打印从根到两个给定节点的两条路径的公共路径
原文:https://www . geesforgeks . org/print-path-common-two-path-root-two-given-nodes/
给定具有不同节点的二叉树(没有两个节点具有相同的数据值)。问题是打印从根到两个给定节点 n1 和 n2 的两条路径的公共路径。如果任一节点不存在，则打印“无公共路径”。
示例:
Input : 1
/ \
2 3
/ \ / \
4 5 6 7
/ \
8 9
n1 = 4, n2 = 8
Output : 1->2
Path form root to n1:
1->2->4
Path form root to n2:
1->2->5->8
Common Path:
1->2
进场:以下步骤为:
C++
// C++ implementation to print the path common to the
// two paths from the root to the two given nodes
#include <bits/stdc++.h>
using namespace std;
// structure of a node of binary tree
struct Node
{
int data;
Node *left, *right;
};
/* Helper function that allocates a new node with the
given data and NULL left and right pointers. */
struct Node* getNode(int data)
{
struct Node *newNode = (struct Node*)malloc(sizeof(struct Node));
newNode->data = data;
newNode->left = newNode->right = NULL;
return newNode;
}
// This function returns pointer to LCA of two given values n1 and n2.
// v1 is set as true by this function if n1 is found
// v2 is set as true by this function if n2 is found
struct Node *findLCAUtil(struct Node* root, int n1, int n2, bool &v1, bool &v2)
{
// Base case
if (root == NULL) return NULL;
// If either n1 or n2 matches with root's data, report the presence
// by setting v1 or v2 as true and return root (Note that if a key
// is ancestor of other, then the ancestor key becomes LCA)
if (root->data == n1)
{
v1 = true;
return root;
}
if (root->data == n2)
{
v2 = true;
return root;
}
// Look for nodes in left and right subtrees
Node *left_lca = findLCAUtil(root->left, n1, n2, v1, v2);
Node *right_lca = findLCAUtil(root->right, n1, n2, v1, v2);
// If both of the above calls return Non-NULL, then one node
// is present in one subtree and other is present in other,
// So this current node is the LCA
if (left_lca && right_lca) return root;
// Otherwise check if left subtree or right subtree is LCA
return (left_lca != NULL)? left_lca: right_lca;
}
// Returns true if key k is present in tree rooted with root
bool find(Node *root, int k)
{
// Base Case
if (root == NULL)
return false;
// If key k is present at root, or in left subtree
// or right subtree, return true
if (root->data == k || find(root->left, k) || find(root->right, k))
return true;
// Else return false
return false;
}
// This function returns LCA of n1 and n2 only if both n1 and n2
// are present in tree, otherwise returns NULL
Node *findLCA(Node *root, int n1, int n2)
{
// Initialize n1 and n2 as not visited
bool v1 = false, v2 = false;
// Find lca of n1 and n2
Node *lca = findLCAUtil(root, n1, n2, v1, v2);
// Return LCA only if both n1 and n2 are present in tree
if (v1 && v2 || v1 && find(lca, n2) || v2 && find(lca, n1))
return lca;
// Else return NULL
return NULL;
}
// function returns true if
// there is a path from root to
// the given node. It also populates
// 'arr' with the given path
bool hasPath(Node *root, vector<int>& arr, int x)
{
// if root is NULL
// there is no path
if (!root)
return false;
// push the node's value in 'arr'
arr.push_back(root->data);
// if it is the required node
// return true
if (root->data == x)
return true;
// else check whether there the required node lies in the
// left subtree or right subtree of the current node
if (hasPath(root->left, arr, x) ||
hasPath(root->right, arr, x))
return true;
// required node does not lie either in the
// left or right subtree of the current node
// Thus, remove current node's value from 'arr'
// and then return false;
arr.pop_back();
return false;
}
// function to print the path common
// to the two paths from the root
// to the two given nodes if the nodes
// lie in the binary tree
void printCommonPath(Node *root, int n1, int n2)
{
// vector to store the common path
vector<int> arr;
// LCA of node n1 and n2
Node *lca = findLCA(root, n1, n2);
// if LCA of both n1 and n2 exists
if (lca)
{
// then print the path from root to
// LCA node
if (hasPath(root, arr, lca->data))
{
for (int i=0; i<arr.size()-1; i++)
cout << arr[i] << "->";
cout << arr[arr.size() - 1];
}
}
// LCA is not present in the binary tree
// either n1 or n2 or both are not present
else
cout << "No Common Path";
}
// Driver program to test above
int main()
{
// binary tree formation
struct Node *root = getNode(1);
root->left = getNode(2);
root->right = getNode(3);
root->left->left = getNode(4);
root->left->right = getNode(5);
root->right->left = getNode(6);
root->right->right = getNode(7);
root->left->right->left = getNode(8);
root->right->left->right = getNode(9);
int n1 = 4, n2 = 8;
printCommonPath(root, n1, n2);
return 0;
}
Java 语言(一种计算机语言，尤用于创建网站)
// Java implementation to print the path common to the
// two paths from the root to the two given nodes
import java.util.ArrayList;
public class PrintCommonPath {
// Initialize n1 and n2 as not visited
static boolean v1 = false, v2 = false;
// This function returns pointer to LCA of two given
// values n1 and n2\. This function assumes that n1 and
// n2 are present in Binary Tree
static Node findLCAUtil(Node node, int n1, int n2)
{
// Base case
if (node == null)
return null;
//Store result in temp, in case of key match so that we can search for other key also.
Node temp=null;
// If either n1 or n2 matches with root's key, report the presence
// by setting v1 or v2 as true and return root (Note that if a key
// is ancestor of other, then the ancestor key becomes LCA)
if (node.data == n1)
{
v1 = true;
temp = node;
}
if (node.data == n2)
{
v2 = true;
temp = node;
}
// Look for keys in left and right subtrees
Node left_lca = findLCAUtil(node.left, n1, n2);
Node right_lca = findLCAUtil(node.right, n1, n2);
if (temp != null)
return temp;
// If both of the above calls return Non-NULL, then one key
// is present in once subtree and other is present in other,
// So this node is the LCA
if (left_lca != null && right_lca != null)
return node;
// Otherwise check if left subtree or right subtree is LCA
return (left_lca != null) ? left_lca : right_lca;
}
// Returns true if key k is present in tree rooted with root
static boolean find(Node root, int k)
{
// Base Case
if (root == null)
return false;
// If key k is present at root, or in left subtree
// or right subtree, return true
if (root.data == k || find(root.left, k) || find(root.right, k))
return true;
// Else return false
return false;
}
// This function returns LCA of n1 and n2 only if both n1 and n2
// are present in tree, otherwise returns null
static Node findLCA(Node root, int n1, int n2)
{
// Find lca of n1 and n2
Node lca = findLCAUtil(root, n1, n2);
// Return LCA only if both n1 and n2 are present in tree
if (v1 && v2 || v1 && find(lca, n2) || v2 && find(lca, n1))
return lca;
// Else return null
return null;
}
// function returns true if
// there is a path from root to
// the given node. It also populates
// 'arr' with the given path
static boolean hasPath(Node root, ArrayList<Integer> arr, int x)
{
// if root is null
// there is no path
if (root==null)
return false;
// push the node's value in 'arr'
arr.add(root.data);
// if it is the required node
// return true
if (root.data == x)
return true;
// else check whether there the required node lies in the
// left subtree or right subtree of the current node
if (hasPath(root.left, arr, x) ||
hasPath(root.right, arr, x))
return true;
// required node does not lie either in the
// left or right subtree of the current node
// Thus, remove current node's value from 'arr'
// and then return false;
arr.remove(arr.size()-1);
return false;
}
// function to print the path common
// to the two paths from the root
// to the two given nodes if the nodes
// lie in the binary tree
static void printCommonPath(Node root, int n1, int n2)
{
// ArrayList to store the common path
ArrayList<Integer> arr=new ArrayList<>();
// LCA of node n1 and n2
Node lca = findLCA(root, n1, n2);
// if LCA of both n1 and n2 exists
if (lca!=null)
{
// then print the path from root to
// LCA node
if (hasPath(root, arr, lca.data))
{
for (int i=0; i<arr.size()-1; i++)
System.out.print(arr.get(i)+"->");
System.out.print(arr.get(arr.size() - 1));
}
}
// LCA is not present in the binary tree
// either n1 or n2 or both are not present
else
System.out.print("No Common Path");
}
public static void main(String args[])
{
Node root = new Node(1);
root.left = new Node(2);
root.right = new Node(3);
root.left.left = new Node(4);
root.left.right = new Node(5);
root.right.left = new Node(6);
root.right.right = new Node(7);
root.left.right.left = new Node(8);
root.right.left.right = new Node(9);
int n1 = 4, n2 = 8;
printCommonPath(root, n1, n2);
}
}
/* Class containing left and right child of current
node and key value*/
class Node
{
int data;
Node left, right;
public Node(int item)
{
data = item;
left = right = null;
}
}
//This code is contributed by Gaurav Tiwari
Python 3
# Python implementation to print the path common to the
# two paths from the root to the two given nodes
# structure of a node of binary tree
class Node:
def __init__(self, data):
