是中序遍历,现在要求后序遍历。
思路:只要知道中序和其余任一个,就可以知道另外一个遍历。现在是中序和先序,即一棵树先序的是第一个是后序的最后一个,然后再通过中序找到其左右子树,重复上述操作。
#include<iostream>#include<string>#include<vector>#include<stack>using namespace std;int num;void getpostorder(vector<int> preorder,int preL,vector<int> inorder,int inL, vector<int>& postorder,int postL,int n){ if (n == 0) return; if (n == 1) { postorder[postL] = preorder[preL]; return; } preorder[preL]; postorder[postL + n - 1] = preorder[preL]; //在中序遍历数组上找出root的位置 int i = 0; while (i < n) { if (inorder[inL + i] == preorder[preL]) break; ++i; } int L = i, R = n - i - 1; getpostorder(preorder, preL + 1, inorder, inL, postorder, postL, L); getpostorder(preorder, preL + 1 + L, inorder, inL + L + 1, postorder, postL + L, R);}vector<vector<int>> getorder(){ cin >> num; vector<int> preOrder(num, 0); vector<int> inOrder(num, 0); stack<int> st; int pre = 0, in = 0; string temp; int data; for (int i = 0; i < 2 * num; i++) { cin >> temp; if (temp == "Push") { cin >> data; st.push(data); preOrder[pre++] = data; } else if (temp == "Pop") { inOrder[in++] = st.top(); st.pop(); } } return{ preOrder, inOrder };}int main(){ auto oredr = getorder(); vector<int> postorder(num, 0); getpostorder(oredr[0], 0, oredr[1], 0, postorder, 0, num); int i = 0; for (; i < num-1; i++) { cout << postorder[i] << ' '; } cout << postorder[i];}
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