Find all possible path between two nodes in a undirected graph

开发者_开发百科Can anybody give me a C Code to find all possible paths between two nodes? eg. if the graph has following edges 1-2 1-3 2-3 2-4 3-4

all paths between 1 and 4 are:

1-2-3-4

1-2-4

1-3-4

1-3-2-4

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A Depth-First Search does this job.

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(I'm assuming you don't want repeated nodes in your path - otherwise the number of possible paths is infinite.)

You can do a relaxation:

while (there is a change) {
  for (v in nodes(G)) {
    for (e in edges(v)) {
      paths_to[v] = paths_to[v] union ((paths_to[e.to] not containing v) append v)
    }
  }
}

The result can still be exponential in the size of the input graph. Getting all paths is probably not what you want to do.

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This is a simple algorithm to the problem. It is not an optimal algorithm.

static struct {
  int value1;
  int value2;
  int used;
} data[] = {
  { 1, 2 },
  { 1, 3 },
  { 2, 3 },
  { 2, 4 },
  { 3, 4 },
};

enum { DATA_SIZE = sizeof data / sizeof *data };

static int output[DATA_SIZE];

int traverse(int from, int to, int depth) {
  output[depth++] = from;

  int i;
  if (from == to) {
    for (i = 0; i < depth; i++) {
      if (i) {
        printf("-");
      }
      printf("%d", output[i]);
    }
    printf("\n");
  } else {
    for (i = 0; i < DATA_SIZE; i++) {
      if (!data[i].used) {
        data[i].used = 1;

        if (from == data[i].value1) {
          traverse(data[i].value2, to, depth);
        } else if (from == data[i].value2) {
          traverse(data[i].value1, to, depth);
        }

        data[i].used = 0;
      }
    }
  }
}

int main() {
  traverse(1, 4, 0);
}

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a recursive method:

findPaths(path = startNode, goal)
    paths = []
    if the last node in path is goal:
        return path
    for each node n connected to the last node in path:
        if n is not already on the path:
            paths.append(findPaths(path.append(node), goal))
    return paths //may still be []

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It is too late and not the C code but may be help others. This algo show how I implement it in java.

findPath(start) 
    Childs = getDirectChildsOf(start)
    foreach child in Childs
        tempRoute;
        tempRoute.add(start)
        if (child == end)
            return tempRoute.add(child) 
        else 
            tempRoute.add(findPath(child))
            if (tempRoute.last() == end)
                return tempRoute;

Here tempRoute may be a Route class that maintain a list of node. Able to add single node and other route to tempRoute. It also not find all possible path. for that you have to maintain a visited flag for each node.