打印距离叶子节点为k的节点 Print nodes that are at distance k from a leaf node

最新推荐文章于 2024-09-01 15:12:54 发布

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最新推荐文章于 2024-09-01 15:12:54 发布

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本文介绍了一个算法，用于在给定的二叉树中查找距离任意叶节点k个位置的所有节点。该算法的时间复杂度为O(n)，其中n为二叉树中的节点数量。通过遍历树并跟踪祖先节点，当遇到叶节点时，算法会打印出距离叶节点k个位置的祖先节点，并使用布尔数组记录已打印的节点。

Print all nodes that are at distance k from a leaf node

Given a Binary Tree and a positive integer k, print all nodes that are distance k from a leaf node.

Here the meaning of distance is different from previous post. Here k distance from a leaf means k levels higher than a leaf node. For example if k is more than height of Binary Tree, then nothing should be printed. Expected time complexity is O(n) where n is the number nodes in the given Binary Tree.

The idea is to traverse the tree. Keep storing all ancestors till we hit a leaf node. When we reach a leaf node, we print the ancestor at distance k. We also need to keep track of nodes that are already printed as output. For that we use a boolean array visited[].

/* Program to print all nodes which are at distance k from a leaf */
#include <iostream>
using namespace std;
#define MAX_HEIGHT 10000
 
struct Node
{
    int key;
    Node *left, *right;
};
 
/* utility that allocates a new Node with the given key  */
Node* newNode(int key)
{
    Node* node = new Node;
    node->key = key;
    node->left = node->right = NULL;
    return (node);
}
 
/* This function prints all nodes that are distance k from a leaf node
   path[] --> Store ancestors of a node
   visited[] --> Stores true if a node is printed as output.  A node may be k
                 distance away from many leaves, we want to print it once */
void kDistantFromLeafUtil(Node* node, int path[], bool visited[],
                          int pathLen, int k)
{
    // Base case
    if (node==NULL) return;
 
    /* append this Node to the path array */
    path[pathLen] = node->key;
    visited[pathLen] = false;
    pathLen++;
 
    /* it's a leaf, so print the ancestor at distance k only
       if the ancestor is not already printed  */
    if (node->left == NULL && node->right == NULL &&
        pathLen-k-1 >= 0 && visited[pathLen-k-1] == false)
    {
        cout << path[pathLen-k-1] << " ";
        visited[pathLen-k-1] = true;
        return;
    }
 
    /* If not leaf node, recur for left and right subtrees */
    kDistantFromLeafUtil(node->left, path, visited, pathLen, k);
    kDistantFromLeafUtil(node->right, path, visited, pathLen, k);
}
 
/* Given a binary tree and a nuber k, print all nodes that are k
   distant from a leaf*/
void printKDistantfromLeaf(Node* node, int k)
{
    int path[MAX_HEIGHT];
    bool visited[MAX_HEIGHT] = {false};
    kDistantFromLeafUtil(node, path, visited, 0, k);
}
 
/* Driver program to test above functions*/
int main()
{
    // Let us create binary tree given in the above example
    Node * root = newNode(1);
    root->left = newNode(2);
    root->right = newNode(3);
    root->left->left = newNode(4);
    root->left->right = newNode(5);
    root->right->left = newNode(6);
    root->right->right = newNode(7);
    root->right->left->right = newNode(8);
 
    cout << "Nodes at distance 2 are: ";
    printKDistantfromLeaf(root, 2);
 
    return 0;
}