# Maximum width of a binary tree in C++

C++Server Side ProgrammingProgramming

## Problem statement

Given a binary tree, write a function to get the maximum width of the given tree. The width of a tree is the maximum of widths of all levels.

Consider below tree −

      10
/ \
7   4
/ \   \
9   2   1
/ \
2   5
1. Width at level 1: 1
2. Width at level 2: 2
3. Width at level 3: 3
4. Width at level 4: 2
For above tree answer is 3.

## Algorithm

1. Use level order traversal to find the answer

## Example

#include <bits/stdc++.h>
using namespace std;
struct node {
public:
int data;
node* left;
node* right;
};
int getWidth(node* root, int level);
int height(node* node);
node* newNode(int data);
int getMaxWidth(node* root){
int maxWidth = 0;
int width;
int h = height(root);
int i;
for (i = 1; i <= h; ++i) {
width = getWidth(root, i);
if (width > maxWidth) {
maxWidth = width;
}
}
return maxWidth;
}
int getWidth(node* root, int level){
if (root == NULL) {
return 0;
}
if (level == 1) {
return 1;
}
else if (level > 1) {
return getWidth(root->left, level - 1) + getWidth(root->right, level - 1);
}
}
int height(node* node){
if (node == NULL) {
return 0;
}
int lHeight = height(node->left);
int rHeight = height(node->right);
return (lHeight > rHeight)? (lHeight + 1): (rHeight + 1);
}
node* newNode(int data){
node* Node = new node();
Node->data = data;
Node->left = NULL;
Node->right = NULL;
return(Node);
}
int main(){
node *root = newNode(10);
root->left = newNode(7);
root->right = newNode(4);
root->left->left = newNode(9);
root->left->right = newNode(2);
root->right->right = newNode(1);
root->right->right->left = newNode(2);
root->right->right->right = newNode(5);
cout<<"Maximum width = " << getMaxWidth(root) << endl;
return 0;
}

## Output

When you compile and execute the above program. It generates the following output −

Maximum width = 3