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

Educative-77 in C++: 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
Given a sorted list of **nonoverlapping** intervals and a new interval, your task is to insert the new interval into the correct position while ensuring that the resulting list of intervals remains sorted and nonoverlapping. Each interval is a pair of nonnegative numbers, the first being the start time and the second being the end time of the interval.

**Constraints:**

- $0 \leq$ `existing_intervals.length` $\leq 10^4$

- `existing_intervals[i].length`, `new_interval.length` == 2

- $0 \leq$ *start time* $<$ *end time* $\leq 10^4$

- The list of intervals is sorted in ascending order based on the $start ~time$.

$[[1, 3], [2, 10], [4, 5], [7, 8], [9, 12], [13, 14]]$

What will be the updated list of intervals?

existing_intervals = $[[1, 3], [4, 5], [7, 8], [9, 12], [13, 14]]$

new_interval = $[2, 10]$

What will be the updated list of intervals?
existing_intervals = <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">[</mo><mo stretchy="false">[</mo><mn>1</mn><mo separator="true">,</mo><mn>3</mn><mo stretchy="false">]</mo><mo separator="true">,</mo><mo stretchy="false">[</mo><mn>4</mn><mo separator="true">,</mo><mn>5</mn><mo stretchy="false">]</mo><mo separator="true">,</mo><mo stretchy="false">[</mo><mn>7</mn><mo separator="true">,</mo><mn>8</mn><mo stretchy="false">]</mo><mo separator="true">,</mo><mo stretchy="false">[</mo><mn>9</mn><mo separator="true">,</mo><mn>12</mn><mo stretchy="false">]</mo><mo separator="true">,</mo><mo stretchy="false">[</mo><mn>13</mn><mo separator="true">,</mo><mn>14</mn><mo stretchy="false">]</mo><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">[[1, 3], [4, 5], [7, 8], [9, 12], [13, 14]]</annotation></semantics></math>[[1,3],[4,5],[7,8],[9,12],[13,14]]
new_interval = <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">[</mo><mn>2</mn><mo separator="true">,</mo><mn>10</mn><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">[2, 10]</annotation></semantics></math>[2,10]

$[[1, 2], [3, 4], [5, 7], [8, 10], [12, 16]]$

What will be the updated list of intervals?

existing_intervals = $[[1, 2],[3, 5],[6, 7],[8, 10],[12, 16]]$

new_interval = $[4, 8]$

What will be the updated list of intervals?
existing_intervals = <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">[</mo><mo stretchy="false">[</mo><mn>1</mn><mo separator="true">,</mo><mn>2</mn><mo stretchy="false">]</mo><mo separator="true">,</mo><mo stretchy="false">[</mo><mn>3</mn><mo separator="true">,</mo><mn>5</mn><mo stretchy="false">]</mo><mo separator="true">,</mo><mo stretchy="false">[</mo><mn>6</mn><mo separator="true">,</mo><mn>7</mn><mo stretchy="false">]</mo><mo separator="true">,</mo><mo stretchy="false">[</mo><mn>8</mn><mo separator="true">,</mo><mn>10</mn><mo stretchy="false">]</mo><mo separator="true">,</mo><mo stretchy="false">[</mo><mn>12</mn><mo separator="true">,</mo><mn>16</mn><mo stretchy="false">]</mo><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">[[1, 2],[3, 5],[6, 7],[8, 10],[12, 16]]</annotation></semantics></math>[[1,2],[3,5],[6,7],[8,10],[12,16]]
new_interval = <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">[</mo><mn>4</mn><mo separator="true">,</mo><mn>8</mn><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">[4, 8]</annotation></semantics></math>[4,8]

What will be the updated list of intervals?

existing_intervals = $[[1, 2],[5, 7],[8, 10]]$

new_interval = $[3,4]$

What will be the updated list of intervals?
existing_intervals = <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">[</mo><mo stretchy="false">[</mo><mn>1</mn><mo separator="true">,</mo><mn>2</mn><mo stretchy="false">]</mo><mo separator="true">,</mo><mo stretchy="false">[</mo><mn>5</mn><mo separator="true">,</mo><mn>7</mn><mo stretchy="false">]</mo><mo separator="true">,</mo><mo stretchy="false">[</mo><mn>8</mn><mo separator="true">,</mo><mn>10</mn><mo stretchy="false">]</mo><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">[[1, 2],[5, 7],[8, 10]]</annotation></semantics></math>[[1,2],[5,7],[8,10]]
new_interval = <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">[</mo><mn>3</mn><mo separator="true">,</mo><mn>4</mn><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">[3,4]</annotation></semantics></math>[3,4]

