Calculate sum of all nodes present in a level for each level of a Tree
Given a Generic Tree consisting of N nodes (rooted at 0) where each node is associated with a value, the task for each level of the Tree is to find the sum of all node values present at that level of the tree.
Examples:
Input: node_number = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }, node_values = { 2, 3, 4, 4, 7, 6, 2, 3, 9, 1 }
Output:
Sum of level 0 = 2
Sum of level 1 = 7
Sum of level 2 = 14
Sum of level 3 = 18
Explanation :
- Nodes on level 0 = {1} with value is 2
- Nodes on level 1 = {2, 3} and their respective values are {3, 4}. Sum = 7.
- Nodes on level 2 = {4, 5, 8} with values {4, 7, 3} respectively. Sum = 14.
- Nodes on level 3 = {6, 7, 9, 10} with values {6, 2, 9, 1} respectively. Sum = 18
Input: node_number = { 1 }, node_values = { 10 }
Output: Sum of level 0 = 10
Approach: Follow the steps below to solve the problem:
- Traverse the tree using DFS or BFS
- Store the level of this node using this approach.
- Then, add the node values to the corresponding level of the node in an array, say sum[ ].
- Print the array sum[] showing the sum of all nodes on each level.
Below is the implementation of the above approach :
C++
// C++ implementation of// the above approach#include <bits/stdc++.h>using namespace std;// Function to add edges to the treevoid 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 treevoid 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 Treevoid 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 Codeint32_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 approachimport java.io.*;import java.util.*;class GFG{ static Map<Integer, Integer> sum = new HashMap<>();static int depth = 0;// Function to add edges to the treestatic 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 treestatic 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 Treestatic 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 Codepublic 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 treedef 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 prsum of# nodes on all levels of a treedef 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 Treedef 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 Codeif __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 approachusing 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 treestatic 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 treestatic 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 Treestatic 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 Codepublic 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. |
Output:
Sum of level 0 = 2 Sum of level 1 = 7 Sum of level 2 = 14 Sum of level 3 = 18
Time Complexity: O(N)
Auxiliary Space: O(N)
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