A* (star) Algorithm

http://web.mit.edu/eranki/www/tutorials/search/

It's the leading pathfinding algorithm! Not a BFS nor a DFS, it's a combination of Dijkstra's algorithm and best fit.

The general idea is :

f = g + h
f is the cost function of the node. 
g if the cost it took to get the target node, pretty much the paths it passed by from the start node.
h is the cost to get to the target node.

Following is the pseudo code:

while the open list is not empty
    find the node with the least f on the open list, call it "q"
    pop q off the open list
    generate q's 8 successors and set their parents to q
    for each successor
        if successor is the goal, stop the search
        successor.g = q.g + distance between successor and q
        successor.h = distance from goal to successor
        successor.f = successor.g + successor.h

        if a node with the same position as successor is in the OPEN list \
            which has a lower f than successor, skip this successor
        if a node with the same position as successor is in the CLOSED list \ 
            which has a lower f than successor, skip this successor
        otherwise, add the node to the open list
    end
    push q on the closed list
end