algorithm - Finding all paths between two nodes on a DAG -

i have dag has following adjacency list

l | g, b, p g | p, b | p | i | r r | \ 

i want find paths l r. know have kind of dfs, , have far. (excuse javascript)

function dfs(g, start_vertex) {      const fringe = []     const visited = new set()     const output = []     fringe.push(start_vertex)      while (fringe.length != 0) {         const vertex = fringe.pop()         if (!visited.has(vertex)) {             output.push(vertex)             (neighbor in g[vertex].neighbors) {                 fringe.push(neighbor)             }             visited.add(vertex)         }     }      return output } 

the output of dfs(g, "l") [ 'l', 'p', 'i', 'r', 'b', 'g' ] indeed depth first traversal of graph, not result i'm looking for. after doing searching, realize there may recursive solution, there comments problem being "np-hard" , "exponential paths" don't understand.

all paths start head vertex vertex can split paths heads head||v v adjacent final vertex of head, unless final vertex of head vertex: (pseudo-javascript, can have syntax problems)

function print_all_rec(g, head, vertex){   if(head[head.length-1] == vertex){     print(head); //we're here     return;   }   for(v in head[head.length-1].neighbors){     var newhead = head; newhead.append(v);     print_all_rec(g, newhead, vertex);   } }  function print_all_routes(g, from, to){   var start = [];   start.append(from);   print_all_rec(g, start, to); }