self.data = data
self.left = None
self.right = None
# This function returns pointer to LCA of two given values n1 and n2.
# v1 is set as True by this function if n1 is found
# v2 is set as True by this function if n2 is found
def findLCAUtil(root: Node, n1: int, n2: int) -> Node:
global v1, v2
# Base case
if (root is None):
return None
# If either n1 or n2 matches with root's data, report the presence
# by setting v1 or v2 as True and return root (Note that if a key
# is ancestor of other, then the ancestor key becomes LCA)
if (root.data == n1):
v1 = True
return root
if (root.data == n2):
v2 = True
return root
# Look for nodes in left and right subtrees
left_lca = findLCAUtil(root.left, n1, n2)
right_lca = findLCAUtil(root.right, n1, n2)
# If both of the above calls return Non-None, then one node
# is present in one subtree and other is present in other,
# So this current node is the LCA
if (left_lca and right_lca):
return root
# Otherwise check if left subtree or right subtree is LCA
return left_lca if (left_lca != None) else right_lca
# Returns True if key k is present in tree rooted with root
def find(root: Node, k: int) -> bool:
# Base Case
if (root == None):
return False
# If key k is present at root, or in left subtree
# or right subtree, return True
if (root.data == k or find(root.left, k) or find(root.right, k)):
return True
# Else return False
return False
# This function returns LCA of n1 and n2 only if both n1 and n2
# are present in tree, otherwise returns None
def findLCA(root: Node, n1: int, n2: int) -> Node:
global v1, v2
# Initialize n1 and n2 as not visited
v1 = False
v2 = False
# Find lca of n1 and n2
lca = findLCAUtil(root, n1, n2)
# Return LCA only if both n1 and n2 are present in tree
if (v1 and v2 or v1 and find(lca, n2) or v2 and find(lca, n1)):
return lca
# Else return None
return None
# function returns True if
# there is a path from root to
# the given node. It also populates
# 'arr' with the given path
def hasPath(root: Node, arr: list, x: int) -> Node:
# if root is None
# there is no path
if (root is None):
return False
# push the node's value in 'arr'
arr.append(root.data)
# if it is the required node
# return True
if (root.data == x):
return True
# else check whether there the required node lies in the
# left subtree or right subtree of the current node
if (hasPath(root.left, arr, x) or hasPath(root.right, arr, x)):
return True
# required node does not lie either in the
# left or right subtree of the current node
# Thus, remove current node's value from 'arr'
# and then return False;
arr.pop()
return False
# function to print the path common
# to the two paths from the root
# to the two given nodes if the nodes
# lie in the binary tree
def printCommonPath(root: Node, n1: int, n2: int):
# vector to store the common path
arr = []
# LCA of node n1 and n2
lca = findLCA(root, n1, n2)
# if LCA of both n1 and n2 exists
if (lca):
# then print the path from root to
# LCA node
if (hasPath(root, arr, lca.data)):
for i in range(len(arr) - 1):
print(arr[i], end="->")
print(arr[-1])
# LCA is not present in the binary tree
# either n1 or n2 or both are not present
else:
print("No Common Path")
# Driver Code
if __name__ == "__main__":
v1 = 0
v2 = 0
root = Node(1)
root.left = Node(2)
root.right = Node(3)
root.left.left = Node(4)
root.left.right = Node(5)
root.right.left = Node(6)
root.right.right = Node(7)
root.left.right.left = Node(8)
root.right.left.right = Node(9)
n1 = 4
n2 = 8
printCommonPath(root, n1, n2)
# This code is contributed by
# sanjeev2552
C
// C# implementation to print the path common to the
// two paths from the root to the two given nodes
using System;
using System.Collections.Generic;
public class PrintCommonPath
{
// Initialize n1 and n2 as not visited
static Boolean v1 = false, v2 = false;
// This function returns pointer to LCA of two given
// values n1 and n2\. This function assumes that n1 and
// n2 are present in Binary Tree
static Node findLCAUtil(Node node, int n1, int n2)
{
// Base case
if (node == null)
return null;
//Store result in temp, in case of key
// match so that we can search for other key also.
