Shortest-Path-special

A shortest path algorithm with special input, solved with recursion

Overview

Given H amount of number h₁,h₂,...,h_H and V amount of number v₁,v₂,...,v_V
Horizontally H, Vertically V, H*V amount of vertex is arranged in a matrix.
These vertex make up a directional graph.
Let V_i,j be the vertex at i^th row and j^th column.
From every V_i,j, there are three directional edge going to V_i+1,j,V_i,j+1,V_i+1,j+1, assuming the vertex exists
Given H amount of number h₁,h₂,...,h_H and V amount of number v₁,v₂,...,v_V ,the cost of each of these edges is the absolute difference between h_i and v_j.
This algorithm finds the shortest path of the given graph

Input
H X
h₁,h₂,...,h_H
v₁,v₂,...,v_V

Output
three matrixes of H*V size.
The first matrix gives the cost of the edges going from the vertex.
The second matrix gives the total cost needed to go from 0,0 to that vertex.
The third matrix prints out the parent of the current vertex.