给定一棵二叉树,任务是从根节点到叶节点的任何路径中找到GCD的最大值。
例子:
Input: Below is the given tree:
Output: 3
Explanation:
Path 1: 15->3->5 = gcd(15, 3, 15) =3
Path 2: 15->3->1 =gcd(15, 3, 1) = 1
Path 3: 15->7->31=gcd(15, 7, 31)= 1
Path 4: 15->7->9 = gcd(15, 7, 9) =1, out of these 3 is the maximum.
Input: Below is the given tree:
Output: 1
方法:思想是遍历从根节点到叶子节点的所有路径,并计算该路径中出现的所有节点的GCD。以下是步骤:
- 对给定的二叉树执行预序遍历。
- 迭代所有路径并跟踪数组中的所有路径值。
- 每当遇到叶值时,就找到数组中所有值的 GCD。
- 将 GCD 更新为最大值。
下面是上述方法的实现:
C++
// C++ program for the above approach
#include
using namespace std;
// Initialise to update the maximum
// gcd value from all the path
int maxm = 0;
// Node structure
struct Node {
int val;
// Left & right child of the node
Node *left, *right;
// Intialize constructor
Node(int x)
{
val = x;
left = NULL;
right = NULL;
}
};
// Function to find gcd of a and b
int gcd(int a, int b)
{
if (b == 0)
return a;
return gcd(b, a % b);
}
// function to find the gcd of a path
int find_gcd(vector arr)
{
if (arr.size() == 1)
return arr[0];
int g = arr[0];
for (int i = 1; i < arr.size(); i++) {
g = gcd(g, arr[i]);
}
return g;
}
// Function to find the maximum value
// of gcd from root to leaf
// in a Binary tree
void maxm_gcd(Node* root, vector ans)
{
// Check if root is not null
if (!root)
return;
if (root->left == NULL
and root->right == NULL) {
ans.push_back(root->val);
// Find the maxmimum gcd of
// path value and store in
// global maxm variable
maxm = max(find_gcd(ans),
maxm);
return;
}
// Traverse left of binary tree
ans.push_back(root->val);
maxm_gcd(root->left, ans);
// Traverse right of the binary tree
maxm_gcd(root->right, ans);
}
// Driver Code
int main()
{
// Given Tree
Node* root = new Node(15);
root->left = new Node(3);
root->right = new Node(7);
root->left->left = new Node(15);
root->left->right = new Node(1);
root->right->left = new Node(31);
root->right->right = new Node(9);
// Function Call
maxm_gcd(root, {});
// Print the maximum AND value
cout << maxm << endl;
return 0;
}
Java
// Java program for the above approach
import java.util.*;
class GFG{
// Initialise to update the maximum
// gcd value from all the path
static int maxm = 0;
// Node structure
static class Node
{
int val;
// Left & right child of the node
Node left, right;
// Intialize constructor
Node(int x)
{
val = x;
left = null;
right = null;
}
};
// Function to find gcd of a and b
static int gcd(int a, int b)
{
if (b == 0)
return a;
return gcd(b, a % b);
}
// Function to find the gcd of a path
static int find_gcd(Vector arr)
{
if (arr.size() == 1)
return arr.get(0);
int g = arr.get(0);
for(int i = 1; i < arr.size(); i++)
{
g = gcd(g, arr.get(1));
}
return g;
}
// Function to find the maximum value
// of gcd from root to leaf
// in a Binary tree
static void maxm_gcd(Node root,
Vector ans)
{
// Check if root is not null
if (root == null)
return;
if (root.left == null &&
root.right == null)
{
ans.add(root.val);
// Find the maxmimum gcd of
// path value and store in
// global maxm variable
maxm = Math.max(find_gcd(ans),
maxm);
return;
}
// Traverse left of binary tree
ans.add(root.val);
maxm_gcd(root.left, ans);
// Traverse right of the binary tree
maxm_gcd(root.right, ans);
}
// Driver Code
public static void main(String[] args)
{
// Given Tree
Node root = new Node(15);
root.left = new Node(3);
root.right = new Node(7);
root.left.left = new Node(15);
