Maximum Path Sum is an algorithm to find out a path such that sum of element(node) of that path is greater than any other path.
For example, let's we have a we a triangle as shown below.
3 7 4 2 4 6 8 5 9 3
In above triangle, find the maximum path which has maximum sum.
3 + 7 + 4 + 9 = 23
To find out the solution, as always we get an idea of Brute-Force method. Brute-Force method is good for this 4 rows triangle but think about a triangle with 100 or more than 100 rows. So, We can not use Brute-Force method to solve this problem.
Let's move to dynamic programming approach.
For each and every node in a triangle or in a binary tree there can be four ways that the max path goes through the node.
Example of Maximum Path Sum Algorithm: