# Posts tagged as “shortest path”

Problem:

Given a binary tree, you need to compute the length of the diameter of the tree. The diameter of a binary tree is the length of the longest path between any two nodes in a tree. This path may or may not pass through the root.

Example:
Given a binary tree

Return 3, which is the length of the path [4,2,1,3] or [5,2,1,3].

Note: The length of path between two nodes is represented by the number of edges between them.

Idea:

Recursion

Solution1:

C++

Solution 2: passed 101/106 TLE

C++ / Floyd-Warshall

Solution 3:

Simulate recursion with a stack. We also need to track the return value of each node.

Python

C++

Related Problems:

Problem:

Given two words (beginWord and endWord), and a dictionary’s word list, find the length of shortest transformation sequence from beginWord to endWord, such that:

1. Only one letter can be changed at a time.
2. Each transformed word must exist in the word list. Note that beginWord is not a transformed word.

For example,

Given:
beginWord = "hit"
endWord = "cog"
wordList = ["hot","dot","dog","lot","log","cog"]

As one shortest transformation is "hit" -> "hot" -> "dot" -> "dog" -> "cog",
return its length 5.

Note:

• Return 0 if there is no such transformation sequence.
• All words have the same length.
• All words contain only lowercase alphabetic characters.
• You may assume no duplicates in the word list.
• You may assume beginWord and endWord are non-empty and are not the same.

Idea:

BFS

Time Complexity: O(n*26^l) -> O(n*26^l/2), l = len(word), n=|wordList|

Space Complexity: O(n)

# Related Problems

https://leetcode.com/problems/cut-off-trees-for-golf-event/

Problem:

You are asked to cut off trees in a forest for a golf event. The forest is represented as a non-negative 2D map, in this map:

1. 0 represents the obstacle can’t be reached.
2. 1 represents the ground can be walked through.
3. The place with number bigger than 1 represents a tree can be walked through, and this positive number represents the tree’s height.

You are asked to cut off all the trees in this forest in the order of tree’s height – always cut off the tree with lowest height first. And after cutting, the original place has the tree will become a grass (value 1).

You will start from the point (0, 0) and you should output the minimum steps you need to walk to cut off all the trees. If you can’t cut off all the trees, output -1 in that situation.

You are guaranteed that no two trees have the same height and there is at least one tree needs to be cut off.

Example 1:

Example 2:

Example 3:

Hint: size of the given matrix will not exceed 50×50.

Idea:

Greedy + Shortest path

Identify and sort the trees by its heights, then find shortest paths between

0,0 to tree[1]
tree[1] to tree[2]

tree[n-1] to tree[n]

Time complexity: O(m^2n^2)

Space complexity: O(mn)

Solution:

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