Learn and practice the Merge Intervals and K-way Merge patterns to solve coding interview problems.

Educative-77 in Python: Accelerate Your Coding Interview Prep

Many information processing and decision-support problems require us to merge information coming from multiple sources to build up a global picture of a situation before making some business decisions. This module will help us understand and deploy two common coding patterns used to merge lists of structurally homogeneous data to solve hard problems that we encounter, for example, in scheduling, social media applications, and I/O algorithms.

Fusion

# Statement

You’re given a list containing the schedules of multiple employees. Each person’s schedule is a list of non-overlapping intervals in sorted order. An interval is specified with the start and end time, both being positive integers. Your task is to find the list of finite intervals representing the free time for all the employees.

> **Note:** The common free intervals are calculated between the earliest start time and the latest end time of all meetings across all employees.

**Constraints:**

* $1 \leq$ `schedule.length` , `schedule[i].length` $\leq 50$

* $0 \leq$ `interval.start` < `interval.end` $\leq 10^8$, where `interval` is any interval in the list of schedules.

# 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:

From the given list of employee schedules, find the list of intervals representing the free time for all the employees.

[[[3, 5], [8, 10]], [[4, 6], [9, 12]], [[5, 6], [8, 10]]]

From the given list of employee schedules, find the list of intervals representing the free time for all the employees.
[[[3, 5], [8, 10]], [[4, 6], [9, 12]], [[5, 6], [8, 10]]]

From the given list of employee schedules, find the list of intervals representing the free time for all the employees.

[[[1, 3], [5, 6], [9, 10]],[[2, 4], [7, 8]], [[8, 11], [12, 14]]]

From the given list of employee schedules, find the list of intervals representing the free time for all the employees.
[[[1, 3], [5, 6], [9, 10]],[[2, 4], [7, 8]], [[8, 11], [12, 14]]]

From the given list of employee schedules, find the list of intervals representing the free time for all the employees.

[[[1, 2], [3, 4]], [[2, 3]], [[4, 6]]]

From the given list of employee schedules, find the list of intervals representing the free time for all the employees.
[[[1, 2], [3, 4]], [[2, 3]], [[4, 6]]]

Employee Free Time

Employee Free Time


# 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 `main.py` in the following coding playground. We have provided the definition of the `Interval` class in the other file. You may add functionality to this class if you wish.




class Interval:
    def __init__(self, start, end):
        self.start = start
        self.end = end
        self.closed = True  # by default, the interval is closed
    # set the flag for closed/open

    def set_closed(self, closed):
        self.closed = closed

    def __str__(self):
        return "[" + str(self.start) + ", " + str(self.end) + "]" \
            if self.closed else \
                "(" + str(self.start) + ", " + str(self.end) + ")"

# 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: `employee_free_time`\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 `employee_free_time` 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 `employee_free_time`.\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) `employee_free_time`. \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) `employee_free_time`. \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.

TwoDArray

ThreeDArray

import sys
import json

sys.path.append("../ds_v1")
from data_structure import DataStructure
from interval import *

# 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 TwoDArray(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, inp_string: str, type_of_arr: int) -> any:
 final_list = json.loads(inp_string) # string to list
 result = []
 result2 = []

 for i in range(len(final_list)):
 for j in range(len(final_list[i])):
 result2.append(Interval(final_list[i][j][0], final_list[i][j][1]))
 result.append(result2)
 result2 = []

 return result

 # input param contains return value of user program
 def traverse(self, input: any, type_of_arr: int) -> str:
 result_str = "["
 for i in range(len(input)):
 result_str += "[" + str(input[i].start) + \
 ", " + str(input[i].end) + "] "
 if i < len(input)-1:
 result_str += ", "
 result_str += "]"
 return result_str

import sys
import json

sys.path.append("../ds_v1")
from data_structure import DataStructure
from interval import *

# 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 ThreeDArray(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, inp_string: str, type_of_arr: int) -> any:
 final_list = json.loads(inp_string) # string to list
 result = []
 result2 = []

 for i in range(len(final_list)):
 for j in range(len(final_list[i])):
 result2.append(Interval(final_list[i][j][0], final_list[i][j][1]))
 result.append(result2)
 result2 = []

 return result

 # input param contains return value of user program
 def traverse(self, input: any, type_of_arr: int) -> str:
 result_str = "["
 for i in range(len(input)):
 result_str += "[" + str(input[i].start) + \
 ", " + str(input[i].end) + "] "
 if i < len(input)-1:
 result_str += ", "
 result_str += "]"
 return result_str

