Find a pair of intersecting ranges from a given array

Given a 2D array ranges[][] of size N * 2, with each row representing a range of the form [L, R], the task is to find two ranges such that the first range completely lies ins the second range and print their indices. If no such pair of ranges can be obtained, print -1. If multiple such ranges exist, print any one of them.

Segment [L1,  R1] lies within segment [L2,  R2] if L1 ≥ L2 and R1 ≤ R2. 

Examples:

Input: N = 5, ranges[][] = {{1, 5}, {2, 10}, {3, 10}, {2, 2}, {2, 15}}
Output: 4 1
Explanation: Segment [2, 2] lies completely within the segment [1, 5], as 1 ≤ 2 and 2 ≤ 5.

Input: N = 4, ranges[][] = {{2, 10}, {1, 9}, {1, 8}, {1, 7}}
Output: -1
Explanation: No such pair of segments exist.

Naive Approach: The simplest approach to solve the problem is to iterate over the array and for each range, traverse over the remaining array to check if any range exists or not which lies completely inside the current range or vice versa. 

Time Complexity: O(N²)
Auxiliary Space: O(1)

Efficient Approach: To optimize the above approach, the idea is to sort the array of ranges using a comparator function and check whether any segment lies inside any other segment or not. Follow the steps given below to solve this problem:

• Sort the segments in increasing order of their starting points. In the case of a pair having equal starting points, sort in decreasing order of ending points.
• Now, traverse the array and maintain the maximum ending point obtained so and compare it with that of the current segment.

Below is the implementation of the above approach:

C++

// C++ program for the above approach

#include <bits/stdc++.h>
using namespace std;

// Store ranges and their
// corresponding array indices
vector<pair<pair<int, int>, int> > tup;

// Function to find a pair of intersecting ranges
void findIntersectingRange(int N, int ranges[][2])
{

    // Stores ending point
    // of every range
    int curr;

    // Stores the maximum
    // ending point obtained
    int currPos;

    // Iterate from 0 to N - 1
    for (int i = 0; i < N; i++) {

        int x, y;

        // Starting point of
        // the current range
        x = ranges[i][0];

        // End point of
        // the current range
        y = ranges[i][1];

        // Push pairs into tup
        tup.push_back({ { x, y }, i + 1 });
    }

    // Sort the tup vector
    sort(tup.begin(), tup.end());

    curr = tup[0].first.second;
    currPos = tup[0].second;

    // Iterate over the ranges
    for (int i = 1; i < N; i++) {

        int Q = tup[i - 1].first.first;
        int R = tup[i].first.first;

        // If starting points are equal
        if (Q == R) {
            if (tup[i - 1].first.second
                < tup[i].first.second)
                cout << tup[i - 1].second << ' '
                     << tup[i].second;

            else
                cout << tup[i].second << ' '
                     << tup[i - 1].second;

            return;
        }

        int T = tup[i].first.second;

        // Print the indices of the
        // intersecting ranges
        if (T <= curr) {
            cout << tup[i].second
                 << ' ' << currPos;
            return;
        }
        else {
            curr = T;
            currPos = tup[i].second;
        }
    }

    // If no such pair of segments exist
    cout << "-1 -1";
}

// Driver Code
int main()
{
    // Given N
    int N = 5;

    // Given 2d ranges[][] array
    int ranges[][2] = {
        { 1, 5 }, { 2, 10 },
        { 3, 10 }, { 2, 2 },
        { 2, 15 }};

    // Function call
    findIntersectingRange(N, ranges);
}

Java

// Java program for the above approach
import java.util.ArrayList;
import java.util.Collections;
import java.util.Comparator;

class GFG{

// Store ranges and their
// corresponding array indices
static ArrayList<int[]> tup = new ArrayList<>();

// Function to find a pair of intersecting ranges
static void findIntersectingRange(int N, int ranges[][])
{

    // Stores ending point
    // of every range
    int curr;

    // Stores the maximum
    // ending point obtained
    int currPos;

    // Iterate from 0 to N - 1
    for(int i = 0; i < N; i++)
    {
        int x, y;

        // Starting point of
        // the current range
        x = ranges[i][0];

