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package tree;

import java.util.ArrayList;

import java.util.HashMap;

import java.util.List;

import java.util.Map;

/**

* Created by gouthamvidyapradhan on 03/05/2018. Given a binary tree, write a function to get the

* maximum width of the given tree. The width of a tree is the maximum width among all levels. The

* binary tree has the same structure as a full binary tree, but some nodes are null.

*

* <p>The width of one level is defined as the length between the end-nodes (the leftmost and right

* most non-null nodes in the level, where the null nodes between the end-nodes are also counted

* into the length calculation.

*

* <p>Example 1: Input:

*

* <p>1 / \ 3 2 / \ \ 5 3 9

*

* <p>Output: 4 Explanation: The maximum width existing in the third level with the length 4

* (5,3,null,9). Example 2: Input:

*

* <p>1 / 3 / \ 5 3

*

* <p>Output: 2 Explanation: The maximum width existing in the third level with the length 2 (5,3).

* Example 3: Input:

*

* <p>1 / \ 3 2 / 5

*

* <p>Output: 2 Explanation: The maximum width existing in the second level with the length 2 (3,2).

* Example 4: Input:

*

* <p>1 / \ 3 2 / \ 5 9 / \ 6 7 Output: 8 Explanation:The maximum width existing in the fourth level

* with the length 8 (6,null,null,null,null,null,null,7).

*

* <p>Solution: O(N): General idea is to give a position value to each node. On every left traversal

* give the value curr_pos * 2 and on every right traversal give the value curr_pos * 2 + 1

* Calculate maximum width for each level using right - left + 1

*/

public class MaximumWidthOfBinaryTree {

public static class TreeNode {

int val;

TreeNode left;

TreeNode right;

TreeNode(int x) {

val = x;

}

}

private Map<Integer, List<Integer>> map;

public static void main(String[] args) {}

public int widthOfBinaryTree(TreeNode root) {

map = new HashMap<>();

preorder(root, 1, 1);

int max = 0;

for (int k : map.keySet()) {

List<Integer> list = map.get(k);

if (list.size() == 1) {

max = Math.max(max, 1);

} else {

max = Math.max(max, list.get(list.size() - 1) - list.get(0) + 1);

}

}

return max;

}

private void preorder(TreeNode node, int level, int pos) {

if (node != null) {

preorder(node.left, level + 1, pos * 2);

map.putIfAbsent(level, new ArrayList<>());

map.get(level).add(pos);

preorder(node.right, level + 1, pos * 2 + 1);

}

}

}