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+---
+title: Topological Sort
+description: 'Topological sort or topological ordering of a directed graph is an ordering of nodes such that every node appears in the ordering before all the nodes it points to. '
+hidden: true
+---
+
+## Directed Graph
+
+Before we get started on topological order, let's talk about directed graphs first. A graph is directed when its edges have directions (these edges are also called arcs). Suppose that v, w are vertices in a directed graph. Let's get familiar with a few concepts.
+
+- in-edge - an edge pointing to or coming into the node
+- out-edge - an edge pointing away or going out from the node (we will refer those nodes on the other end of the out-edges of v to v's neighbors)
+- in-degree - the number of in-edges coming into the node
+- out-degree - the number of out-edges going out from the node
+- dependency - "v depends on w" / "v is dependent on w" means that there is a directed path from w to v where v, w are vertices in a directed graph. With these new terms under our belt, it will make more sense when we talk about directed graphs.
+
+## What is a topological order?
+
+Topological sort is not unique. For example, for a graph like this:
+
+![Topological sort example](../../public/topo_intro_1.png)
+
+Both `[4, 5, 2]` and `[5, 4, 2]` are valid topological orders. 
+
+![Topological sort example](../../public/topo_intro_2.png)
+
+Task 3 is completely independent of task 2 and 4, and it can be anywhere in the order as long as it is before task 1 which depends on it. All of the following ordering are valid topological orderings.
+
+`[4, 2, 3, 1], [4, 3, 2, 1], [3, 4, 2, 1]`
+
+
+:::warning[Graphs with Cycles Do Not Have Topological Ordering]
+It should be obvious that if a graph with a cycle does not have a topological ordering. In the above example, 2 has to come before 5 which has come before 4 which has to come before 2 which has to come before 5... which is impossible.
+:::
+
+
+##  Example Code
+
+:::note
+Notice the topological sort algorithm is very similar to BFS. The main difference is that we only push nodes with 0 in-degree into the queue in topological sort whereas in BFS we push all the neighboring nodes into the queue.
+:::
+
+```py
+from collections import deque
+
+def find_indegree(graph):
+    indegree = { node: 0 for node in graph }  # dict
+    for node in graph:
+        for neighbor in graph[node]:
+            indegree[neighbor] += 1
+    return indegree
+
+
+def topo_sort(graph):
+    res = []
+    q = deque()
+    indegree = find_indegree(graph)
+    for node in indegree:
+        if indegree[node] == 0:
+            q.append(node)
+    while len(q) > 0:
+        node = q.popleft()
+        res.append(node)
+        for neighbor in graph[node]:
+            indegree[neighbor] -= 1
+            if indegree[neighbor] == 0:
+                q.append(neighbor)
+    return res if len(graph) == len(res) else None
+```
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