Level with maximum number of nodes using DFS in a N-ary tree

Given a N-ary tree, the task is to print the level with the maximum number of nodes.

Examples:

Input : For example, consider the following tree
          1               - Level 1
       /     \
      2       3           - Level 2
    /   \       \
   4     5       6        - Level 3
        /  \     /
       7    8   9         - Level 4


Output : Level-3 and Level-4


Approach:

  • Insert all the connecting nodes to a 2-D vector tree.
  • Run a DFS on the tree such that height[node] = 1 + height[parent]
  • Once DFS traversal is completed, increase the count[] array by 1, for every node’s level.
  • Iterate from first level to last level, and find the level with the maximum number of nodes.
  • Re-traverse from first to last level, and print all the levels which have the same number of maximum nodes.

Below is the implementation of the above approach.

C++

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// C++ program to print the level
// with maximum number of nodes
  
#include <bits/stdc++.h>
using namespace std;
  
// Function for DFS in a tree
void dfs(int node, int parent, int height[], int vis[],
         vector<int> tree[])
{
    // calculate the level of every node
    height[node] = 1 + height[parent];
  
    // mark every node as visited
    vis[node] = 1;
  
    // iterate in the subtree
    for (auto it : tree[node]) {
  
        // if the node is not visited
        if (!vis[it]) {
  
            // call the dfs function
            dfs(it, node, height, vis, tree);
        }
    }
}
  
// Function to insert edges
void insertEdges(int x, int y, vector<int> tree[])
{
    tree[x].push_back(y);
    tree[y].push_back(x);
}
  
// Function to print all levels
void printLevelswithMaximumNodes(int N, int vis[], int height[])
{
    int mark[N + 1];
    memset(mark, 0, sizeof mark);
  
    int maxLevel = 0;
    for (int i = 1; i <= N; i++) {
  
        // count number of nodes
        // in every level
        if (vis[i])
            mark[height[i]]++;
  
        // find the maximum height of tree
        maxLevel = max(height[i], maxLevel);
    }
  
    int maxi = 0;
  
    for (int i = 1; i <= maxLevel; i++) {
        maxi = max(mark[i], maxi);
    }
  
    // print even number of nodes
    cout << "The levels with maximum number of nodes are: ";
    for (int i = 1; i <= maxLevel; i++) {
        if (mark[i] == maxi)
            cout << i << " ";
    }
}
  
// Driver Code
int main()
{
    // Construct the tree
  
    /* 1 
     /  \ 
    2    3 
    / \   \ 
   4   5   6 
      / \  / 
     7   8 9  */
  
    const int N = 9;
  
    vector<int> tree[N + 1];
  
    insertEdges(1, 2, tree);
    insertEdges(1, 3, tree);
    insertEdges(2, 4, tree);
    insertEdges(2, 5, tree);
    insertEdges(5, 7, tree);
    insertEdges(5, 8, tree);
    insertEdges(3, 6, tree);
    insertEdges(6, 9, tree);
  
    int height[N + 1];
    int vis[N + 1] = { 0 };
  
    height[0] = 0;
  
    // call the dfs function
    dfs(1, 0, height, vis, tree);
  
    // Function to print
    printLevelswithMaximumNodes(N, vis, height);
  
    return 0;
}

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Python3

# Python3 program to print the level
# with the maximum number of nodes

# Function for DFS in a tree
def dfs(node, parent, height, vis, tree):

# calculate the level of every node
height[node] = 1 + height[parent]

# mark every node as visited
vis[node] = 1

# iterate in the subtree
for it in tree[node]:

# if the node is not visited
if vis[it] == 0:

# call the dfs function
dfs(it, node, height, vis, tree)

# Function to insert edges
def insertEdges(x, y, tree):

tree[x].append(y)
tree[y].append(x)

# Function to print all levels
def printLevelswithMaximumNodes(N, vis, height):

mark = [0] * (N + 1)

maxLevel = 0
for i in range (1, N + 1):

# count number of nodes
# in every level
if vis[i] == 1:
mark[height[i]] += 1

# find the maximum height of tree
maxLevel = max(height[i], maxLevel)

maxi = 0

for i in range(1, maxLevel + 1):
maxi = max(mark[i], maxi)

# print even number of nodes
print(“The levels with maximum number”,
“of nodes are:”, end = ” “)
for i in range(1, maxLevel + 1):
if mark[i] == maxi:
print(i, end = ” “)

# Driver Code
if __name__ == “__main__”:

# Construct the tree
N = 9

# Create an empty 2-D list
tree = [[] for i in range(N + 1)]

insertEdges(1, 2, tree)
insertEdges(1, 3, tree)
insertEdges(2, 4, tree)
insertEdges(2, 5, tree)
insertEdges(5, 7, tree)
insertEdges(5, 8, tree)
insertEdges(3, 6, tree)
insertEdges(6, 9, tree)

height = [None] * (N + 1)
vis = [0] * (N + 1)

height[0] = 0

# call the dfs function
dfs(1, 0, height, vis, tree)

# Function to print
printLevelswithMaximumNodes(N, vis, height)

# This code is contributed
# by Rituraj Jain

Output:

The levels with maximum number of nodes are: 3 4

Time Complexity: O(N)
Auxiliary Space: O(N)



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