Find all paths of length L in 2 D grid in C++ - c++

Question

I'm trying to find all paths of length L in a 2-D grid(forgetting boundaries for the moment) by calling route(string s) recursively and appending to the stringth.
'l' stands for left
'r' stands for right
'd' stands for down
and
'u' stands for up
My logic is correct I think. I need to call route(string s) recursively with each of these values and append to s.
I can see the flaw in my code but cannot think of a way to correct it. I am changing the value of string s by appending to it 'r','l','u' or 'd' at each call but since successive calls are in the same scope, i get garbage answers and not the permutations of u,l,d,r that I am expecting.
#include <iostream>
#include <vector>
using namespace std;
void route(string s, int k);
int main(void){
string result="";
route("",5);
}
void route(string initial, int k){
if(initial.length()>5){
cout<<initial<<endl;
cout<<"Length of initial:"<<initial.length();
return;
}
for(int i=0;i<4;i++){
switch(i){
case 0:
{
initial.append("r");
route(initial);
}
case 1:
{
initial.append("l");
route(initial);
}
case 2:
{
initial.append("u");
route(initial);
}
case 3:
{
initial.append("d");
route(initial);
}
}
}
}

Answer 1

There is no need to change initial, just pass the new string to route. e.g.
route(initial + "u",k-1);
Note that you aren't using the k value currently, and you also aren't recursing for the r and l cases.
One more thing - a for loop with a switch in it for each different case, is a strange construction. Why not just call the 4 different options one after the other?
route(initial + "l",k-1);
route(initial + "r",k-1);
route(initial + "u",k-1);
route(initial + "d",k-1);