In A* after the finding the next node with the lowest F value, you have to search the adjacent nodes again. When you find a node that was already in the open list, you're supposed to check if the g score for that node would be lower if you went through the current node to get there. My question is, what is the point of this? Won't it always be the same? If you take G = 14 for diagonal and G = 10 for horizontal/vertical wouldn't the G always be more if you went through 2 nodes instead of one?
Say the last node on the closed list's G value was 50. It has an adjacent square to the right with a G value of 60. Your current node has a G value of 64. If you went through the current node to get to the node adjacent to the one with the G value of 50, the G would be 74. You could switch the numbers all you want but the recalculated G would always be higher so what is the point of recalculating it?