Node temp=null;
// If either n1 or n2 matches with root's key, report the presence
// by setting v1 or v2 as true and return root (Note that if a key
// is ancestor of other, then the ancestor key becomes LCA)
if (node.data == n1)
{
v1 = true;
temp = node;
}
if (node.data == n2)
{
v2 = true;
temp = node;
}
// Look for keys in left and right subtrees
Node left_lca = findLCAUtil(node.left, n1, n2);
Node right_lca = findLCAUtil(node.right, n1, n2);
if (temp != null)
return temp;
// If both of the above calls return Non-NULL, then one key
// is present in once subtree and other is present in other,
// So this node is the LCA
if (left_lca != null && right_lca != null)
return node;
// Otherwise check if left subtree or right subtree is LCA
return (left_lca != null) ? left_lca : right_lca;
}
// Returns true if key k is present in tree rooted with root
static Boolean find(Node root, int k)
{
// Base Case
if (root == null)
return false;
// If key k is present at root, or in left subtree
// or right subtree, return true
if (root.data == k || find(root.left, k) || find(root.right, k))
return true;
// Else return false
return false;
}
// This function returns LCA of n1 and n2 only if both n1 and n2
// are present in tree, otherwise returns null
static Node findLCA(Node root, int n1, int n2)
{
// Find lca of n1 and n2
Node lca = findLCAUtil(root, n1, n2);
// Return LCA only if both n1 and n2 are present in tree
if (v1 && v2 || v1 && find(lca, n2) || v2 && find(lca, n1))
return lca;
// Else return null
return null;
}
// function returns true if
// there is a path from root to
// the given node. It also populates
// 'arr' with the given path
static Boolean hasPath(Node root, List<int> arr, int x)
{
// if root is null
// there is no path
if (root == null)
return false;
// push the node's value in 'arr'
arr.Add(root.data);
// if it is the required node
// return true
if (root.data == x)
return true;
// else check whether there the required node lies in the
// left subtree or right subtree of the current node
if (hasPath(root.left, arr, x) ||
hasPath(root.right, arr, x))
return true;
// required node does not lie either in the
// left or right subtree of the current node
// Thus, remove current node's value from 'arr'
// and then return false;
arr.Remove(arr.Count-1);
return false;
}
// function to print the path common
// to the two paths from the root
// to the two given nodes if the nodes
// lie in the binary tree
static void printCommonPath(Node root, int n1, int n2)
{
// ArrayList to store the common path
List<int> arr = new List<int>();
// LCA of node n1 and n2
Node lca = findLCA(root, n1, n2);
// if LCA of both n1 and n2 exists
if (lca!=null)
{
// then print the path from root to
// LCA node
if (hasPath(root, arr, lca.data))
{
for (int i=0; i<arr.Count-1; i++)
Console.Write(arr[i]+"->");
Console.Write(arr[arr.Count - 1]);
}
}
// LCA is not present in the binary tree
// either n1 or n2 or both are not present
else
Console.Write("No Common Path");
}
// Driver code
public static void Main(String []args)
{
Node root = new Node(1);
root.left = new Node(2);
root.right = new Node(3);
root.left.left = new Node(4);
root.left.right = new Node(5);
root.right.left = new Node(6);
root.right.right = new Node(7);
root.left.right.left = new Node(8);
root.right.left.right = new Node(9);
int n1 = 4, n2 = 8;
printCommonPath(root, n1, n2);
}
}
/* Class containing left and right child of current
node and key value*/
public class Node
{
public int data;
public Node left, right;
public Node(int item)
{
data = item;
left = right = null;
}
}
// This code has been contributed by 29AjayKumar
java 描述语言
<script>
// Javascript implementation to print the path
