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Minimum points to be selected such that removal of line segments passing through them empties given array
  • Last Updated : 25 May, 2021

Given a 2D array arr[][], where each row is of the form {start, end} representing the start and endpoints of each line segment on the X-axis. In one step, select a point on the X-axis and delete all the line segments passing through that point. The task is to find the minimum number of such points that need to be selected to delete all the line segments of the array.

Examples:

Input: arr[][]= { {9, 15}, {3, 8}, {1, 6}, {7, 12}, {5,10} } 
Output :
Explanation: 
Select the point arr[2][1](= (6, 0) on the X-axis and delete the second(= arr[1]), third(= arr[2]), and fifth(= arr[4]) line segments. 
Select the point arr[3][1](= (12, 0)) on the X-axis and delete the first(=arr[0]) and the fourth(=arr[3]) line segments. 
Therefore, the required count is 2.

Input: arr[][]={ {1, 4}, {5, 7}, {9, 13} } 
Output: 3

Approach: The problem can be solved using the Greedy technique. Follow the steps below to solve the problem:



  • Initialize a variable, say cntSteps to count total number of steps required to delete all the line segments.
  • Sort the array arr[][] based on the end points of the line segments.
  • Initialize a variable, say Points = arr[0][1] to store the points of the X-axis.
  • Traverse the array and check if the value of arr[i][0] greater than Points or not. If found to be true then increment the value cntSteps by 1 and update the value of Points = arr[i][1].
  • Finally, print the value of cntSteps.

C++




// C++ program to implement
// the above approach
 
 
#include <bits/stdc++.h>
using namespace std;
 
 
// Comparator function
bool comp(vector<int> &x, vector<int> y)
{
    return x[1] < y[1];
}
 
 
// Function to count the minimum number of
// steps required to delete all the segments
int cntMinSteps(vector<vector<int> > &arr,
                                   int N)
{
     
 
    // Stores count of steps required
    // to delete all the line segments
    int cntSteps = 1;
     
 
    // Sort the array based on end points
    // of line segments
    sort(arr.begin(), arr.end(), comp);
     
 
    // Stores point on X-axis
    int Points = arr[0][1];
     
 
    // Traverse the array
    for(int i = 0; i < N; i++) {
         
 
        // If arr[1][0] is
        // greater than Points
        if(arr[i][0] > Points) {
             
 
            // Update cntSteps
            cntSteps++;
             
 
            // Update Points
            Points = arr[i][1];
        }
    }
     
    return cntSteps;
     
}
 
 
// Driver Code
int main() {
     
    vector<vector<int> > arr
       = { { 9, 15 }, { 3, 8 },
            { 1, 6 }, { 7, 12 },
                      { 5, 10 } };
                             
    int N = arr.size();
     
    cout<< cntMinSteps(arr, N);
    return 0;
}

Java




// Java program to implement
// the above approach
import java.util.*;
 
class GFG{
 
// Function to sort by column
public static void sortbyColumn(int arr[][],
                                int col)
{
     
    // Using built-in sort function Arrays.sort
    Arrays.sort(arr, new Comparator<int[]>()
    {
        @Override
         
        // Compare values according to columns
        public int compare(final int[] entry1, 
                           final int[] entry2)
        {
             
            // To sort in descending order revert 
            // the '>' Operator
            if (entry1[col] > entry2[col])
                return 1;
            else
                return -1;
        }
    });  // End of function call sort().
}
 
// Function to count the minimum number of
// steps required to delete all the segments
static int cntMinSteps(int[][] arr, int N)
{
     
    // Stores count of steps required
    // to delete all the line segments
    int cntSteps = 1;
     
    // Sort the array based on end points
    // of line segments
    sortbyColumn(arr, 1);
     
    // Stores point on X-axis
    int Points = arr[0][1];
     
    // Traverse the array
    for(int i = 0; i < N; i++)
    {
         
        // If arr[1][0] is
        // greater than Points
        if(arr[i][0] > Points)
        {
             
            // Update cntSteps
            cntSteps++;
             
            // Update Points
            Points = arr[i][1];
        }
    }
    return cntSteps;
}
 
// Driver Code
public static void main(String[] args)
{
    int[][] arr = { { 9, 15 }, { 3, 8 },
                    { 1, 6 }, { 7, 12 },
                    { 5, 10 } };
                             
    int N = arr.length;
     
    System.out.print(cntMinSteps(arr, N));
}
}
 
// This code is contributed by shikhasingrajput

Python3




# Python3 program to implement
# the above approach
 
# Comparator function
def comp(x, y):
    return x[1] < y[1]
   
# Function to count the
# minimum number of steps
# required to delete all
# the segments
def cntMinSteps(arr, N):
   
    # Stores count of steps
    # required to delete all
    # the line segments
    cntSteps = 1
 
    # Sort the array based
    # on end points of line
    # segments
    arr.sort(reverse = False)   
 
    # Stores point on X-axis
    Points = arr[0][1]   
 
    # Traverse the array
    for i in range(N):
       
        # If arr[1][0] is
        # greater than Points
        if(arr[i][0] > Points):
           
            # Update cntSteps
            cntSteps += 1
             
            # Update Points
            Points = arr[i][1]
     
    return cntSteps
 
# Driver Code
if __name__ == '__main__':
   
    arr = [[9, 15], [3, 8],
           [1, 6], [7, 12],
           [5, 10]]           
    N = len(arr)
    print(cntMinSteps(arr, N))
 
# This code is contributed by bgangwar59
Output: 
2

 

Time Complexity: O(N * log(N)) 
Auxiliary Space: O(N)

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