1155 Heap Paths

In computer science, a heap is a specialized tree-based data structure that satisfies the heap property: if P is a parent node of C, then the key (the value) of P is either greater than or equal to (in a max heap) or less than or equal to (in a min heap) the key of C. A common implementation of a heap is the binary heap, in which the tree is a complete binary tree. (Quoted from Wikipedia at https://en.wikipedia.org/wiki/Heap_(data_structure))

One thing for sure is that all the keys along any path from the root to a leaf in a max/min heap must be in non-increasing/non-decreasing order.

Your job is to check every path in a given complete binary tree, in order to tell if it is a heap or not.

Input Specification:

Each input file contains one test case. For each case, the first line gives a positive integer N (1), the number of keys in the tree. Then the next line contains N distinct integer keys (all in the range of int), which gives the level order traversal sequence of a complete binary tree.

Output Specification:

For each given tree, first print all the paths from the root to the leaves. Each path occupies a line, with all the numbers separated by a space, and no extra space at the beginning or the end of the line. The paths must be printed in the following order: for each node in the tree, all the paths in its right subtree must be printed before those in its left subtree.

Finally print in a line Max Heap if it is a max heap, or Min Heap for a min heap, or Not Heap if it is not a heap at all.

Sample Input 1:

8
98 72 86 60 65 12 23 50

 

Sample Output 1:

98 86 23
98 86 12
98 72 65
98 72 60 50
Max Heap

 

Sample Input 2:

8
8 38 25 58 52 82 70 60

 

Sample Output 2:

8 25 70
8 25 82
8 38 52
8 38 58 60
Min Heap

 

Sample Input 3:

8
10 28 15 12 34 9 8 56

 

Sample Output 3:

10 15 8
10 15 9
10 28 34
10 28 12 56
Not Heap

题意：

给出一组由完全二叉树按照层序遍历的序列，从右到左输出由根节点到各个叶子结点的序列，并判断是大顶堆还是小顶堆。

思路：

根据序列先构建这颗完全二叉树，然后在遍历从根节点到叶子结（先右后左），遍历的过程中用一个stack存放路径上的数字，遍历的时候入栈，遍历完右，左结点之后再出栈。判断是大顶堆还是小顶堆的时候，可以用反证的方法，即：如果存在一个根节点小于子节点则一定不是大顶堆，如果存在一个子节点大于根节点则一定不是大顶堆。

Code:

#include<iostream>
#include<queue>
#include<stack>

using namespace std;

queue<int> que;
stack<int> path;
queue<int> temp;
bool isMaxHeap = true;
bool isMinHeap = true;

typedef struct Node* node;

struct Node {
    int value;
    node left;
    node right;
    Node() {
        value = 0;
        left = NULL;
        right = NULL;
    }
};

node root = new Node();
queue<node> nodeQue;

void buildTree() {
    root->value = que.front();
    que.pop();
    nodeQue.push(root);
    while(!que.empty()) {
        node parent = nodeQue.front(); 
        nodeQue.pop();
        node left = new Node();
        node right = new Node();
        if (!que.empty()) {
            left->value = que.front();
            parent->left = left;
            nodeQue.push(left);
            que.pop();
        }
        if (!que.empty()) {
            right->value = que.front();
            parent->right = right;
            nodeQue.push(right);
            que.pop();
        }
    }
}

void print(stack<int> path) {
    stack<int> temp;
    bool first = true;
    while (!path.empty()) {
        temp.push(path.top());
        path.pop();
    }
    int last = temp.top(); temp.pop();
    int next;
    while (!temp.empty()) {
        next = temp.top();
        if (last < next) isMaxHeap = false;
        if (last > next) isMinHeap = false;
        if (first) {
            first = false;
            cout << last;
        } else
            cout << " " << last;
        temp.pop();
        last = next;
    }
    cout << " " << last << endl;
}

void travel(node root) {
    path.push(root->value);
    if (root->left == NULL && root->right == NULL) {
        print(path);
        path.pop();
        return;
    }
    if (root->right) travel(root->right);
    if (root->left) travel(root->left);
    path.pop();
}

int main() {
    int num, value;
    cin >> num;
    for (int i = 0; i < num; ++i) {
        cin >> value;
        que.push(value);
    }
    buildTree();
    travel(root);
    if (isMaxHeap) cout << "Max Heap" << endl;
    else if (isMinHeap) cout << "Min Heap" << endl;
    else cout << "Not Heap" << endl;

    return 0;
}

　　

当我声明一个全局变量queue<node> nodeQue时因为结构体是在main()函数中构建的，所以在main()函数外使用queue<node> nodeQue时，会提示没有node这种数据类型。 

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2020-07-13 18:22:21

一种不用建树的写法：

#include <bits/stdc++.h>

using namespace std;

int n;
bool isIncreasing = false;
bool isDecreasing = false;
vector<int> a(10005);
vector<int> v;
void DFS(int index) {
    int i;
    if (index * 2 > n && index * 2 + 1 > n) {
        if (index <= n) {
            cout << v[0];
            for (i = 1; i < v.size(); ++i) {
                cout << " " << v[i];
                if (v[i] > v[i - 1])
                    isIncreasing = true;
                else if (v[i] < v[i - 1])
                    isDecreasing = true;
            }
            cout << endl;
        }
    } else {
        v.push_back(a[index * 2 + 1]);
        DFS(index * 2 + 1);
        v.pop_back();
        v.push_back(a[index * 2]);
        DFS(index * 2);
        v.pop_back();
    }
}

int main() {
    cin >> n;
    for (int i = 1; i <= n; ++i) cin >> a[i];
    v.push_back(a[1]);
    DFS(1);
    if (isIncreasing && isDecreasing)
        cout << "Not Heap" << endl;
    else if (isIncreasing)
        cout << "Min Heap" << endl;
    else if (isDecreasing)
        cout << "Max Heap" << endl;
    return 0;
}