ctci/04. Trees and graphs/4.1. route_between_nodes.md

75 lines
1.8 KiB
Markdown

# 4.1. Route between nodes
> Given a directed graph and two nodes (S and E), is there a route from S to E?
A graph can be written like this:
```java
class Graph {
public Node[] nodes;
}
class Node {
public String name;
public Node[] children;
}
```
The function to find a route from S to E:
```java
bool findRoute(Node S, Node E) {
Node[] children = S.children;
for (int i = 0; i < children.size(); i++){
if (children[i] == E) {
return True;
}
if (children[i].children == Null) {
continue;
}
else if (findRoute(Node children[i].children, E)){
return True;
}
}
return False;
}
```
Example, Route from 5 to 11:
* 5
* 2
* 3
* 4
* 1
* 9
* 11
* 6
1. children = [2, 1, 6]
1. Recursive of 2, children = [3, 4]
2. None of them have children, continue, return False
2. Back to main loop, continue with children
1. recursive of 1, children = [9, 11]
2. found in children[1] == E, return True
3. Back to main loop, return True
Looks good, O(N) where N = all elements in graph, well if the graph isn't balanced at all we might have to iterate through it all.
## Hints
Two well known algorithms can do this, what are the tradeoffs between them?
1. Depth-first search (mine)
1. Check each node until the end
2. Breadth-first search
1. Cheack each main children first, then go deep
## Solution
Remember to **mark the found nodes as visited to avoid cycles and repetitions of nodes**.
For an iterative solution of breadh-first search, see Java files.
Depth-first search is a bit simpler to implement since it can be done with simple recursion. Breadth-first search can also be useful to find the shortest path, whereas depth-first search might traverse one adjacent node very deeply before ever going onto the immediate neighbors.