This notebook was prepared by Donne Martin. Source and license info is on GitHub.

# Solution Notebook¶

## Constraints¶

• Is it possible to have a cyclic graph as the input?
• Yes
• Can we assume we already have Graph and Node classes?
• Yes
• Can we assume this is a connected graph?
• Yes
• Can we assume the inputs are valid?
• Yes
• Can we assume this fits memory?
• Yes

## Test Cases¶

• projects: a, b, c, d, e, f, g
• dependencies: (d, g), (f, c), (f, b), (f, a), (c, a), (b, a), (a, e), (b, e)
• output: d, f, c, b, g, a, e

Note: Edge direction is down

    f     d
/|\    |
c | b   g
\|/|
a |
|/
e


Test a graph with a cycle, output should be None

## Algorithm¶

We can determine the build order using a topological sort.

• Build the graph with projects (nodes) and dependencies (directed edges)
• Add initially non-dependent nodes to processed_nodes
• If none exist, we have a circular dependency, return None
• While the length processed_nodes < the length of graph nodes
• Remove outgoing edges from newly added items in processed_nodes
• Add non-dependent nodes to processed_nodes
• If we didn't add any nodes, we have a circular dependency, return None
• Return processed_nodes

Complexity:

• Time: O(V + E)
• Space: O(V + E)

## Code¶

In [1]:
from collections import deque

class Dependency(object):

def __init__(self, node_key_before, node_key_after):
self.node_key_before = node_key_before
self.node_key_after = node_key_after

In [2]:
%run ../graph/graph.py

In [3]:
class BuildOrder(object):

def __init__(self, dependencies):
self.dependencies = dependencies
self.graph = Graph()
self._build_graph()

def _build_graph(self):
for dependency in self.dependencies:
dependency.node_key_after)

def _find_start_nodes(self, processed_nodes):
nodes_to_process = {}
for key, node in self.graph.nodes.items():
if node.incoming_edges == 0 and key not in processed_nodes:
nodes_to_process[key] = node
return nodes_to_process

def _process_nodes(self, nodes_to_process, processed_nodes):
for node in nodes_to_process.values():
# We'll need to iterate on copies since we'll need
# to change the dictionaries during iteration with
# the remove_neighbor call
processed_nodes[node.key] = node
nodes_to_process = {}

def find_build_order(self):
result = []
nodes_to_process = {}
processed_nodes = {}
while len(result) != len(self.graph.nodes):
nodes_to_process = self._find_start_nodes(processed_nodes)
if not nodes_to_process:
return None
result.extend(nodes_to_process.values())
self._process_nodes(nodes_to_process, processed_nodes)
return result


## Unit Test¶

In [4]:
%run ../utils/results.py

In [5]:
%%writefile test_build_order.py
import unittest

class TestBuildOrder(unittest.TestCase):

def __init__(self, *args, **kwargs):
super(TestBuildOrder, self).__init__()
self.dependencies = [
Dependency('d', 'g'),
Dependency('f', 'c'),
Dependency('f', 'b'),
Dependency('f', 'a'),
Dependency('c', 'a'),
Dependency('b', 'a'),
Dependency('a', 'e'),
Dependency('b', 'e'),
]

def test_build_order(self):
build_order = BuildOrder(self.dependencies)
processed_nodes = build_order.find_build_order()

expected_result0 = ('d', 'f')
expected_result1 = ('c', 'b', 'g')
self.assertTrue(processed_nodes[0].key in expected_result0)
self.assertTrue(processed_nodes[1].key in expected_result0)
self.assertTrue(processed_nodes[2].key in expected_result1)
self.assertTrue(processed_nodes[3].key in expected_result1)
self.assertTrue(processed_nodes[4].key in expected_result1)
self.assertTrue(processed_nodes[5].key is 'a')
self.assertTrue(processed_nodes[6].key is 'e')

print('Success: test_build_order')

def test_build_order_circular(self):
self.dependencies.append(Dependency('e', 'f'))
build_order = BuildOrder(self.dependencies)
processed_nodes = build_order.find_build_order()
self.assertTrue(processed_nodes is None)

print('Success: test_build_order_circular')

def main():
test = TestBuildOrder()
test.test_build_order()
test.test_build_order_circular()

if __name__ == '__main__':
main()

Overwriting test_build_order.py

In [6]:
%run -i test_build_order.py

Success: test_build_order
Success: test_build_order_circular