What will be the updated list of intervals?

existing_intervals = $[[3, 5]]$

new_interval = $[1, 10]$

What will be the updated list of intervals?
existing_intervals = <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">[</mo><mo stretchy="false">[</mo><mn>3</mn><mo separator="true">,</mo><mn>5</mn><mo stretchy="false">]</mo><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">[[3, 5]]</annotation></semantics></math>[[3,5]]
new_interval = <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">[</mo><mn>1</mn><mo separator="true">,</mo><mn>10</mn><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">[1, 10]</annotation></semantics></math>[1,10]

Insert Interval

Insert Interval

vector<vector<int>> InsertInterval(vector<vector<int>> existingIntervals, vector<int> newInterval)
{
 // Replace this placeholder return statement with your code
 
 return {};
}

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) + ")"

Help me debug only the function Insert Interval . . I don't need the corrected code.I don't want explanations or code review. Just provide me the exact and to-the-point error that helps me run the code successfully on the test cases provided.

Please help me understand why this code failed for the last failed test case. Don't give me the corrected code. . If yes, then Just provide me the exact and to-the-point error that helps me run the code successfully on the test cases provided.

Your current task is to review only the InsertInterval function and the other function(s) invoked in it/them. Do not review extra/helper files or functions not invoked in the solution function InsertInterval. Do not review the code of data structures 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. Also, Answer the following questions: Is the Merge Intervals pattern used? Take your time and review the code.

Please provide a brief time complexity analysis of the function InsertInterval. While calculating time complexity, include the time complexity of built-in C++ functions invoked by the code. The Answer should be to the point and in a few lines.

Please provide a brief Space complexity analysis of the function InsertInterval. While calculating space complexity, include the space complexity of built-in C++ functions invoked by the code. 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). The Answer should be to the point and in a few lines

TwoDArray

#include <string>

using namespace std;

class TwoDArray : public DataStructure
{

 // define class attributes

private:
 void generateError(string data)
 {
 cerr << "TwoDArray is not parsable: " << data;
 exit(-1);
 }

public:
 std::vector<vector<int>> val;

 TwoDArray()
 {
 // constructor
 }
 TwoDArray(std::vector<vector<int>> v)
 {
 this->val = v;
 // constructor
 }
 
 // return value will be passed to user program
 void *construct(string new_value, int typeOfDs)
 {
 json j_complete = json::parse(new_value);
 std::vector<std::vector<int>> temp = j_complete;
 this->val = temp;
 // cout << this->val.size();
 return this;
 // parse test case in json string 'value' to your desired data structure
 }

 // input param contains return value of user program
 string traverse(void *input, int typeOfDs)
 {
 TwoDArray * custom_ds =(TwoDArray *)input; 
 json result = (json)(custom_ds->val);
 return result.dump();
 // convert your data structure 'input' to a json string representing a test case output
 }

 // override operator<< for your data structure if required
};

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 insert_interval(existing_intervals, new_interval):
 new_start, new_end = new_interval[0], new_interval[1]
 i = 0
 n = len(existing_intervals)
 output = []
 while i < n and existing_intervals[i][0] < new_start:
 output.append(existing_intervals[i])
 i = i + 1
 if not output or output[-1][1] < new_start:
 output.append(new_interval)
 else:
 output[-1][1] = max(output[-1][1], new_end)
 while i < n:
 ei = existing_intervals[i]
 start, end = ei[0], ei[1]
 if output[-1][1] < start:
 output.append(ei)
 else:
 output[-1][1] = max(output[-1][1], end)
 i += 1
 return output




 # 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(insert_interval(self.__inputs[0], self.__inputs[1])))

 if json.dumps(sorted(insert_interval(self.__inputs[0], self.__inputs[1]))) == json.dumps(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

#include "InsertInterval.cpp"
#include "TwoDArray.cpp"


TwoDArray InsertIntervalMain(TwoDArray v, vector<int> v2)
{
 vector<vector<int>> res = InsertInterval(v.val, v2);
 TwoDArray convert = *(new TwoDArray(res));
 return convert;
}

private_insert_interval2.yaml

testcases:
  - name: "testcase 1"
    inputs:
    - 1 : [[1, 2], [3, 4], [5, 8], [9, 15]]
    - 2 : [2, 5]
    output: 
    - 1 : [[1, 8], [9, 15]]

