Dado un árbol genérico que consta de N Nodes ( con raíz en 0 ) donde cada Node está asociado con un valor, la tarea para cada nivel del árbol es encontrar la suma de todos los valores de los Nodes presentes en ese nivel del árbol.
Ejemplos:
Entrada: número_Node = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }, valores_Node = { 2, 3, 4, 4, 7, 6, 2, 3, 9, 1 }
Salida:
Suma del nivel 0 = 2
Suma del nivel 1 = 7
Suma del nivel 2 = 14
Suma del nivel 3 = 18
Explicación:
- Nodes en el nivel 0 = {1} con valor 2
- Nodes en el nivel 1 = {2, 3} y sus respectivos valores son {3, 4}. Suma = 7.
- Nodes en el nivel 2 = {4, 5, 8} con valores {4, 7, 3} respectivamente. Suma = 14.
- Nodes en el nivel 3 = {6, 7, 9, 10} con valores {6, 2, 9, 1} respectivamente. Suma = 18
Entrada: número_Node = { 1 }, valores_Node = { 10 }
Salida: Suma del nivel 0 = 10
Enfoque: siga los pasos a continuación para resolver el problema:
- Atraviesa el árbol usando DFS o BFS
- Almacene el nivel de este Node usando este enfoque.
- Luego, agregue los valores del Node al nivel correspondiente del Node en una array, digamos sum[].
- Imprima la array sum[] que muestra la suma de todos los Nodes en cada nivel.
A continuación se muestra la implementación del enfoque anterior:
C++
// C++ implementation of
// the above approach
#include <bits/stdc++.h>
using namespace std;
// Function to add edges to the tree
void add_edge(int a, int b,
vector<vector<int> >& tree)
{
// 0-based indexing
a--, b--;
tree[a].push_back(b);
tree[b].push_back(a);
}
// Function to print sum of
// nodes on all levels of a tree
void dfs(int u, int level, int par,
int node_values[], vector<vector<int> >& tree,
map<int, int>& sum, int& depth)
{
// update max depth of tree
depth = max(depth, level);
// Add value of current node
// to its corresponding level
sum[level] += node_values[u];
for (int child : tree[u]) {
if (child == par)
continue;
// Recursive traverse child nodes
dfs(child, level + 1, u, node_values,
tree, sum, depth);
}
}
// Function to calculate sum of
// nodes of each level of the Tree
void getSum(int node_values[],
vector<vector<int> >& tree)
{
// Depth of the tree
int depth = 0;
// Stores sum at each level
map<int, int> sum;
dfs(0, 0,
-1, node_values,
tree, sum, depth);
// Print final sum
for (int i = 0; i <= depth; i++) {
cout << "Sum of level " << i
<< " = " << sum[i] << endl;
}
}
// Driver Code
int32_t main()
{
// Create a tree structure
int N = 10;
vector<vector<int> > tree(N);
add_edge(1, 2, tree);
add_edge(1, 3, tree);
add_edge(2, 4, tree);
add_edge(3, 5, tree);
add_edge(3, 8, tree);
add_edge(5, 6, tree);
add_edge(5, 7, tree);
add_edge(8, 9, tree);
add_edge(8, 10, tree);
int node_values[]
= { 2, 3, 4, 4, 7,
6, 2, 3, 9, 1 };
// Function call to get the sum
// of nodes of different level
getSum(node_values, tree);
return 0;
}
Java
// Java implementation of
// the above approach
import java.io.*;
import java.util.*;
class GFG{
static Map<Integer, Integer> sum = new HashMap<>();
static int depth = 0;
// Function to add edges to the tree
static void add_edge(int a, int b,
ArrayList<ArrayList<Integer>> tree)
{
// 0-based indexing
a--;
b--;
tree.get(a).add(b);
tree.get(b).add(a);
}
// Function to print sum of
// Nodes on all levels of a tree
static void dfs(int u, int level, int par,
int []node_values,
ArrayList<ArrayList<Integer>> tree)
{
// Update max depth of tree
depth = Math.max(depth, level);
// Add value of current node
// to its corresponding level
if (sum.containsKey(level))
{
sum.put(level, sum.get(level) +
node_values[u]);
}
else
sum.put(level,node_values[u]);
for(int child : tree.get(u))
{
if (child == par)
continue;
// Recursive traverse child nodes
dfs(child, level + 1, u, node_values,
tree);
}
}
// Function to calculate sum of
// nodes of each level of the Tree
static void getSum(int []node_values,
ArrayList<ArrayList<Integer>> tree)
{
dfs(0, 0, -1, node_values, tree);
// Print final sum
for(int i = 0; i <= depth; i++)
{
System.out.println("Sum of level " + (int) i +
" = " + sum.get(i));
}
}
// Driver Code
public static void main (String[] args)
{
// Create a tree structure
int N = 10;
ArrayList<ArrayList<Integer>> tree = new ArrayList<ArrayList<Integer>>();
for(int i = 0; i < N; i++)
tree.add(new ArrayList<Integer>());
add_edge(1, 2, tree);
add_edge(1, 3, tree);
add_edge(2, 4, tree);
add_edge(3, 5, tree);
add_edge(3, 8, tree);
add_edge(5, 6, tree);
add_edge(5, 7, tree);
add_edge(8, 9, tree);
add_edge(8, 10, tree);
int []node_values = { 2, 3, 4, 4, 7,
6, 2, 3, 9, 1 };
// Function call to get the sum
// of nodes of different level
getSum(node_values, tree);
}
}
// This code is contributed by avanitrachhadiya2155
Python3
# Python3 implementation of
# the above approach
# Function to add edges to the tree
def add_edge(a, b):
global tree
# 0-based indexing
a, b = a - 1, b - 1
tree[a].append(b)
tree[b].append(a)
# Function to print sum of
# nodes on all levels of a tree
def dfs(u, level, par, node_values):
global sum, tree, depth
# update max depth of tree
depth = max(depth, level)
# Add value of current node
# to its corresponding level
sum[level] = sum.get(level, 0) + node_values[u]
for child in tree[u]:
if (child == par):
continue
# Recursive traverse child nodes
dfs(child, level + 1, u, node_values)
# Function to calculate sum of
# nodes of each level of the Tree
def getSum(node_values):
global sum, depth, tree
# Depth of the tree
# depth = 0
# Stores sum at each level
# map<int, int> sum
dfs(0, 0, -1, node_values)
# Prfinal sum
for i in range(depth + 1):
print("Sum of level", i, "=", sum[i])
# Driver Code
if __name__ == '__main__':
# Create a tree structure
N = 10
tree = [[] for i in range(N+1)]
sum = {}
depth = 0
add_edge(1, 2)
add_edge(1, 3)
add_edge(2, 4)
add_edge(3, 5)
add_edge(3, 8)
add_edge(5, 6)
add_edge(5, 7)
add_edge(8, 9)
add_edge(8, 10)
node_values = [2, 3, 4, 4, 7, 6, 2, 3, 9, 1]
# Function call to get the sum
# of nodes of different level
getSum(node_values)
