Question Definition
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.
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. Example 1:
Input:
1
/ \
3 2
/ \ \
5 3 9
Output: 4
Explanation: The maximum width existing in the third level with the length 4 (5,3,null,9).
Example 2:
Input:
1
/
3
/ \
5 3
Output: 2
Explanation: The maximum width existing in the third level with the length 2 (5,3).
Example 3:
Input:
1
/ \
3 2
/
5
Output: 2
Explanation: The maximum width existing in the second level with the length 2 (3,2).
Example 4:
Input:
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).
Note: Answer will in the range of 32-bit signed integer.
Java Solution
public int widthOfBinaryTree(TreeNode root) {
int res = 0;
List<Integer> start = new LinkedList();
return helper(root, 0, 1, start, 0);
}
private int helper(TreeNode node, int h, int idx, List<Integer> start, int res) {
if (node == null) return res;
if (h >= start.size()) start.add(idx);
res = Math.max(res, idx - start.get(h) + 1);
res = Math.max(res, helper(node.left, h + 1, idx * 2, start, res));
res = Math.max(res, helper(node.right, h + 1, idx * 2 + 1, start, res));
return res;
}
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