Skip to content

Navigation Menu

Sign in
Appearance settings

Search code, repositories, users, issues, pull requests...

Provide feedback

We read every piece of feedback, and take your input very seriously.

Saved searches

Use saved searches to filter your results more quickly
Sign up
Appearance settings

Commit 068dd9c

Browse files
feat(book/bt): add binary tree diameter problem
1 parent 464417e commit 068dd9c

File tree

7 files changed

+234
-1
lines changed

7 files changed

+234
-1
lines changed

‎book/D-interview-questions-solutions.asc

Lines changed: 78 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -332,6 +332,84 @@ As you can see, we opted for using a set to trade speed for memory.
332332

333333

334334

335+
:leveloffset: +1
336+
337+
=== Solutions for Binary Tree Questions
338+
(((Interview Questions Solutions, Binary Tree)))
339+
340+
:leveloffset: -1
341+
342+
[#binary-tree-q-diameter-of-binary-tree]
343+
include::content/part03/tree-intro.asc[tag=binary-tree-q-diameter-of-binary-tree]
344+
345+
We are asked to find the longest path on binary tree that might or might not pass through the root node.
346+
347+
We can calculate the height (distance from root to farthest leaf) of a binary tree using this recursive function:
348+
349+
[source, javascript]
350+
----
351+
function getHeight(node) {
352+
if (!node) return 0;
353+
const leftHeight = getHeight(node.left);
354+
const rightHeight = getHeight(node.right);
355+
return 1 + Math.max(leftHeight, rightHeight);
356+
}
357+
----
358+
359+
That will give use the height from furthest leaf to root. However, the problem says that it might or might not go through the root.
360+
In that case, we can keep track of the maximun distance (`leftHeight + rightHeight`) seen so far.
361+
362+
*Algorithm*:
363+
364+
- Initialize diameter to `0`
365+
- Recursively find the height of the tree from root.
366+
- Keep track of the maximun diameter length seen so far (left + right).
367+
- Return the diameter.
368+
369+
*Implementation*:
370+
371+
[source, javascript]
372+
----
373+
include::interview-questions/diameter-of-binary-tree.js[tags=description;solution]
374+
----
375+
376+
We are using `Math.max` to keep track of the longest diameter seen.
377+
378+
*Complexity Analysis*:
379+
380+
- Time: `O(n)`, where `n` is each one of the nodes on the tree. We visite each one once.
381+
- Space: `O(n)`. We use `O(1)` variables, but because we are using the `height` recursive function we are using the implicit call stack, thus `O(n)`.
382+
383+
384+
385+
386+
[#binary-tree-q-diameter-of-binary-tree2]
387+
include::content/part03/tree-intro.asc[tag=binary-tree-q-diameter-of-binary-tree]
388+
389+
RESTATE REQUIREMENTS AND DESCRIPTIONS
390+
391+
*Algorithm*:
392+
393+
- STEP 1
394+
- STEP 2
395+
- STEP 2.1
396+
- STEP 2.2
397+
398+
*Implementation*:
399+
400+
[source, javascript]
401+
----
402+
include::interview-questions/diameter-of-binary-tree.js[tag=description]
403+
include::interview-questions/diameter-of-binary-tree.js[tag=solution]
404+
----
405+
406+
IMPLEMENTATION NOTES
407+
408+
*Complexity Analysis*:
409+
410+
- Time: `O(?)`. WHY?
411+
- Space: `O(?)`. WHY?
412+
335413

336414
// [#linkedlist-q-FILENAME]
337415
// include::content/part02/linked-list.asc[tag=linkedlist-q-FILENAME]

