# Print all the levels with odd and even number of nodes in it | Set-2

Given an N-ary tree, print all the levels with odd and even number of nodes in it.

Examples:

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

The levels with odd number of nodes are: 1 3 4
The levels with even number of nodes are: 2
```

Note: The level numbers starts from 1. That is, the root node is at the level 1.

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach:

• Insert all the connecting nodes to a 2-D vector tree.
• Run a BFS on the tree such that height[node] = 1 + height[parent]
• Once BFS traversal is completed, increase the count[] array by 1, for every node’s level.
• Iterate from first level to last level, and print all nodes with count[] values as odd to get level with odd number nodes.
• Iterate from first level to last level, and print all nodes with count[] values as even to get level with even number nodes.

Below is the implementation of the above approach:

## C++

 `// C++ program to print all levels ` `// with odd and even number of nodes ` ` `  `#include ` `using` `namespace` `std; ` ` `  `// Function for BFS in a tree ` `void` `bfs(``int` `node, ``int` `parent, ``int` `height[], ``int` `vis[], ` `         ``vector<``int``> tree[]) ` `{ ` ` `  `    ``// mark first node as visited ` `    ``vis[node] = 1; ` ` `  `    ``// Declare Queue ` `    ``queue<``int``> q; ` ` `  `    ``// Push the first element ` `    ``q.push(1); ` ` `  `    ``// calculate the level of every node ` `    ``height[node] = 1 + height[parent]; ` ` `  `    ``// Check if the queue is empty or not ` `    ``while` `(!q.empty()) { ` ` `  `        ``// Get the top element in the queue ` `        ``int` `top = q.front(); ` ` `  `        ``// pop the element ` `        ``q.pop(); ` ` `  `        ``// mark as visited ` `        ``vis[top] = 1; ` ` `  `        ``// Iterate for the connected nodes ` `        ``for` `(``int` `i = 0; i < tree[top].size(); i++) { ` ` `  `            ``// if not visited ` `            ``if` `(!vis[tree[top][i]]) { ` ` `  `                ``// Insert into queue ` `                ``q.push(tree[top][i]); ` ` `  `                ``// Increase level ` `                ``height[tree[top][i]] = 1 + height[top]; ` `            ``} ` `        ``} ` `    ``} ` `} ` ` `  `// 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` `printLevelsOddEven(``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); ` `    ``} ` ` `  `    ``// print odd number of nodes ` `    ``cout << ``"The levels with odd number of nodes are: "``; ` `    ``for` `(``int` `i = 1; i <= maxLevel; i++) { ` `        ``if` `(mark[i] % 2) ` `            ``cout << i << ``" "``; ` `    ``} ` ` `  `    ``// print even number of nodes ` `    ``cout << ``"\nThe levels with even number of nodes are: "``; ` `    ``for` `(``int` `i = 1; i <= maxLevel; i++) { ` `        ``if` `(mark[i] % 2 == 0) ` `            ``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 }; ` ` `  `    ``// call the bfs function ` `    ``bfs(1, 0, height, vis, tree); ` ` `  `    ``// Function to print ` `    ``printLevelsOddEven(N, vis, height); ` ` `  `    ``return` `0; ` `} `

## Python3

 `# Python3 program to print all levels  ` `# with odd and even number of nodes  ` ` `  `# Function for BFS in a tree  ` `def` `bfs(node, parent, height, vis, tree): ` ` `  `    ``# mark first node as visited  ` `    ``vis[node] ``=` `1` ` `  `    ``# Declare Queue  ` `    ``q ``=` `[]  ` ` `  `    ``# append the first element  ` `    ``q.append(``1``)  ` ` `  `    ``# calculate the level of every node  ` `    ``height[node] ``=` `1` `+` `height[parent]  ` ` `  `    ``# Check if the queue is empty or not  ` `    ``while` `(``len``(q)): ` ` `  `        ``# Get the top element in  ` `        ``# the queue  ` `        ``top ``=` `q[``0``]  ` ` `  `        ``# pop the element  ` `        ``q.pop(``0``)  ` ` `  `        ``# mark as visited  ` `        ``vis[top] ``=` `1` ` `  `        ``# Iterate for the connected nodes  ` `        ``for` `i ``in` `range``(``len``(tree[top])):  ` `             `  `            ``# if not visited  ` `            ``if` `(``not` `vis[tree[top][i]]):  ` ` `  `                ``# Insert into queue  ` `                ``q.append(tree[top][i])  ` ` `  `                ``# Increase level  ` `                ``height[tree[top][i]] ``=` `1` `+` `height[top]  ` ` `  `# Function to insert edges  ` `def` `insertEdges(x, y, tree): ` ` `  `    ``tree[x].append(y)  ` `    ``tree[y].append(x) ` `     `  `# Function to print all levels  ` `def` `printLevelsOddEven(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]) : ` `            ``mark[height[i]] ``+``=` `1` ` `  `        ``# find the maximum height of tree  ` `        ``maxLevel ``=` `max``(height[i], maxLevel)  ` `     `  `    ``# prodd number of nodes  ` `    ``print``(``"The levels with odd number"``, ` `          ``"of nodes are:"``, end ``=` `" "``) ` `    ``for` `i ``in` `range``(``1``, maxLevel ``+` `1``): ` `        ``if` `(mark[i] ``%` `2``):  ` `            ``print``(i, end ``=` `" "` `) ` `     `  `    ``# print even number of nodes  ` `    ``print``(``"\nThe levels with even number"``,  ` `            ``"of nodes are:"``, end ``=` `" "``)  ` `    ``for` `i ``in` `range``(``1``, maxLevel ):  ` `        ``if` `(mark[i] ``%` `2` `=``=` `0``):  ` `            ``print``(i, end ``=` `" "``) ` ` `  `# Driver Code  ` `if` `__name__ ``=``=` `'__main__'``: ` `     `  `    ``# Construct the tree  ` `    ``""" 1  ` `    ``/ \  ` `    ``2 3  ` `    ``/ \ \  ` `    ``4 5 6  ` `        ``/ \ /  ` `    ``7 8 9 """` ` `  `    ``N ``=` `9` ` `  `    ``tree ``=` `[[``0``]] ``*` `(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 ``=` `[``0``] ``*` `(N ``+` `1``) ` `    ``vis ``=` `[``0``] ``*` `(N ``+` `1``) ` ` `  `    ``# call the bfs function  ` `    ``bfs(``1``, ``0``, height, vis, tree)  ` ` `  `    ``# Function to pr ` `    ``printLevelsOddEven(N, vis, height) ` ` `  `# This code is contributed  ` `# by SHUBHAMSINGH10 `

Output:

```The levels with odd number of nodes are: 1 3 4
The levels with even number of nodes are: 2
```

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

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