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
 """
 def employee_free_time(schedule):
 import heapq
 heap = []

 for i in range(len(schedule)):
 heap.append((schedule[i][0][0], i, 0))

 heapq.heapify(heap)

 result = []
 previous = schedule[heap[0][1]][heap[0][2]][0]

 while heap:
 _, i, j = heapq.heappop(heap)
 interval = schedule[i][j]

 if interval[0] > previous:
 result.append([previous, interval[0]])

 previous = max(previous, interval[1])

 if j + 1 < len(schedule[i]):
 heapq.heappush(heap, (schedule[i][j + 1][0], i, j + 1))

 return result





 # multiple outputs will be added at each index respectively for a single test_case
 expected_outputs = [] 
 # store the 1st expected output that should be displayed to the user 
 expected_outputs.append(sorted(employee_free_time(self.__inputs[0])))

 if json.dumps(sorted(employee_free_time(self.__inputs[0]))) == json.dumps(sorted(self.__actual_outputs[0])):
 self.__edu_result.store_result(expected_outputs, TestCaseResult.PASS)
 else:
 self.__edu_result.store_result(expected_outputs, TestCaseResult.FAIL)

 return self.__edu_result

from interval import Interval

# The input parameter `schedule` is a list of lists, where each inner
# list contains `Interval` objects representing an employee's schedule.
def employee_free_time(schedule):  
          
    # Replace this placeholder return statement with your code
    return [Interval(0, 0), Interval(0, 0)]
    

employee_free_time.yaml

testcases:
  - name: "testcase 1"
    inputs:
    - 1 : [[[1, 2], [5, 6]], [[1, 3]], [[4, 10]]]
    output: 
    - 1 : [[3,4]]
  - name: "testcase 2"
    inputs:
    - 1 : [[[1, 3], [6, 7]], [[2, 4]], [[2, 5], [9, 12]]]
    output: 
    - 1 : [[5,6],[7,9]]
  - name: "testcase 3"
    inputs:
    - 1 : [[[2, 3], [7, 9]], [[1, 4], [6, 7]]]
    output: 
    - 1 : [[4,6]]
  - name: "testcase 4"
    inputs:
    - 1 : [[[3, 5], [8, 10]], [[4, 6], [9, 12]], [[5, 6], [8, 10]]]
    output: 
    - 1 : [[6,8]]
  - name: "testcase 5"
    inputs:
    - 1 : [[[1, 2], [3, 4], [5, 6], [7, 8], [9, 10], [11, 12]], [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10], [11, 12]], [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10], [11, 12]], [[1, 2], [3, 4], [5, 6], [7, 8], [9, 10], [11, 12]]]
    output: 
    - 1 : [[2, 3], [4, 5], [6, 7], [8, 9], [10, 11]]

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 function
 store the result using the self.store_result(error_msg, status)
 return : void
 """
 # inputs can be accessed using self.__inputs starting from 0 to len(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 
 return True

 
 
 if not isinstance(self.__inputs[0],list):
 self.store_result ("Invalid input type", ValidationFunction.FAIL)



 elif not all(is_valid_2d_array(schedule) for schedule in self.__inputs[0]):
 self.store_result ("Invalid input type", ValidationFunction.FAIL)

 
 
 elif not isinstance(self.__inputs[0],list):
 self.store_result ("The input should be a list", ValidationFunction.FAIL)
 
 elif not all(isinstance(x,list) for x in self.__inputs[0]):
 self.store_result ("The input array should contain only lists", ValidationFunction.FAIL)

 
 elif not all([len(x)==2 for schedule in self.__inputs[0] for x in schedule]):

 self.store_result("Length of each interval should be exactly 2", ValidationFunction.FAIL)
 
 
 elif not all(isinstance(x,int) and isinstance(y,int) for i in self.__inputs[0] for x,y in i):
 self.store_result ("Each interval inside an employee's schedule should contain only integers", ValidationFunction.FAIL)

 
 
 
 elif not (1 <= len(self.__inputs[0]) <= 50):
 self.store_result ("Length of input should be between 1 and 50", ValidationFunction.FAIL)

 elif not all( (1 <= len(x) <= 50 ) for x in self.__inputs[0]):
 self.store_result ("Length of each employee's schedule should be between 1 and 50", ValidationFunction.FAIL)
 

 
 elif not all(0 <= start < end for i in self.__inputs[0] for start,end in i):
 self.store_result ("Start time in each interval should be greater than or equal to 0 and less than its end time", ValidationFunction.FAIL)

 
 elif not all(end<=10**8 for i in self.__inputs[0] for start,end in i):
 self.store_result ("End time in each interval should be less than or equal to 10^8", ValidationFunction.FAIL)

 
 
 

 

 elif not all([x[y+1][0]>=x[y][1] for x in self.__inputs[0] for y in range(len(x)-1)]):
 self.store_result ("Intervals in each schedule should be non-overlapping", ValidationFunction.FAIL)

 


 else:
 self.store_result("", ValidationFunction.PASS)

Try to solve the Employee Free Time problem.

Merge Intervals

K-way Merge

Conclusion

Employee Free Time

Statement

Examples

Understand the problem

Figure it out!

Try it yourself