给定一棵二叉树和一个整数K ，任务是打印从根到叶的路径，其中最大元素大于或等于K 。如果不存在这样的路径，则打印 -1。
例子：
Input: K = 25,
10
/ \
5 8
/ \ / \
29 2 1 98
/ \
20 50
Output: (10, 5, 29, 20), (10, 8, 98, 50)
Explanation:
The maximum value in the path 10
-> 5 -> 29 -> 20
is 29 which is greater than 25.
The maximum value in the path 10
-> 8 -> 98 -> 50
is 98 which is greater than 25.
Input: K = 5
2
/ \
1 4
/
0
Output: -1
Explanation:
None of the paths from the root to a leaf
has the value greater than 5.
方法：想法是检查节点是否包含大于或等于“K”的值。如果是，则该节点的所有子树都是有效路径。可以按照以下步骤计算答案：
- 对于每个节点，检查当前节点值是否大于“K”。
- 如果是，则将其插入向量并将标志变量设置为 1。这表示将打印通过此节点的所有路径。
- 使用递归重复上述步骤。对左右子树递归调用该函数。
- 最后，通过使用回溯的概念，从向量打印路径。
下面是上述方法的实现：
CPP
// C++ program to print paths with maximum
// element in the path greater than K
#include
using namespace std;
// A Binary Tree node
struct Node {
int data;
struct Node *left, *right;
};
// A utility function to create a new node
struct Node* newNode(int data)
{
struct Node* newNode = new Node;
newNode->data = data;
newNode->left = newNode->right = NULL;
return (newNode);
}
// A recursive function to print the paths
// whose maximum element is greater than
// or equal to K.
void findPathUtil(Node* root, int k,
vector path,
int flag, int& ans)
{
if (root == NULL)
return;
// If the current node value is greater than
// or equal to k, then all the subtrees
// following that node will get printed,
// flag = 1 indicates to print the required path
if (root->data >= k)
flag = 1;
// If the leaf node is encountered, then the path is
// printed if the size of the path vector is
// greater than 0
if (root->left == NULL && root->right == NULL) {
if (flag == 1) {
ans = 1;
cout << "(";
for (int i = 0; i < path.size(); i++) {
cout << path[i] << ", ";
}
cout << root->data << "), ";
}
return;
}
// Append the node to the path vector
path.push_back(root->data);
// Recur left and right subtrees
findPathUtil(root->left, k, path, flag, ans);
findPathUtil(root->right, k, path, flag, ans);
// Backtracking to return the vector
// and print the path if the flag is 1
path.pop_back();
}
// Function to initialize the variables
// and call the utility function to print
// the paths with maximum values greater than
// or equal to K
void findPath(Node* root, int k)
{
// Initialize flag
int flag = 0;
// ans is used to check empty condition
int ans = 0;
vector v;
// Call function that print path
findPathUtil(root, k, v, flag, ans);
// If the path doesn't exist
if (ans == 0)
cout << "-1";
}
// Driver code
int main(void)
{
int K = 25;
/* Constructing the following tree:
10
/ \
5 8
/ \ / \
29 2 1 98
/ \
20 50
*/
struct Node* root = newNode(10);
root->left = newNode(5);
root->right = newNode(8);
root->left->left = newNode(29);
root->left->right = newNode(2);
root->right->right = newNode(98);
root->right->left = newNode(1);
root->right->right->right = newNode(50);
root->left->left->left = newNode(20);
findPath(root, K);
return 0;
} Java
// Java program to print paths with maximum
// element in the path greater than K
import java.util.*;
class GFG
{
// A Binary Tree node
static class Node
{
int data;
Node left, right;
};
static int ans;
// A utility function to create a new node
static Node newNode(int data)
{
Node newNode = new Node();
newNode.data = data;
newNode.left = newNode.right = null;
return (newNode);
}
// A recursive function to print the paths
// whose maximum element is greater than
// or equal to K.
static void findPathUtil(Node root, int k,
Vector path,
int flag)
{
if (root == null)
return;
// If the current node value is greater than
// or equal to k, then all the subtrees
// following that node will get printed,
// flag = 1 indicates to print the required path
if (root.data >= k)
flag = 1;
// If the leaf node is encountered, then the path is
// printed if the size of the path vector is
// greater than 0
if (root.left == null && root.right == null)
{
if (flag == 1)
{
ans = 1;
System.out.print("(");
for (int i = 0; i < path.size(); i++)
{
System.out.print(path.get(i)+ ", ");
}
System.out.print(root.data+ "), ");
}
return;
}
// Append the node to the path vector
path.add(root.data);
// Recur left and right subtrees
findPathUtil(root.left, k, path, flag);
findPathUtil(root.right, k, path, flag);
// Backtracking to return the vector
// and print the path if the flag is 1
path.remove(path.size()-1);
}
// Function to initialize the variables
// and call the utility function to print
// the paths with maximum values greater than
// or equal to K
static void findPath(Node root, int k)
{
// Initialize flag
int flag = 0;
// ans is used to check empty condition
ans = 0;
Vector v = new Vector();
// Call function that print path
findPathUtil(root, k, v, flag);
// If the path doesn't exist
if (ans == 0)
System.out.print("-1");
}
// Driver code
public static void main(String [] args)
{
int K = 25;
/* Constructing the following tree:
10
/ \
5 8
/ \ / \
29 2 1 98
/ \
20 50
*/
Node root = newNode(10);
root.left = newNode(5);
root.right = newNode(8);
root.left.left = newNode(29);
root.left.right = newNode(2);
root.right.right = newNode(98);
root.right.left = newNode(1);
root.right.right.right = newNode(50);
root.left.left.left = newNode(20);
findPath(root, K);
}
}
// This code is contributed by PrinciRaj1992 Python3
# Python3 program to construct string from binary tree
# A Binary Tree node
class Node:
def __init__(self, data):
