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Find all the intersecting pairs from a given array
  • Difficulty Level : Basic
  • Last Updated : 27 Apr, 2020

Given n pairs (S[i], F[i]) where for every i, S[i]< F[i]. Two ranges are said to intersect if and only if either of them does not fully lie inside the other one that is only one point of a pair lies between the start and end of the other pair. We have to print all the intersecting ranges for each pair.

Note: All the endpoints that is F[i] are integers and are also unique. None of the pairs start and end at the same time. Also, no pair’s endpoint is the same as the start of the other.

Examples:

Input :
n = 6, v = {{9, 12}, {2, 11}, {1, 3}, {6, 10}, {5, 7}, {4, 8}}
Output :
{9, 12} is intersecting with: {6, 10} {2, 11}
{2, 11} is intersecting with: {1, 3} {9, 12}
{1, 3} is intersecting with: {2, 11}
{6, 10} is intersecting with: {5, 7} {4, 8} {9, 12}
{5, 7} is intersecting with: {6, 10}
{4, 8} is intersecting with: {6, 10}
Explanation:
The first pair(9, 12) is intersecting with second(2, 11) and fourth(6, 10) pair.
The second pair(2, 11) is intersecting with third(1, 3) and first(9, 12) pairs.
The third pair(1, 3) is intersecting with the second(2, 11) pair.
The forth pair(6, 10) is intersecting with fifth(5, 7), sixth(4, 8) and first(9, 12) pair.
The fifth pair(5, 7) is intersecting with the fourth(6, 10) pair.
The sixth pair(4, 8) is intersecting with the fourth(6, 10) pair.

Input : n = 5, v = {1, 3}, {2, 4}, {5, 9}, {6, 8}, {7, 10}}
Output :
{1, 3} is intersecting with: {2, 4}
{2, 4} is intersecting with: {1, 3}
{5, 9} is intersecting with: {7, 10}
{6, 8} is intersecting with: {7, 10}
{7, 10} is intersecting with: {6, 8} {5, 9}
Explanation:
The first pair(1, 3) is intersecting with the second(2, 4) pair.
The second pair(2, 4) is intersecting with the first(1, 3) pair.
The third pair(5, 9) is intersecting with the fifth(7, 10) pair.
The fourth pair(6, 8) is intersecting with the fifth(7, 10) pair.
The fifth pair(7, 10) is intersecting with the third(5, 9) and fourth(6, 8) pair.



Approach:

The above-mentioned problem can be solved by using sorting. Firstly, we have to insert every first element of the pair and the second element of the pair in a single vector along with the position of each. Then sort all the elements with respect to the first element of the pair. After that use a set data structure for second elements in the pair. Then we have to iterate in the vector in which we have stored the first and second element with their respective positions and if the first element is found then compute all ranges that are intersecting with the current pair from the set and if the second element of the pair is encountered then simply erase that second pair from the set. Otherwise add the second element of the current pair.

Below is the implementation of above approach:




// CPP Program to Find all the
// intersecting pairs from a given array
  
#include <bits/stdc++.h>
using namespace std;
  
// Function that print intersecting pairs
// for each pair in the vector
void findIntersection(vector<pair<int, int> > v, int n)
{
    vector<pair<int, int> > data;
  
    vector<vector<int> > answer(n);
  
    // Store each pair with their positions
    for (int i = 0; i < n; i++) {
        data.push_back(make_pair(v[i].first, i));
  
        data.push_back(make_pair(v[i].second, i));
    }
  
    // Sort the vector with respect to
    // first element in the pair
    sort(data.begin(), data.end());
  
    int curr = 0;
  
    // set data structure for keeping
    // the second element of each pair
    set<pair<int, int> > s;
  
    // Iterating data vector
    for (auto it : data) {
  
        // check if all pairs are taken
        if (curr >= n)
            break;
  
        // check if current value is a second element
        // then remove it from the set
        if (s.count(it))
  
            s.erase(it);
  
        else {
  
            // index of the current pair
            int i = it.second;
  
            // Computing the second element of current pair
            int j = v[i].second;
  
            // Iterating in the set
            for (auto k : s) {
  
                // Check if the set element
                // has higher value than the current
                // element's second element
                if (k.first > j)
                    break;
  
                int index = k.second;
  
                answer[i].push_back(index);
  
                answer[index].push_back(i);
  
                curr++;
  
                // Check if curr is equal to
                // all available pairs or not
                if (curr >= n)
                    break;
            }
  
            // Insert second element
            // of current pair in the set
            s.insert(make_pair(j, i));
        }
    }
  
    // Printing the result
    for (int i = 0; i < n; i++) {
  
        cout << "{" << v[i].first << ", " << v[i].second << "}"
             << " is intersecting with: ";
  
        for (int j = 0; j < answer[i].size(); j++)
  
            cout << "{" << v[answer[i][j]].first << ", "
                 << v[answer[i][j]].second << "}"
                 << " ";
  
        cout << "\n";
    }
}
  
// Driver Code
int main()
{
  
    // initialise the size of vector
    int n = 6;
  
    // initialise the vector
    vector<pair<int, int> > v = { { 9, 12 },
                                  { 2, 11 },
                                  { 1, 3 },
                                  { 6, 10 },
                                  { 5, 7 },
                                  { 4, 8 } };
  
    findIntersection(v, n);
  
    return 0;
}
Output:
{9, 12} is intersecting with: {6, 10} {2, 11} 
{2, 11} is intersecting with: {1, 3} {9, 12} 
{1, 3} is intersecting with: {2, 11} 
{6, 10} is intersecting with: {5, 7} {4, 8} {9, 12} 
{5, 7} is intersecting with: {6, 10} 
{4, 8} is intersecting with: {6, 10}

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