Depth first search: return values

Suppose we have the following graph:

            1 ——— 2
            |     
            4 ——— 5 ——— 6
            |     |     |     
            7 ——— 8 ——— 9

Where soughtValue is node 9. Starting from node 1 as source:

   wrong code:
   ===========
   dfs(1,9,…)                          dfs(2,9,…)  
       …                                    …
       // neighbors                        // neighbors          
       return dfs(2,9,…)  <———|            NO return dfs(1,9,…) as 1 has been visited
       return dfs(4,9,…)      |             
                              |             
                              |            so return false
                              |             |
                              |-------------|

   result
   dfs(1,9,…) terminates with a false even without going to dfs(4,9,…)



   correct code:
   ============
   dfs(1,9,…)                  dfs(2,9,…)     
        …                           …
       // neighbors                // neighbors                
       if (dfs(2,9,…)) <———|       NO if dfs(1,9,…) as as 1 has been visited
            return true    |           return true
                           |
       if (dfs(4,9,…))     |    
            return true    |    
                           |             
                           |        so return false
                           |             |
                           |-------------|

   result
   dfs(1,9,…) doesn't terminate and does continue to other neighbors (i.e., dfs(4,9,…)) and so on until we reach the soughtValue 9 and return true

We can't return any value, because if it's False, the for loop breaks and never finds the True that may be later..

Example:

def divisible_by_five_A():
    for n in range(100):
        if n and not n % 5:
            return n, 1

divisible_by_five_A()
# O: 5, 1

vs

def divisible_by_five_B():
    for n in range(100):
        return n, (n and not n % 5)

divisible_by_five_B()
# O: 0, 0

Yes, the search needs to continue if depthFirst(adjNode, soughtValue, visitedNodes) returns False. Only when you've found the sought value in that part of the graph then you can return True for your search.

If you were to replace that with return depthFirst(adjNode, soughtValue, visitedNodes) then you'll only search for the value in that part of the graph (starting from that adjacent node) but you won't continue your search in case the value isn't found there.