给定一棵树,以及所有节点的权重(以字符串的形式),任务是计算权重为回文的节点。
例子:
Input:
Output: 3
Only the weights of the nodes 2, 3 and 5 are palindromes.
方法:在树上执行 dfs,对于每个节点,检查它的字符串是否为回文。如果是,则增加计数。
执行:
C++
// C++ implementation of the approach
#include
using namespace std;
int cnt = 0;
vector graph[100];
vector weight(100);
// Function that returns true
// if x is a palindrome
bool isPalindrome(string x)
{
int n = x.size();
for (int i = 0; i < n / 2; i++) {
if (x[i] != x[n - 1 - i])
return false;
}
return true;
}
// Function to perform dfs
void dfs(int node, int parent)
{
// Weight of the current node
string x = weight[node];
// If the weight is a palindrome
if (isPalindrome(x))
cnt += 1;
for (int to : graph[node]) {
if (to == parent)
continue;
dfs(to, node);
}
}
// Driver code
int main()
{
// Weights of the node
weight[1] = "abc";
weight[2] = "aba";
weight[3] = "bcb";
weight[4] = "moh";
weight[5] = "aa";
// Edges of the tree
graph[1].push_back(2);
graph[2].push_back(3);
graph[2].push_back(4);
graph[1].push_back(5);
dfs(1, 1);
cout << cnt;
return 0;
}
Java
// Java implementation of the approach
import java.util.*;
class GFG
{
static int cnt = 0;
static Vector> graph = new Vector>();
static Vector weight = new Vector();
// Function that returns true
// if x is a palindrome
static boolean isPalindrome(String x)
{
int n = x.length();
for (int i = 0; i < n / 2; i++)
{
if (x.charAt(i) != x.charAt(n - 1 - i))
return false;
}
return true;
}
// Function to perform dfs
static void dfs(int node, int parent)
{
// Weight of the current node
String x = weight.get(node);
// If the weight is a palindrome
if (isPalindrome(x))
cnt += 1;
for (int i=0;i());
// Edges of the tree
graph.get(1).add(2);
graph.get(2).add(3);
graph.get(2).add(4);
graph.get(1).add(5);
dfs(1, 1);
System.out.println( cnt);
}
}
// This code is contributed by Arnab Kundu
Python3
# Python3 implementation of the approach
cnt = 0
graph = [0] * 100
for i in range(100):
graph[i] = []
weight = ["0"] * 100
# Function that returns true
# if x is a palindrome
def isPalindrome(x):
n = len(x)
for i in range(0, n // 2):
if x[i] != x[n - 1 - i]:
return False
return True
# Function to perform dfs
def dfs(node, parent):
global cnt
# Weight of the current node
x = weight[node]
# If the weight is a palindrome
if (isPalindrome(x)):
cnt += 1
for to in graph[node]:
if to == parent:
continue
dfs(to, node)
# Driver Code
if __name__ == "__main__":
# Weights of the node
weight[0] = ""
weight[1] = "abc"
weight[2] = "aba"
weight[3] = "bcb"
weight[4] = "moh"
weight[5] = "aa"
# Edges of the tree
graph[1].append(2)
graph[2].append(3)
graph[2].append(4)
graph[1].append(5)
dfs(1, 1)
print(cnt)
# This code is contributed by
# sanjeev2552
C#
// C# implementation of the approach
using System;
using System.Collections.Generic;
class GFG
{
static int cnt = 0;
static List> graph = new List>();
static List weight = new List();
// Function that returns true
// if x is a palindrome
static bool isPalindrome(string x)
{
int n = x.Length;
for (int i = 0; i < n / 2; i++)
{
if (x[i] != x[n - 1 - i])
return false;
}
return true;
}
// Function to perform dfs
static void dfs(int node, int parent)
{
// Weight of the current node
String x = weight[node];
// If the weight is a palindrome
if (isPalindrome(x))
cnt += 1;
for (int i = 0; i < graph[node].Count; i++)
{
if (graph[node][i] == parent)
continue;
dfs(graph[node][i], node);
}
}
// Driver code
public static void Main(String []args)
{
// Weights of the node
weight.Add( "");
weight.Add( "abc");
weight.Add( "aba");
weight.Add( "bcb");
weight.Add( "moh");
weight.Add( "aa");
for(int i = 0; i < 100; i++)
graph.Add(new List());
// Edges of the tree
graph[1].Add(2);
graph[2].Add(3);
graph[2].Add(4);
graph[1].Add(5);
dfs(1, 1);
Console.WriteLine( cnt);
}
}
// This code has been contributed by 29AjayKumar
Javascript
输出:
3
复杂度分析:
- 时间复杂度: O(N*Len) 其中 Len 是给定树中节点的加权字符串的最大长度。
在 DFS 中,树的每个节点都被处理一次,因此对于树中的 N 个节点,由于 DFS 的复杂性是 O(N)。此外,每个节点的处理都涉及遍历该节点的加权字符串一次,因此增加了 O(Len) 的复杂度,其中 Len 是加权字符串的长度。因此,总时间复杂度为 O(N*Len)。 - 辅助空间: O(1)。
不需要任何额外的空间,因此空间复杂度是恒定的。
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