        // End point of
        // the current range
        y = ranges[i][1];

        // Push pairs into tup
        int[] arr = { x, y, i + 1 };
        tup.add(arr);
    }

    // Sort the tup vector
    // sort(tup.begin(), tup.end());
    Collections.sort(tup, new Comparator<int[]>()
    {
        public int compare(int[] a, int[] b)
        {
            if (a[0] == b[0])
            {
                if (a[1] == b[1])
                {
                    return a[2] - b[2];
                }
                else
                {
                    return a[1] - b[1];
                }
            }
            return a[0] - b[0];
        }
    });

    curr = tup.get(0)[1];
    currPos = tup.get(0)[2];

    // Iterate over the ranges
    for(int i = 1; i < N; i++)
    {
        int Q = tup.get(i - 1)[0];
        int R = tup.get(i)[0];

        // If starting points are equal
        if (Q == R)
        {
            if (tup.get(i - 1)[1] < tup.get(i)[1])
                System.out.print(tup.get(i - 1)[2] + " " +
                                 tup.get(i)[2]);

            else
                System.out.print(tup.get(i)[2] + " " +
                                 tup.get(i - 1)[2]);
            return;
        }

        int T = tup.get(i)[1];

        // Print the indices of the
        // intersecting ranges
        if (T <= curr)
        {
            System.out.print(tup.get(i)[2] + " " +
                             currPos);
            return;
        }
        else
        {
            curr = T;
            currPos = tup.get(i)[2];
        }
    }

    // If no such pair of segments exist
    System.out.print("-1 -1");
}

// Driver Code
public static void main(String[] args)
{

    // Given N
    int N = 5;

    // Given 2d ranges[][] array
    int ranges[][] = { { 1, 5 }, { 2, 10 },
                       { 3, 10 }, { 2, 2 },
                       { 2, 15 } };

    // Function call
    findIntersectingRange(N, ranges);
}
}

// This code is contributed by sanjeev2552

Python3

# Python3 program for the above approach

# Store ranges and their
# corresponding array indices

# Function to find a pair of intersecting ranges
def findIntersectingRange(tup, N, ranges):

    # Stores ending point
    # of every range
    curr = 0

    # Stores the maximum
    # ending point obtained
    currPos = 0

    # Iterate from 0 to N - 1
    for i in range(N):

        # Starting point of
        # the current range
        x = ranges[i][0]

        # End point of
        # the current range
        y = ranges[i][1]

        # Push pairs into tup
        tup.append([ [ x, y ], i + 1 ])

    # Sort the tup vector
    tup = sorted(tup)

    curr = tup[0][0][1]
    currPos = tup[0][1]

    # Iterate over the ranges
    for i in range(1, N):

        Q = tup[i - 1][0][0]
        R = tup[i][0][0]

        #If starting points are equal
        if (Q == R):
            if (tup[i - 1][0][1] < tup[i][0][1]):
                print(tup[i - 1][1], tup[i][1])
            else:
                print(tup[i][1], tup[i - 1][1])
            return

        T = tup[i][0][1]

        # Print the indices of the
        # intersecting ranges
        if (T <= curr):
            print(tup[i][1], currPos)
            return
        else:
            curr = T
            currPos = tup[i][1]

    # If no such pair of segments exist
    print("-1 -1")

# Driver Code
if __name__ == '__main__':
    # Given N
    N = 5

    # Given 2d ranges[][] array
    ranges= [[ 1, 5 ], [ 2, 10 ],
            [ 3, 10 ], [ 2, 2 ],
            [ 2, 15 ]]

    # Function call
    findIntersectingRange([], N, ranges)

    # This code is contributed by mohit kumar 29

C#

// C# program for the above approach

using System;
using System.Collections.Generic;
using System.Linq;

class GFG{

  // Store ranges and their
  // corresponding array indices
  static List<int[]> tup = new List<int[]>();

  // Function to find a pair of intersecting ranges
  static void findIntersectingRange(int N, int[][] ranges)
  {

    // Stores ending point
    // of every range
    int curr;

    // Stores the maximum
    // ending point obtained
    int currPos;

