Test Yourself #1

1. A:1 B:2 C:3 D:4 E:5
2. A:1 B:2 D:3 C:4 E:4
3. A:1 C:2 B:3 D:4 E:5
4. A:1 C:2 D:3 B:4 E:5
5. A:1 C:2 D:3 E:4 B:5
6. A:1 D:2 B:3 C:4 E:5
7. A:1 D:2 C:3 B:4 E:5
8. A:1 D:2 C:3 E:4 B:5

Question 2:

static boolean numberGraph(Graph G) throws CycleException {
    int N = G.numNodes();
    mark all nodes unvisited;
    for each node k in the graph {
       if (node k is marked unvisited) {
          N = topNum(k, N);
       }
    }
}

Question 3: The following code determines whether graph G is connected, assuming that each node has a list of its predecessors as well as a list of its successors:

static boolean isConnected(Graph G) {
    if G has 0 nodes return true
    else {
        mark all nodes "unvisited"
        pick a node n
	modifiedDfs(n)  // mark all nodes reachable from n going
	                // either forwards or backwards along edges
    }

    // if any node is NOT marked "visited", the graph is not connected
    for each node k {
        if k is marked "unvisited" return false
    }
    return true
}

private static void modifiedDfs(Node n) {
    mark n "visited"

    // go backwards along edges into n
    for each predecessor m {
       if m is marked "unvisited" modifiedDfs(m)
    }

    // go forwards along edges out of n
    for each succecessor m {
       if m is marked "unvisited" modifiedDfs(m)
    }
}