path-finding

I'm sure you've all heard of the "Word game", where you try to change one word to another by changing one letter at a time, and only going through valid English words. I'm trying to implement an A* Algorithm to solve it (just to flesh out my understanding of A*) and one of the things that is needed is a minimum-distance heuristic. That is, the minimum number of one of these three mutations that can turn an arbitrary string a into another string b: 1) Change one letter for another 2) Add one letter at a spot before or after any letter 3) Remove any letter Examples aabca => abaca: aabca abca

I want to make a code giving the shortest route when given a labyrinth as a matrix. In this case, the matrix representation of this labyrinth is as follows. ## [,1] [,2] [,3] [,4] ## [1,] 2 0 0 0 ## [2,] 1 1 0 1 ## [3,] 0 1 0 0 ## [4,] 1 1 1 3 , where 0 denotes inaccessible points, 1 denotes accessible points. 2 denotes the starting point, and 3 denotes the destination. And, the desired result is this : c(4,1,4,4,1,1) , where 1 denotes East, 2 denotes North, 3 denotes West, and 4 denotes South. I guess that one possible code might be a function giving the shortest route as a vector when it is

Algorithms like the Bellman-Ford algorithm and Dijkstra's algorithm exist to find the shortest path from a single starting vertex on a graph to every other vertex. However, in the program I'm writing, the starting vertex changes a lot more often than the destination vertex does. What algorithm is there that does the reverse--that is, given a single destination vertex, to find the shortest path from every starting vertex? Just reverse all the edges, and treated destination as start node. Problem solved. If this is an undirected graph: I think inverting the problem would give you advantages.

We are given a weighed graph G and its Shortest path distance's matrix delta. So that delta(i,j) denotes the weight of shortest path from i to j (i and j are two vertexes of the graph). delta is initially given containing the value of the shortest paths. Suddenly weight of edge E is decreased from W to W'. How to update delta(i,j) in O(n^2)? (n=number of vertexes of graph) The problem is NOT computing all-pair shortest paths again which has the best O(n^3) complexity. the problem is UPDATING delta, so that we won't need to re-compute all-pair shortest paths. More clarified : All we have is a

How can I find a non-linear path through raster image data? e.g., least cost algorithm? Starting and ending points are known and given as: Start point = (0,0) End point = (12,-5) For example, extract the approximate path of a winding river through a (greyscale) raster image. # fake up some noisy, but reproducible, "winding river" data set.seed(123) df <- data.frame(x=seq(0,12,by=.01), y=sapply(seq(0,12,by=.01), FUN = function(i) 10*sin(i)+rnorm(1))) # convert to "pixels" of raster data # assumption: image color is greyscale, only need one numeric value, v img <- data.frame(table(round(df$y,0),

I know that A* is better than Dijkstra's algorithm because it takes heuristic values into account, but from A* and Jump Point search which is the most efficient algorithm for finding the shortest path in an environment with obstacles? and what are the differences? Jump Point Search is an improved A* based on some conditions on the graph. Thus, if you meet these conditions (uniform-cost grid mostly), JPS is strictly better than A* (same optimality, best cases can be order of magnitudes better and worse case is probably the same complexity but with a slightly worse constant), but if you do not