self.data = data
self.left = None
self.right = None
# A recursive function to print the paths
# whose maximum element is greater than
# or equal to K.
def findPathUtil(root: Node, k: int, path: list, flag: int):
global ans
if root is None:
return
# If the current node value is greater than
# or equal to k, then all the subtrees
# following that node will get printed,
# flag = 1 indicates to print the required path
if root.data >= k:
flag = 1
# If the leaf node is encountered, then the path is
# printed if the size of the path vector is
# greater than 0
if root.left is None and root.right is None:
if flag:
ans = 1
print("(", end = "")
for i in range(len(path)):
print(path[i], end = ", ")
print(root.data, end = "), ")
return
# Append the node to the path vector
path.append(root.data)
# Recur left and right subtrees
findPathUtil(root.left, k, path, flag)
findPathUtil(root.right, k, path, flag)
# Backtracking to return the vector
# and print the path if the flag is 1
path.pop()
# Function to initialize the variables
# and call the utility function to print
# the paths with maximum values greater than
# or equal to K
def findPath(root: Node, k: int):
global ans
# Initialize flag
flag = 0
# ans is used to check empty condition
ans = 0
v = []
# Call function that print path
findPathUtil(root, k, v, flag)
# If the path doesn't exist
if ans == 0:
print(-1)
# Driver Code
if __name__ == "__main__":
ans = 0
k = 25
# Constructing the following tree:
# 10
# / \
# 5 8
# / \ / \
# 29 2 1 98
# / \
# 20 50
root = Node(10)
root.left = Node(5)
root.right = Node(8)
root.left.left = Node(29)
root.left.right = Node(2)
root.right.right = Node(98)
root.right.left = Node(1)
root.right.right.right = Node(50)
root.left.left.left = Node(20)
findPath(root, k)
# This code is contributed by
# sanjeev2552C#
// C# program to print paths with maximum
// element in the path greater than K
using System;
using System.Collections.Generic;
class GFG
{
// A Binary Tree node
class Node
{
public int data;
public Node left, right;
};
static int ans;
// A utility function to create a new node
static Node newNode(int data)
{
Node newNode = new Node();
newNode.data = data;
newNode.left = newNode.right = null;
return (newNode);
}
// A recursive function to print the paths
// whose maximum element is greater than
// or equal to K.
static void findPathUtil(Node root, int k,
List path,
int flag)
{
if (root == null)
return;
// If the current node value is greater than
// or equal to k, then all the subtrees
// following that node will get printed,
// flag = 1 indicates to print the required path
if (root.data >= k)
flag = 1;
// If the leaf node is encountered, then the path is
// printed if the size of the path vector is
// greater than 0
if (root.left == null && root.right == null)
{
if (flag == 1)
{
ans = 1;
Console.Write("(");
for (int i = 0; i < path.Count; i++)
{
Console.Write(path[i] + ", ");
}
Console.Write(root.data + "), ");
}
return;
}
// Append the node to the path vector
path.Add(root.data);
// Recur left and right subtrees
findPathUtil(root.left, k, path, flag);
findPathUtil(root.right, k, path, flag);
// Backtracking to return the vector
// and print the path if the flag is 1
path.RemoveAt(path.Count-1);
}
// Function to initialize the variables
// and call the utility function to print
// the paths with maximum values greater than
// or equal to K
static void findPath(Node root, int k)
{
// Initialize flag
int flag = 0;
// ans is used to check empty condition
ans = 0;
List v = new List();
// Call function that print path
findPathUtil(root, k, v, flag);
// If the path doesn't exist
if (ans == 0)
Console.Write("-1");
}
// Driver code
public static void Main(String [] args)
{
int K = 25;
/* Constructing the following tree:
10
/ \
5 8
/ \ / \
29 2 1 98
/ \
20 50
*/
Node root = newNode(10);
root.left = newNode(5);
root.right = newNode(8);
root.left.left = newNode(29);
root.left.right = newNode(2);
root.right.right = newNode(98);
root.right.left = newNode(1);
root.right.right.right = newNode(50);
root.left.left.left = newNode(20);
findPath(root, K);
}
}
// This code is contributed by Rajput-Ji 输出：
(10, 5, 29, 20), (10, 8, 98, 50),
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