‎book/config

Submodule config updated from d3399d4 to 2134d49

‎book/content/part03/tree-intro.asc

Lines changed: 103 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -109,3 +109,106 @@ image::image35.png[image,width=258,height=169]
109109
Heap is better at finding max or min values in constant time *O(1)*, while a balanced BST is good a finding any element in *O(log n)*. Heaps are often used to implement priority queues while BST is used when you need every value sorted.
110110
****
111111
indexterm:[Runtime, Logarithmic]
112+
113+
114+
==== Practice Questions
115+
(((Interview Questions, Binary Tree)))
116+
117+
118+
// tag::binary-tree-q-diameter-of-binary-tree[]
119+
===== Binary Tree Diameter
120+
121+
*BT-1*) _Find the diameter of a binary tree. The diameter of a tree is defined as the longest possible path from two nodes (it doesn't need to include the root). The lenth of diameter is calculated by couting the number of edges on the path._
122+
123+
// end::binary-tree-q-diameter-of-binary-tree[]
124+
125+
_Seen in interviews at: Facebook, Amazon, Google_
126+
127+
Example 1:
128+
129+
[graphviz, tree-diameter-example-1, png]
130+
....
131+
graph G {
132+
1 -- 2 [color=red]
133+
1 -- 3 [color=red]
134+
135+
2 -- 4
136+
2 -- 5 [color=red]
137+
}
138+
....
139+
140+
[source, javascript]
141+
----
142+
diameterOfBinaryTree(toBinaryTree([1,2,3,4,5])); // 3 (the path 3-1-2-5 or 3-1-2-4)
143+
----
144+
145+
Example 2:
146+
147+
[graphviz, tree-diameter-example-2, png]
148+
....
149+
graph G {
150+
1
151+
2
152+
3
153+
4
154+
5
155+
6
156+
"null" [color=white, fontcolor = white]
157+
"null." [color=white, fontcolor = white]
158+
7
159+
8
160+
"null.." [color=white, fontcolor = white]
161+
"null..." [color=white, fontcolor = white]
162+
9
163+
164+
1 -- 2
165+
1 -- 3
166+
167+
3 -- 4 [color=red]
168+
3 -- 5 [color=red]
169+
170+
4 -- 6 [color=red]
171+
4 -- "null." [color=white]
172+
173+
5 -- "null" [color=white]
174+
5 -- 7 [color=red]
175+
176+
6 -- 8 [color=red]
177+
6 -- "null.." [color=white]
178+
179+
7 -- "null..." [color=white]
180+
7 -- 9 [color=red]
181+
}
182+
....
183+
184+
[source, javascript]
185+
----
186+
diameterOfBinaryTree(toBinaryTree([1,2,3,null,null,4,5,6,null,null,7,8,null,null,9])); // 6 (the path 8-6-4-3-5-7-9)
187+
----
188+
189+
Starter code:
190+
191+
[source, javascript]
192+
----
193+
include::../../interview-questions/diameter-of-binary-tree.js[tags=description;placeholder]
194+
----
195+
196+
197+
_Solution: <<binary-tree-q-diameter-of-binary-tree>>_
198+
199+
200+
201+
// tag::binary-tree-q-FILENAME[]
202+
===== Recent Counter
203+
204+
*BT-2*) _._
205+
206+
Example:
207+
208+
[source, javascript]
209+
----
210+
211+
----
212+
213+
_Seen in interviews at: X_
214+
// end::binary-tree-q-FILENAME[]

‎book/images/tree-diameter-example-1.png

10.7 KB
Loading[フレーム]

‎book/images/tree-diameter-example-2.png

22.3 KB
Loading[フレーム]
Lines changed: 31 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,31 @@
1+
// tag::description[]
2+
/**
3+
* Find the length of the binary tree diameter.
4+
*
5+
* @param {BinaryTreeNode | null} root - Binary Tree's root.
6+
* @returns {number} tree's diameter (longest possible path on the tree)
7+
*/
8+
function diameterOfBinaryTree(root) {
9+
// end::description[]
10+
// tag::placeholder[]
11+
// write your code here...
12+
// end::placeholder[]
13+
// tag::solution[]
14+
let diameter = 0;
15+
16+
const height = (node) => {
17+
if (!node) return 0;
18+
const left = height(node.left);
19+
const right = height(node.right);
20+
diameter = Math.max(diameter, left + right);
21+
return 1 + Math.max(left, right);
22+
};
23+
24+
height(root);
25+
return diameter;
26+
// end::solution[]
27+
// tag::description[]
28+
}
29+
// end::description[]
30+
31+
module.exports = { diameterOfBinaryTree };
Lines changed: 21 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,21 @@
1+
const { diameterOfBinaryTree } = require('./diameter-of-binary-tree');
2+
const { BinaryTreeNode } = require('../../src/index');
3+
4+
describe('Binary Tree: Diameter', () => {
5+
function toBinaryTree(array, index = 0) {
6+
if (index >= array.length) return null;
7+
const node = new BinaryTreeNode(array[index]);
8+
node.left = toBinaryTree(array, index * 2 + 1);
9+
node.right = toBinaryTree(array, index * 2 + 2);
10+
return node;
11+
}
12+
13+
it('should find the diameter', () => {
14+
expect(diameterOfBinaryTree(toBinaryTree([1, 2, 3, 4, 5]))).toEqual(3);
15+
});
16+
17+
it('should find the diameter when does not pass through the root node', () => {
18+
const tree = [1, 2, 3, null, null, 4, 5, 6, null, null, 7, 8, null, null, 9];
19+
expect(diameterOfBinaryTree(toBinaryTree(tree))).toEqual(6);
20+
});
21+
});

0 commit comments

Comments
(0)

AltStyle によって変換されたページ (->オリジナル) /