Learn and practice the Cyclic Sort and Topological Sort patterns to solve coding interview problems.

Speedrun the Netflix Coding Interview: Top Problems in Python

This module will focus on two advanced sorting algorithms, Cyclic Sort and Topological Sort. These are often used in coding interviews as a way to distinguish between average and outstanding candidates. Cyclic Sort may only be used if the input list meets certain criteria, and in those situations, it’s the most efficient sorting algorithm possible. Topological Sort utilizes graph-based algorithms to deal with partially ordered elements. This module teaches us to recognize whether either of these advanced sorting techniques is applicable, as well as how to use them to solve the given problem.

Advanced Sorting Techniques

# Statement

You are given an integer, `num_courses`, representing the total number of courses you need to complete, labeled from `0` to `num_courses - 1`.

You are also given a `prerequisites` array, where `prerequisites[i] = [a[i], b[i]]` indicates that you must take course `b[i]` first if you want to take the course `a[i]`. For example, the pair $[1, 0]$ indicates that to take course $1$, you have to first take course $0$.

Return TRUE if all of the courses can be finished. Otherwise, return FALSE.

**Constraints:**

- $1 \leq$ `num_courses` $\leq 1500$
- $0 \leq$ `prerequisites.length` $\leq 1000$
- `prerequisites[i].length` $= 2$
- $0 \leq$ `a[i]`, `b[i]` $<$ `num_courses`
- All the pairs `prerequisites[i]` are unique.

# Solution

Initialize the hash map with the vertices and their children. We'll use another hash map to keep track of the number of in-degrees of each vertex. Then we'll find the source vertex (with $0$ in-degree) and increment the `counter`. Retrieve the source node's children and add them to the queue. Decrement the in-degrees of the retrieved children.
We'll check whether the in-degree of the child vertex becomes equal to zero, and we increment the `counter`.
Repeat the process until the queue is empty.

> **Note:** The in-degree is the number of edges coming into a vertex in a directed graph.

The primary purpose of finding a vertex with 0 in-degree is to find a course with a pre-requisite count of 0. When we take a course, say a (that is the pre-requisite of another course, say b), we'll decrement the in-degree of b by 1, and if the in-degree count becomes 0, we can say that the b's pre-requisites have been completed.


The slide deck below illustrates the algorithm above, where `num_courses = 6`:




Let's solve the Course Schedule problem using the Topological Sort pattern.

Cyclic Sort

Topological Sort

Conclusion

Solution: Course Schedule

Statement