// common to the two paths from the root to the
// two given nodes
class Node
{
constructor(d)
{
this.data = d;
this.left = this.right = null;
}
}
let v1 = false;
let v2 = false;
// This function returns pointer to LCA of two given
// values n1 and n2\. This function assumes that n1 and
// n2 are present in Binary Tree
function findLCAUtil(node, n1, n2)
{
// Base case
if (node == null)
return null;
// If either n1 or n2 matches with root's key,
// report the presence by setting v1 or v2 as
// true and return root (Note that if a key
// is ancestor of other, then the ancestor
// key becomes LCA)
if (node.data == n1)
{
v1 = true;
return node;
}
if (node.data == n2)
{
v2 = true;
return node;
}
// Look for keys in left and right subtrees
let left_lca = findLCAUtil(node.left, n1, n2);
let right_lca = findLCAUtil(node.right, n1, n2);
// If both of the above calls return Non-NULL,
// then one key is present in once subtree and
// other is present in other, So this node is the LCA
if (left_lca != null && right_lca != null)
return node;
// Otherwise check if left subtree or right
// subtree is LCA
return (left_lca != null) ? left_lca : right_lca;
}
function find(root, k)
{
// Base Case
if (root == null)
return false;
// If key k is present at root, or in left subtree
// or right subtree, return true
if ((root.data == k) || find(root.left, k) ||
find(root.right, k))
return true;
// Else return false
return false;
}
// This function returns LCA of n1 and n2 only
// if both n1 and n2 are present in tree,
// otherwise returns null
function findLCA(root, n1, n2)
{
// Find lca of n1 and n2
let lca = findLCAUtil(root, n1, n2);
// Return LCA only if both n1 and n2
// are present in tree
if ((v1 && v2) || (v1 && find(lca, n2)) ||
(v2 && find(lca, n1)))
return lca;
// Else return null
return null;
}
// Function returns true if
// there is a path from root to
// the given node. It also populates
// 'arr' with the given path
function hasPath(root, arr, x)
{
// If root is null
// there is no path
if (root == null)
return false;
// Push the node's value in 'arr'
arr.push(root.data);
// If it is the required node
// return true
if (root.data == x)
return true;
// Else check whether the required node lies in the
// left subtree or right subtree of the current node
if (hasPath(root.left, arr, x) ||
hasPath(root.right, arr, x))
return true;
// Required node does not lie either in the
// left or right subtree of the current node
// Thus, remove current node's value from 'arr'
// and then return false;
arr.pop();
return false;
}
// Function to print the path common
// to the two paths from the root
// to the two given nodes if the nodes
// lie in the binary tree
function printCommonPath(root, n1, n2)
{
// ArrayList to store the common path
let arr = [];
// LCA of node n1 and n2
let lca = findLCA(root, n1, n2);
// If LCA of both n1 and n2 exists
if (lca != null)
{
// Then print the path from root to
// LCA node
if (hasPath(root, arr, lca.data))
{
for(let i = 0; i < arr.length - 1; i++)
{ document.write(arr[i] + "->");
document.write(arr[arr.length - 1]);
}
}
}
// LCA is not present in the binary tree
// either n1 or n2 or both are not present
else
{
document.write("No Common Path");
}
}
// Driver code
let root = new Node(1);
root.left = new Node(2);
root.right = new Node(3);
root.left.left = new Node(4);
root.left.right = new Node(5);
root.right.left = new Node(6);
root.right.right = new Node(7);
root.left.right.left = new Node(8);
root.right.left.right = new Node(9);
let n1 = 4, n2 = 8;
printCommonPath(root, n1, n2);
// This code is contributed by rag2127
</script>
输出:
1->2
时间复杂度: O(n)，其中 n 为二叉树中的节点数。
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