  - name: "testcase 2"
    inputs:
    - 1: [[1, 6], [8, 9], [10, 15], [16, 18]]
    - 2: [9, 10]
    output:
    - 1 : [[1, 6], [8, 15], [16, 18]]

  - name: "testcase 3"
    inputs:
    - 1 : [[1, 2], [3, 4], [5, 8], [9, 15]]
    - 2 : [16, 17]
    output: 
    - 1 : [[1, 2], [3, 4], [5, 8], [9, 15], [16,17]]

  - name: "testcase 4"
    inputs:
    - 1: [[1, 4], [5, 6], [7, 8], [9, 10]]
    - 2: [1, 5]
    output:
    - 1 : [[1, 6], [7, 8], [9, 10]]
  - name: "testcase 5"
    inputs:
    - 1: [[1, 3], [4, 6], [7, 8], [9, 10]]
    - 2: [1, 10]
    output:
    - 1 : [[1,10]]

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
 """
 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

 def is_valid_1d_array(arr):
 if not isinstance(arr, list):
 return False # Not a valid 1D array if it's not a list
 
 return all(isinstance(elem, int) and not isinstance(elem, bool) for elem in arr)
 





 # inputs can be accessed using self.__inputs starting from 0 to len(self.__inputs) - 1
 
 if not is_valid_2d_array(self.__inputs[0]):
 self.store_result("The 'existing_intervals' array is invalid input type", ValidationFunction.FAIL)

 elif not is_valid_1d_array(self.__inputs[1]):
 self.store_result("The 'new_interval' array is invalid input type", ValidationFunction.FAIL)

 elif not all([len(x)==2 for x in self.__inputs[0]]):

 self.store_result("Length of each existing interval should be exactly 2", ValidationFunction.FAIL)


 elif not len(self.__inputs[1])==2:
 self.store_result ("The 'new_interval' should be of length 2", ValidationFunction.FAIL)
 
 
 elif any(x is None for x in self.__inputs[1]):
 self.store_result ("The 'new_interval' is invalid", ValidationFunction.FAIL)
 
 

 
 

 
 
 elif not isinstance(self.__inputs[0],list):
 self.store_result ("First argument should be a list", ValidationFunction.FAIL)

 

 elif not isinstance(self.__inputs[1],list):
 self.store_result ("Second argument should be a list", ValidationFunction.FAIL)

 elif not all(isinstance(x,list) for x in self.__inputs[0]):
 self.store_result ("List a should contain only lists", ValidationFunction.FAIL)

 elif not all(isinstance(x,int) and isinstance(y,int) for x,y in self.__inputs[0]):
 self.store_result ("Each interval in 'existing_intervals' should contain only integers", ValidationFunction.FAIL)
 
 elif not isinstance(self.__inputs[1][0],int) or not isinstance(self.__inputs[1][1],int):
 self.store_result ("'new_interval' should contain only integers", ValidationFunction.FAIL)


 
 
 
 
 
 elif not (0 <=len(self.__inputs[0]) <= 10**4):
 self.store_result("Length of 'existing_intervals' array should be between 0 and 10^4", ValidationFunction.FAIL)
 
 
 elif not len(self.__inputs[1])==2:

 self.store_result("Length of 'new_interval' should be exactly 2", ValidationFunction.FAIL)
 elif not all([(0 <= start < end) for start,end in self.__inputs[0]]):
 self.store_result("Start time of each 'existing_interval' should be greater than or equal to 0 and less than its End time", ValidationFunction.FAIL)
 
 elif not all([end <= 10**4 for start,end in self.__inputs[0]]):
 self.store_result("End time should be less than or equal to 10^4", ValidationFunction.FAIL)
 
 
 elif not (0 <= self.__inputs[1][0] < self.__inputs[1][1]):
 self.store_result("Start time of the 'new_interval' should be greater than or equal to 0 and less than its end time ", ValidationFunction.FAIL)
 
 
 elif not ( self.__inputs[1][1] <= 10**4):
 self.store_result("End time of the 'new_interval' should be less than or equal to 10^4 ", ValidationFunction.FAIL)
 
 
 elif self.__inputs[0]!=sorted(self.__inputs[0]):
 self.store_result("'existing_intervals' should be sorted in ascending order based on Start time", ValidationFunction.FAIL)


 else:
 self.store_result("", ValidationFunction.PASS)

Try to solve the Insert Interval problem.

Merge Intervals

K-way Merge

Conclusion

Insert Interval

Statement

Examples

Understand the problem

Figure it out

Try it yourself