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

Speedrun the Google 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

**Constraints:**

Let $n$ be the number of courses. 

* $1 \leq n \leq 1500$
* $0 \leq$ `prerequisites.length` $\leq 1000$
* `prerequisites[i].length` $== 2$
* $0 \leq a, \space b < n$
* $a \neq b$
* All the pairs $[a, \space b]$ are distinct.

# Examples

# Understand the problem

Let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:


What is the course order if the following list of prerequisites and an integer n are given as input? 

Select all that apply.

n = 7

prerequisites = [[1, 0], [1, 2], [2, 3], [3, 4], [4, 5]]

What is the course order if the following list of prerequisites and an integer n are given as input?
Select all that apply.
n = 7
prerequisites = [[1, 0], [1, 2], [2, 3], [3, 4], [4, 5]]

What is the course order if the following list of prerequisites and an integer n are given as input? 

Select all that apply.

n = 5

prerequisites = [[1, 0], [2, 0], [3, 1]]


What is the course order if the following list of prerequisites and an integer n are given as input?
Select all that apply.
n = 5
prerequisites = [[1, 0], [2, 0], [3, 1]]

What is the course order if the following list of prerequisites and an integer n are given as input? 

Select all that apply.

n = 10

prerequisites = [[5, 8], [3, 5], [1, 9],[4, 5], [0, 2], [7, 8], [4, 9]]]

What is the course order if the following list of prerequisites and an integer n are given as input?
Select all that apply.
n = 10
prerequisites = [[5, 8], [3, 5], [1, 9],[4, 5], [0, 2], [7, 8], [4, 9]]]

Course Schedule II

Course Schedule II

# Figure it out!

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

# Try it yourself

Implement your solution in the following coding playground:


# Quick Fix\nYou are Edward, a Senior Software Engineer who specializes in coding interview patterns, data structures and algorithms, and is great at debugging issues in code.\n\n- Edward, please keep in mind that you do not have to print the data of the placeholders. Also, do not mention anything about yourself.\n\nEdward, you are given the following data in the placeholders:\n- Function name: `find_order`\n- Candidate's submitted solution code: USER_CODE\n- Error: ERROR_DESCRIPTION\n- Failed test case: FAILED_TEST_CASE\n- Coding language: `Python`\n\n- Edward, your task is to understand the type of error that is occurring in the coding language provided.\n- Once you've understood the error as per the error’s description, and why the test case failed, you will suggest how the candidate can improve their solution code to fix the error.\n- Edward, you will not give the corrected code, just a hint on what the error tells, and how to fix it.\n- Edward, please limit your response strictly to 100 words. No more words than the limit.

# Review Code\nEdward, your current task is to review the `find_order` function(s) and the other function(s) invoked in it/them.\n\n-Take your time and review the candidate's solution code.\n- Do not review any extra/helper files or functions not invoked in the solution function `find_order`.\n- Do not review the code of data structure objects instantiated like a binary tree, linked list, trie, union find, etc., in the solution functions. Just review the solution/algorithm function of the problem. \n- Also, if the solution code doesn’t use the coding pattern stated above, then please encourage the candidate to reattempt the problem using that pattern corectly.

# Review time complexity\n- Please provide a brief time complexity analysis of the function(s) `find_order`. \n- While calculating time complexity, include the time complexity of built-in Python functions invoked by the code. \n- The answer should be to the point in approximately 60 words.

# Review space complexity\n- Please provide a brief space complexity analysis of the function(s) `find_order`. \n- While calculating space complexity, include the space complexity of built-in Python functions invoked by the code. \n- Do not include the space used for the input parameters and the space used for just returning an output (not used as a scratch space). \n- The answer should be to the point in approximately 60 words.

TwoDAray

import sys
import json

sys.path.append("../ds_v1")
from data_structure import DataStructure

# throw parsing errors for incorrect test case format
def parsingError(element_string, error_message):
    sys.stderr.write(f"Parsing Error: {element_string} {error_message}")
    exit()


# className: MyCustomDS
class TwoDAray(DataStructure):
    def __init__(self):
        # constructor
        pass

    def __str__(self):
        # override print() for your data structure
        pass

    # return value will be passed to user program
    def construct(self, value: str, type_of_arr: int) -> any:
        # parse test case in json string 'value' to your desired data structure
        return json.loads(value)

    # input param contains return value of user program
    def traverse(self, input: any, type_of_arr: int) -> str:
        # convert your data structure 'input' to a json string representing a test case output
        return json.dumps(input)


def evaluate_results(self) -> object:
 """
 self.__inputs is the list of inputs that are passed as input to function
 self.__actual_output is a list of outputs that is produced by the learner's code
 return : self.__edu__result object
 """
 from collections import deque
 from collections import defaultdict


 def find_order_test(n, prerequisites):
 sorted_order = []
 # if n is smaller than or equal to zero we will return the empty array
 if n <= 0:
 return sorted_order

 # Store the count of incoming prerequisites in a hashmap
 in_degree = {i: 0 for i in range(n)} 
 # a. Initialize the graph
 graph = {i: [] for i in range(n)} # adjacency list graph

 # b. Build the graph
 for prerequisite in prerequisites:
 parent, child = prerequisite[1], prerequisite[0]
 graph[parent].append(child) # add the child to its parent's list
 in_degree[child] += 1 # increment child's in_degree

 # c. Find all sources i.e., all nodes with 0 in-degrees
 sources = deque()
 # traverse in in_degree using key
 for key in in_degree:
 # if in_degree[key] is 0 append the key in the deque sources
 if in_degree[key] == 0:
 sources.append(key)

