给定一棵树,以及所有节点的权重,任务是计算权重为完美Square的节点的数量。
例子:
Input:
Output: 3
Only the weights of nodes 1, 4 and 5 are perfect squares.
方法:在树上执行dfs,对于每个节点,检查其权重是否为理想平方。
下面是上述方法的实现:
C++
// C++ implementation of the approach
#include
using namespace std;
int ans = 0;
vector graph[100];
vector weight(100);
// Function that returns true
// if n is a perfect square
bool isPerfectSquare(int n)
{
double x = sqrt(n);
if (floor(x) != ceil(x))
return false;
return true;
}
// Function to perform dfs
void dfs(int node, int parent)
{
// If weight of the current node
// is a perfect square
if (isPerfectSquare(weight[node]))
ans += 1;
for (int to : graph[node]) {
if (to == parent)
continue;
dfs(to, node);
}
}
// Driver code
int main()
{
int x = 15;
// Weights of the node
weight[1] = 4;
weight[2] = 5;
weight[3] = 3;
weight[4] = 25;
weight[5] = 16;
weight[6] = 30;
// Edges of the tree
graph[1].push_back(2);
graph[2].push_back(3);
graph[2].push_back(4);
graph[1].push_back(5);
graph[5].push_back(6);
dfs(1, 1);
cout << ans;
return 0;
}
Java
// Java implementation of the approach
import java.util.*;
class GFG{
static int ans = 0;
static Vector[] graph = new Vector[100];
static int[] weight = new int[100];
// Function that returns true
// if n is a perfect square
static boolean isPerfectSquare(int n)
{
double x = Math.sqrt(n);
if (Math.floor(x) != Math.ceil(x))
return false;
return true;
}
// Function to perform dfs
static void dfs(int node, int parent)
{
// If weight of the current node
// is a perfect square
if (isPerfectSquare(weight[node]))
ans += 1;
for (int to : graph[node]) {
if (to == parent)
continue;
dfs(to, node);
}
}
// Driver code
public static void main(String[] args)
{
int x = 15;
for (int i = 0; i < 100; i++)
graph[i] = new Vector<>();
// Weights of the node
weight[1] = 4;
weight[2] = 5;
weight[3] = 3;
weight[4] = 25;
weight[5] = 16;
weight[6] = 30;
// Edges of the tree
graph[1].add(2);
graph[2].add(3);
graph[2].add(4);
graph[1].add(5);
graph[5].add(6);
dfs(1, 1);
System.out.print(ans);
}
}
// This code is contributed by Rajput-Ji
Python3
# Python3 implementation of the approach
from math import *
ans = 0
graph = [[] for i in range(100)]
weight = [0] * 100
# Function that returns true
# if n is a perfect square
def isPerfectSquare(n):
x = sqrt(n)
if (floor(x) != ceil(x)):
return False
return True
# Function to perform dfs
def dfs(node, parent):
global ans
# If weight of the current node
# is a perfect square
if (isPerfectSquare(weight[node])):
ans += 1;
for to in graph[node]:
if (to == parent):
continue
dfs(to, node)
# Driver code
x = 15
# Weights of the node
weight[1] = 4
weight[2] = 5
weight[3] = 3
weight[4] = 25
weight[5] = 16
weight[6] = 30
# Edges of the tree
graph[1].append(2)
graph[2].append(3)
graph[2].append(4)
graph[1].append(5)
graph[5].append(6)
dfs(1, 1)
print(ans)
# This code is contributed by SHUBHAMSINGH10
C#
// C# program for the above approach
using System;
using System.Collections;
using System.Collections.Generic;
using System.Text;
class GFG{
static int ans = 0;
static ArrayList[] graph = new ArrayList[100];
static int[] weight = new int[100];
// Function that returns true
// if n is a perfect square
static bool isPerfectSquare(int n)
{
double x = Math.Sqrt(n);
if (Math.Floor(x) != Math.Ceiling(x))
return false;
return true;
}
// Function to perform dfs
static void dfs(int node, int parent)
{
// If weight of the current node
// is a perfect square
if (isPerfectSquare(weight[node]))
ans += 1;
foreach(int to in graph[node])
{
if (to == parent)
continue;
dfs(to, node);
}
}
// Driver Code
public static void Main(string[] args)
{
//int x = 15;
for(int i = 0; i < 100; i++)
graph[i] = new ArrayList();
// Weights of the node
weight[1] = 4;
weight[2] = 5;
weight[3] = 3;
weight[4] = 25;
weight[5] = 16;
weight[6] = 30;
// Edges of the tree
graph[1].Add(2);
graph[2].Add(3);
graph[2].Add(4);
graph[1].Add(5);
graph[5].Add(6);
dfs(1, 1);
Console.Write(ans);
}
}
// This code is contributed by rutvik_56
Javascript
输出:
3
复杂度分析:
- 时间复杂度: O(N * logV)其中V是树中节点的最大权重。
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而导致的复杂度为O(N)。同样,在处理每个节点时,为了检查节点值是否为完美平方,将调用内置的sqrt(V),其中V是节点的权重,此函数的复杂度为O(log V)。因此,对于每个节点,都会增加O(log V)的复杂度。因此,总时间复杂度为O(N * logV)。 - 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。