root.left.right = new Node(1);
root.right.left = new Node(31);
root.right.right = new Node(9);
// Function call
maxm_gcd(root, new Vector<>());
// Print the maximum AND value
System.out.print(maxm + "\n");
}
}
// This code is contributed by Rajput-Ji
Python3
# Python3 implementation of
# the above approach
# Initialise to update the maximum
# gcd value from all the path
global maxm
maxm = 0
# Node structure
class Node:
# Intialize constructor
def __init__(self, x):
self.val = x
self.left = None
self.right = None
# Function to find gcd of a and b
def gcd(a, b):
if(b == 0):
return a
return gcd(b, a % b)
# Function to find the gcd of a path
def find_gcd(arr):
if(len(arr) == 1):
return arr[0]
g = arr[0]
for i in range(1, len(arr)):
g = gcd(g, arr[i])
return g
# Function to find the maximum value
# of gcd from root to leaf
# in a Binary tree
def maxm_gcd(root, ans):
global maxm
# Check if root is not null
if(not root):
return
if(root.left == None and
root.right == None):
ans.append(root.val)
# Find the maxmimum gcd of
# path value and store in
# global maxm variable
maxm = max(find_gcd(ans), maxm)
return
# Traverse left of binary tree
ans.append(root.val)
maxm_gcd(root.left, ans)
# Traverse right of the binary tree
maxm_gcd(root.right, ans)
# Driver Code
if __name__ == '__main__':
# Given Tree
root = Node(15)
root.left = Node(3)
root.right = Node(7)
root.left.left = Node(15)
root.left.right = Node(1)
root.right.left = Node(31)
root.right.right = Node(9)
# Function call
maxm_gcd(root, [])
# Print the maximum AND value
print(maxm)
# This code is contributed by Shivam Singh
C#
// C# program for the above approach
using System;
using System.Collections.Generic;
class GFG{
// Initialise to update the maximum
// gcd value from all the path
static int maxm = 0;
// Node structure
class Node
{
public int val;
// Left & right child of the node
public Node left, right;
// Intialize constructor
public Node(int x)
{
val = x;
left = null;
right = null;
}
};
// Function to find gcd of a and b
static int gcd(int a, int b)
{
if (b == 0)
return a;
return gcd(b, a % b);
}
// Function to find the gcd of a path
static int find_gcd(List arr)
{
if (arr.Count == 1)
return arr[0];
int g = arr[0];
for(int i = 1; i < arr.Count; i++)
{
g = gcd(g, arr[1]);
}
return g;
}
// Function to find the maximum value
// of gcd from root to leaf
// in a Binary tree
static void maxm_gcd(Node root,
List ans)
{
// Check if root is not null
if (root == null)
return;
if (root.left == null &&
root.right == null)
{
ans.Add(root.val);
// Find the maxmimum gcd of
// path value and store in
// global maxm variable
maxm = Math.Max(find_gcd(ans),
maxm);
return;
}
// Traverse left of binary tree
ans.Add(root.val);
maxm_gcd(root.left, ans);
// Traverse right of the binary tree
maxm_gcd(root.right, ans);
}
// Driver Code
public static void Main(String[] args)
{
// Given Tree
Node root = new Node(15);
root.left = new Node(3);
root.right = new Node(7);
root.left.left = new Node(15);
root.left.right = new Node(1);
root.right.left = new Node(31);
root.right.right = new Node(9);
// Function call
maxm_gcd(root, new List());
// Print the maximum AND value
Console.Write(maxm + "\n");
}
}
// This code is contributed by sapnasingh4991
输出:
3
时间复杂度: O(N 2 )
辅助空间: O(N)
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