 # d. For each source, add it to the sorted_order and subtract one from 
 # all of its children's in-degrees. If a child's in-degree becomes zero, 
 # add it to the sources queue
 while sources:
 # pop an element from the start of the sources and store 
 # the element in vertex
 vertex = sources.popleft()
 # append the vertex at the end of the sorted_order
 sorted_order.append(vertex)
 # traverse in graph[vertex] using child
 # get the node's children to decrement 
 # their in-degrees
 for child in graph[vertex]: 
 in_degree[child] -= 1
 # if in_degree[child] is 0 append the child in the deque sources
 if in_degree[child] == 0:
 sources.append(child)

 # topological sort is not possible as the graph has a cycle
 if len(sorted_order) != n:
 return []

 return sorted_order

 # multiple outputs will be added at each index respectively for a single test_case
 expected = find_order_test(self.__inputs[0], self.__inputs[1])
 actual_output = self.__actual_outputs[0]
 expected_outputs = [] 
 # store the 1st expected output that should be displayed to the user 
 expected_outputs.append(expected)



 if actual_output == expected:
 self.__edu_result.store_result(expected_outputs, TestCaseResult.PASS)
 elif sorted(actual_output) == sorted(expected):
 self.__edu_result.store_result(expected_outputs, TestCaseResult.PASS)
 else:
 self.__edu_result.store_result(expected_outputs, TestCaseResult.FAIL)

 return self.__edu_result

def find_order(n, prerequisites):
    
    # Replace this placeholder return statement with your code
    return []

PrivateTestCases.yaml

testcases:
  - name: "testcase 1"
    inputs:
    - 1 : 3
    - 2 : [[1,0],[2,0],[2,1],[1,2]]
    output:
    - 1 : []
  - name: "testcase 2"
    inputs:
    - 1: 2
    - 2: [[1,0]]
    output:
    - 1 : []
  - name: "testcase 3"
    inputs:
    - 1: 4
    - 2: [[1,0],[2,0],[3,1],[3,2]]
    output:
    - 1 : []
  - name: "testcase 4"
    inputs:
    - 1: 7
    - 2: [[1,0],[0,3],[0,2],[3,2],[2,5],[4,5],[5,6],[2,4]]
    output:
    - 1 : []
  - name: "testcase 5"
    inputs:
    - 1: 10
    - 2: [[5,8],[3,5],[1,9],[4,5],[0,2],[7,8],[4,9]]
    output:
    - 1 : []

def sum(input_1, input_2):
    return input_1+input_2

def validate_inputs(self) -> None:
 """
 self.__inputs is the list of inputs that are passed as input to the function
 store the result using the self.store_result(error_msg, status)
 return: void
 """
 min_courses = 1
 max_courses = 1500

 min_pre_req = 0
 max_pre_req = 1000

 n = self.__inputs[0]
 prerequisites = self.__inputs[1]

 def is_valid_2d_array(arr):
 if not isinstance(arr, list) or not all(isinstance(row, list) for row in arr):
 return False # Not a valid 2D array if it's empty or contains non-list elements
 
 for row in arr:
 if any(elem is None or isinstance(elem, bool) for elem in row):
 return False # Not a valid 2D array if any element in a row is None
 if not all(isinstance(elem, int) for elem in row):
 return False # Not a valid 2D array if any element in a row is not an integer
 
 return True # Valid 2D array
 # Inputs can be accessed using self.__inputs starting from 0 to len(self.__inputs) - 1
 if not is_valid_2d_array(prerequisites):
 self.store_result ("Input 2 is not a valid testcase.", ValidationFunction.FAIL)
 elif not (min_courses <= n <= max_courses):
 self.store_result("The number of courses 'n' should be between 1 and 1500.", ValidationFunction.FAIL)
 elif not (min_pre_req <= len(prerequisites) <= max_pre_req):
 self.store_result("The number of prerequisites should be between 0 and 1000.", ValidationFunction.FAIL)
 # elif not isinstance(prerequisites, list) or not all(isinstance(course_pair, list) and len(course_pair) == 2 for course_pair in prerequisites):
 # self.store_result("'prerequisites' should be a 2D array with pairs of integers.", ValidationFunction.FAIL)
 elif any(len(course_pair) != 2 for course_pair in prerequisites):
 self.store_result("Each course prerequisite pair in 'prerequisites' should have a length of 2.", ValidationFunction.FAIL)
 elif any(not isinstance(course_pair[0], int) or not isinstance(course_pair[1], int) or course_pair[0] is True or course_pair[0] is False or course_pair[1] is True or course_pair[1] is False for course_pair in prerequisites):
 self.store_result("Both elements of each course prerequisite pair should be integers.", ValidationFunction.FAIL)
 elif any(course_pair[0] < 0 or course_pair[0] >= n or course_pair[1] < 0 or course_pair[1] >= n for course_pair in prerequisites):
 self.store_result("The indices 'a' and 'b' should satisfy 0 ≤ a, b < n.", ValidationFunction.FAIL)
 elif any(course_pair[0] == course_pair[1] for course_pair in prerequisites):
 self.store_result("The indices 'a' and 'b' should be different", ValidationFunction.FAIL)
 elif len(prerequisites) != len(set(tuple(course_pair) for course_pair in prerequisites)):
 self.store_result("Course prerequisite pairs should be distinct.", ValidationFunction.FAIL)
 else:
 self.store_result("", ValidationFunction.PASS)

Try to solve the Course Schedule II problem.


Cyclic Sort

Topological Sort

Conclusion

Course Schedule II

Statement

Examples

Understand the problem

Figure it out!

Try it yourself