    // Iterate from 0 to N - 1
    for(int i = 0; i < N; i++)
    {
      int x, y;

      // Starting point of
      // the current range
      x = ranges[i][0];

      // End point of
      // the current range
      y = ranges[i][1];

      // Push pairs into tup
      int[] arr = { x, y, i + 1 };
      tup.Add(arr);
    }

    // Sort the tup vector
    // sort(tup.begin(), tup.end());
    tup = tup.OrderBy(a => a[0]).ThenBy(a => a[1]).ThenBy(a => a[2]).ToList();


    curr = tup[0][1];
    currPos = tup[0][2];

    // Iterate over the ranges
    for(int i = 1; i < N; i++)
    {
      int Q = tup[i - 1][0];
      int R = tup[i][0];

      // If starting points are equal
      if (Q == R)
      {
        if (tup[i - 1][1] < tup[i][1])
          Console.Write(tup[i - 1][2] + " " +
                        tup[i][2]);

        else
          Console.Write(tup[i][2] + " " +
                        tup[i - 1][2]);
        return;
      }

      int T = tup[i][1];

      // Print the indices of the
      // intersecting ranges
      if (T <= curr)
      {
        Console.Write(tup[i][2] + " " +
                      currPos);
        return;
      }
      else
      {
        curr = T;
        currPos = tup[i][2];
      }
    }

    // If no such pair of segments exist
    Console.Write("-1 -1");
  }

  // Driver Code
  public static void Main(string[] args)
  {

    // Given N
    int N = 5;

    // Given 2d ranges[][] array
    int[][] ranges = { new int[] { 1, 5 },new int[]  { 2, 10 },
                      new int[] { 3, 10 },new int[]  { 2, 2 },
                      new int[]  { 2, 15 } };

    // Function call
    findIntersectingRange(N, ranges);
  }
}

// This code is contributed by phasing17

Javascript

<script>

// JavaScript program for the above approach

// Store ranges and their
// corresponding array indices
let tup = [];

// Function to find a pair of intersecting ranges
function findIntersectingRange(N,ranges)
{
    // Stores ending point
    // of every range
    let curr;

    // Stores the maximum
    // ending point obtained
    let currPos;

    // Iterate from 0 to N - 1
    for(let i = 0; i < N; i++)
    {
        let x, y;

        // Starting point of
        // the current range
        x = ranges[i][0];

        // End point of
        // the current range
        y = ranges[i][1];

        // Push pairs into tup
        let arr = [ x, y, i + 1 ];
        tup.push(arr);
    }

    // Sort the tup vector
    // sort(tup.begin(), tup.end());
    tup.sort(function(a,b)
    {
            if (a[0] == b[0])
            {
                if (a[1] == b[1])
                {
                    return a[2] - b[2];
                }
                else
                {
                    return a[1] - b[1];
                }
            }
            return a[0] - b[0];

    });

    curr = tup[0][1];
    currPos = tup[0][2];

    // Iterate over the ranges
    for(let i = 1; i < N; i++)
    {
        let Q = tup[i - 1][0];
        let R = tup[i][0];

        // If starting points are equal
        if (Q == R)
        {
            if (tup[i - 1][1] < tup[i][1])
                document.write(tup[i - 1][2] + " " +
                                 tup[i][2]);

            else
                document.write(tup[i][2] + " " +
                                 tup[i - 1][2]);
            return;
        }

        let T = tup[i][1];

        // Print the indices of the
        // intersecting ranges
        if (T <= curr)
        {
            document.write(tup[i][2] + " " +
                             currPos);
            return;
        }
        else
        {
            curr = T;
            currPos = tup[i][2];
        }
    }

    // If no such pair of segments exist
    document.write("-1 -1");
}

// Driver Code
let N = 5;

// Given 2d ranges[][] array
let ranges = [[ 1, 5 ], [ 2, 10 ],
[ 3, 10 ], [ 2, 2 ],
[ 2, 15 ]];

// Function call
findIntersectingRange(N, ranges);


// This code is contributed by patel2127

</script>

Output:

4 1

Time Complexity: O(N LogN)
Auxiliary Space: O(N)