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03-树3 Tree Traversals Again (25分)

25 03 Tree again
2023-09-14 08:57:14 时间

03-树3 Tree Traversals Again (25分)

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 N (≤) which is the total number of nodes in a tree (and hence the nodes are numbered from 1 to N). Then 2 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

 问题分析：

push的为前序遍历序列，pop的为中序遍历序列，所以问题转化为：给定前序遍历和中序遍历，输出后序遍历；

核心：前序遍历和中序遍历转化为后序遍历，前序遍历中找根节点，然后在中序找左右节点，最后保存根节点，递归调用，分而治之即可；

提测代码：

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#define ERROR -1
#define Null -1

typedef int ElemType;
typedef int Position;
typedef struct SNode* Stack;

struct SNode {
    ElemType* pData;
    Position top;
    Position maxSize;
};

Stack CreateStack(int maxSize) {
    Stack S = (Stack)malloc(sizeof(int));
    S->pData = (ElemType*)malloc(sizeof(int)*maxSize);
    S->top = -1;
    S->maxSize = maxSize;
    return S;
}

int IsFull(Stack S) {
    return (S->top == S->maxSize);
}

int Push(Stack S, ElemType data) {
    if (IsFull(S)) {
        return 0;
    }
    S->pData[++(S->top)] = data;
    return 1;
}

int IsEmpty(Stack S) {
    return (S->top == -1);
}

ElemType Pop(Stack S) {
    if (IsEmpty(S)) {
        return ERROR;
    }
    return S->pData[(S->top)--];
}

void PostFromInAndPre(int pre[], int in[], int post[],int root, int left, int right) {
    static int counter = 0;
    if (left > right) {
        return;
    }
    ElemType data = pre[root];
    int i = left;
    while (i < right && in[i] != data) ++i;
    PostFromInAndPre(pre, in, post, root + 1, left, i - 1);
    PostFromInAndPre(pre, in, post, root + 1 + i - left, i + 1, right);
    post[counter++] = data;
}

void PrintfTraversal(int tree[], int N) {
    if (N == 0) {
        return;
    }
    printf("%d", tree[0]);
    for (int i = 1; i < N; ++i) {
        printf(" %d", tree[i]);
    }
}

int main()
{
    int N;
    scanf("%d", &N);
    Stack origin = CreateStack(N);
    int *pre = (int*)malloc(sizeof(int)*N);
    int *in = (int*)malloc(sizeof(int)*N);
    int *post = (int*)malloc(sizeof(int)*N);
    char strOperation[5];
    int data;
    int preCounter = 0;
    int inCounter = 0;
    for(int i = 0; i < N*2; ++i)
    {
        scanf("%s", strOperation);
        if (strcmp(("Push"), strOperation) == 0) {
            scanf("%d", &data);
            Push(origin, data);
            pre[preCounter++] = data;
        }
        else {
            ElemType data = Pop(origin);
            in[inCounter++] = data;
        }
    }

    PostFromInAndPre(pre, in, post,0, 0, N - 1);
    
    PrintfTraversal(post, N);

    return 0;
}

 

提测结果：

 

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