# This code is contributed by mohit kumar 29.
C#
// C# implementation of
// the above approach
using System;
using System.Collections.Generic;
class GFG
{
static Dictionary<int, int> sum = new Dictionary<int,int>();
static int depth = 0;
// Function to add edges to the tree
static void add_edge(int a, int b, List<List<int>> tree)
{
// 0-based indexing
a--;
b--;
tree[a].Add(b);
tree[b].Add(a);
}
// Function to print sum of
// Nodes on all levels of a tree
static void dfs(int u, int level, int par,
int []node_values, List<List<int>> tree
)
{
// update max depth of tree
depth = Math.Max(depth, level);
// Add value of current node
// to its corresponding level
if(sum.ContainsKey(level))
sum[level] += node_values[u];
else
sum[level] = node_values[u];
foreach (int child in tree[u]) {
if (child == par)
continue;
// Recursive traverse child nodes
dfs(child, level + 1, u, node_values,
tree);
}
}
// Function to calculate sum of
// nodes of each level of the Tree
static void getSum(int []node_values, List<List<int>> tree)
{
dfs(0, 0, -1, node_values, tree);
// Print final sum
for (int i = 0; i <= depth; i++) {
Console.WriteLine("Sum of level " + (int) i + " = "+ sum[i]);
}
}
// Driver Code
public static void Main()
{
// Create a tree structure
int N = 10;
List<List<int> > tree = new List<List<int>>();
for(int i = 0; i < N; i++)
tree.Add(new List<int>());
add_edge(1, 2, tree);
add_edge(1, 3, tree);
add_edge(2, 4, tree);
add_edge(3, 5, tree);
add_edge(3, 8, tree);
add_edge(5, 6, tree);
add_edge(5, 7, tree);
add_edge(8, 9, tree);
add_edge(8, 10, tree);
int []node_values = {2, 3, 4, 4, 7,6, 2, 3, 9, 1};
// Function call to get the sum
// of nodes of different level
getSum(node_values, tree);
}
}
// This code is contributed by bgangwar59.
Javascript
<script>
// Javascript implementation of
// the above approach
var sum = new Map();
var depth = 0;
// Function to add edges to the tree
function add_edge(a, b, tree)
{
// 0-based indexing
a--;
b--;
tree[a].push(b);
tree[b].push(a);
}
// Function to print sum of
// Nodes on all levels of a tree
function dfs(u, level, par, node_values, tree)
{
// Update max depth of tree
depth = Math.max(depth, level);
// Push value of current node
// to its corresponding level
if (sum.has(level))
sum.set(level, sum.get(level) +
node_values[u]);
else
sum.set(level, node_values[u])
for(var child of tree[u])
{
if (child == par)
continue;
// Recursive traverse child nodes
dfs(child, level + 1, u, node_values,
tree);
}
}
// Function to calculate sum of
// nodes of each level of the Tree
function getSum(node_values, tree)
{
dfs(0, 0, -1, node_values, tree);
// Print final sum
for(var i = 0; i <= depth; i++)
{
document.write("Sum of level " + i +
" = "+ sum.get(i) + "<br>");
}
}
// Driver Code
// Create a tree structure
var N = 10;
var tree = [];
for(var i = 0; i < N; i++)
tree.push([]);
add_edge(1, 2, tree);
add_edge(1, 3, tree);
add_edge(2, 4, tree);
add_edge(3, 5, tree);
add_edge(3, 8, tree);
add_edge(5, 6, tree);
add_edge(5, 7, tree);
add_edge(8, 9, tree);
add_edge(8, 10, tree);
var node_values = [ 2, 3, 4, 4, 7,6, 2, 3, 9, 1 ];
// Function call to get the sum
// of nodes of different level
getSum(node_values, tree);
// This code is contributed by rrrtnx
</script>
Producción:
Sum of level 0 = 2 Sum of level 1 = 7 Sum of level 2 = 14 Sum of level 3 = 18
Complejidad temporal: O(N)
Espacio auxiliar: O(N)
Publicación traducida automáticamente
Artículo escrito por Stream_Cipher y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA