Find number of segments covering each point in an given array

Given segments and some points, for each point find the number of segments covering that point.

A segment (l, r) covers a point x if and only if l < = x < = r.

Examples:

Input: Segments = {{0, 3}, {1, 3}, {3, 8}}, 
Points = {-1, 3, 8}.
Output : {0, 3, 1}
Explanation :

• No segments passing through point -1
• All the segments passing through point 3
• Segment 3rd passing through point 8

Input: Segments = {{1, 3}, {2, 4}, {5, 7}}, 
Points = {0, 2, 5}.
Output: {0, 2, 1}
Explanation :

• No segments passing through point 0
• 1st and 2nd segment passing through point 2
• Segment 3rd passing through point 5

Approach:

• We can do this by using logic similar to prefix sum.
• Let’s represent a segment with (l, r). Form a vector of pairs, for each segment push two pairs in vector with values (l, +1) ans (r + 1, -1).
• Sort the points in ascending order, but we also need it’s position so mapped it with it’s position.
• Sort the segment vector in descending order because we iterate on it from back.
• Make a variable count of segments, which is initially zero.
• Then, we will iterate on the point and pop the pair from the segment vector until it’s first value is less than equal to current point and add it’s second value to the count.
• Finally, Store the values of count in an array to his respective position and print the array.

Below is the implementation of the above approach. 

C++

// C++ program to find the number of
// segments covering each points
#include<bits/stdc++.h>
using namespace std;

// Function to print an array
void PrintArray(int n,int arr[])
{
     for(int i = 0; i < n; i++)
     {
         cout<<arr[i]<<" ";
     }
}

// Function prints number of segments
// covering by each points
void NumberOfSegments(vector<pair<int,int> >segments,
                      vector<int>points, int s, int p)
{
   vector< pair<int, int> >pts, seg;

   // Pushing points and index in
   // vector as a pairs
   for(int i = 0; i < p; i++)
   {
      pts.push_back({points[i], i});;
   }

   for(int i = 0; i < s; i++)
   {
      // (l,+1)
      seg.push_back({segments[i].first, 1});
      // (r+1,-1)
      seg.push_back({segments[i].second+1, -1});
   }

   // Sort the vectors
   sort(seg.begin(), seg.end(),
        greater<pair<int,int>>());
   sort(pts.begin(),pts.end());

   int count = 0;
   int ans[p];

   for(int i = 0; i < p; i++)
   {
        int x = pts[i].first;

        while(!seg.empty() &&
              seg.back().first <= x)
        {
            count+= seg.back().second;
            seg.pop_back();
        }
        ans[pts[i].second] = count;
   }

   // Print the answer
   PrintArray(p, ans);

}

//Driver code
int main()
{
  // Initializing vector of pairs
  vector<pair<int,int>>seg;

  // Push segments
  seg.push_back({0, 3});
  seg.push_back({1, 3});
  seg.push_back({3, 8});

  // Given points
  vector<int>point{-1, 3, 7};

  int s = seg.size();
  int p = point.size();

  NumberOfSegments(seg, point, s, p);

  return 0;
}

Java

// Java program to find the number of
// segments covering each points
import java.util.*;
import java.lang.*;

class GFG{

// Function to print an array
static void PrintArray(int n,int arr[])
{
    for(int i = 0; i < n; i++)
    {
        System.out.print(arr[i] + " ");
    }
}

// Function prints number of segments
// covering by each points
static void NumberOfSegments(ArrayList<int[]> segments,
                         int[] points, int s, int p)
{
    ArrayList<int[]> pts = new ArrayList<>(),
                     seg = new ArrayList<>();

    // Pushing points and index in
    // vector as a pairs
    for(int i = 0; i < p; i++)
    {
        pts.add(new int[]{points[i], i});
    }

    for(int i = 0; i < s; i++)
    {
        // (l,+1)
        seg.add(new int[]{segments.get(i)[0], 1});

        // (r+1,-1)
        seg.add(new int[]{segments.get(i)[1] + 1, -1});
    }

    // Sort the vectors
    Collections.sort(seg, (a, b) -> b[0] - a[0]);
    Collections.sort(pts, (a, b) -> a[0] - b[0]);

    int count = 0;
    int[] ans = new int[p];

    for(int i = 0; i < p; i++)
    {
        int x = pts.get(i)[0];

        while (seg.size() != 0 &&
               seg.get(seg.size() - 1)[0] <= x)
        {
            count += seg.get(seg.size() - 1)[1];
            seg.remove(seg.size() - 1);
        }
        ans[pts.get(i)[1]] = count;
    }

    // Print the answer
    PrintArray(p, ans);
}

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

    // Initializing vector of pairs
    ArrayList<int[]>seg = new ArrayList<>();

    // Push segments
    seg.add(new int[]{0, 3});
    seg.add(new int[]{1, 3});
    seg.add(new int[]{3, 8});

    // Given points
    int[] point = {-1, 3, 7};

    int s = seg.size();
    int p = point.length;

    NumberOfSegments(seg, point, s, p);
}
}

// This code is contributed by offbeat

Python3

# Python3 program to find the number
# of segments covering each point

# Function to print an array
def PrintArray(n, arr):

    for i in range(n):
        print(arr[i], end = " ")

# Function prints number of segments
# covering by each points
def NumberOfSegments(segments, points, s, p):

    pts = []
    seg = []

    # Pushing points and index in
    # vector as a pairs
    for i in range(p):
        pts.append([points[i], i])

    for i in range(s):

        # (l, +1)
        seg.append([segments[i][0], 1])

        # (r+1, -1)
        seg.append([segments[i][1] + 1, -1])

    # Sort the vectors
    seg.sort(reverse = True)
    pts.sort(reverse = False)

    count = 0
    ans = [0 for i in range(p)]

    for i in range(p):
        x = pts[i][0]

        while(len(seg) != 0 and
          seg[len(seg) - 1][0] <= x):

            count += seg[len(seg) - 1][1]
            seg.remove(seg[len(seg) - 1])

        ans[pts[i][1]] = count

    # Print the answer
    PrintArray(p, ans)

# Driver code
if __name__ == '__main__':

    # Initializing vector of pairs
    seg = []

    # Push segments
    seg.append([ 0, 3 ])
    seg.append([ 1, 3 ])
    seg.append([ 3, 8 ])

    # Given points
    point = [ -1, 3, 7 ]

    s = len(seg)
    p = len(point)

    NumberOfSegments(seg, point, s, p)

# This code is contributed by Bhupendra_Singh

C#

// C# program to find the number of
// segments covering each points
using System;
using System.Collections.Generic;

namespace ConsoleApp1
{
    class Program
    {
        // Function to print an array
        static void PrintArray(int[] arr)
        {
            foreach (int x in arr)
            {
                Console.Write(x + " ");
            }
        }

        // Function to find the number of segments covering each points
        static void NumberOfSegments(List<Tuple<int, int>> segments, int[] points)
        {
            List<Tuple<int, int>> pts = new List<Tuple<int, int>>();
            List<Tuple<int, int>> seg = new List<Tuple<int, int>>();

            // Pushing points and index in
            // list as a tuples
            for (int i = 0; i < points.Length; i++)
            {
                pts.Add(Tuple.Create(points[i], i));
            }

            for (int i = 0; i < segments.Count; i++)
            {
                // (l,+1)
                seg.Add(Tuple.Create(segments[i].Item1, 1));
                // (r+1,-1)
                seg.Add(Tuple.Create(segments[i].Item2 + 1, -1));
            }

            // Sort the lists
            seg.Sort((x, y) => y.Item1.CompareTo(x.Item1));
            pts.Sort();

            int count = 0;
            int[] ans = new int[points.Length];

            for (int i = 0; i < points.Length; i++)
            {
                int x = pts[i].Item1;

                while (seg.Count > 0 && seg[seg.Count - 1].Item1 <= x)
                {
                    count += seg[seg.Count - 1].Item2;
                    seg.RemoveAt(seg.Count - 1);
                }

                ans[pts[i].Item2] = count;
            }

            // Print the answer
            PrintArray(ans);
        }

        static void Main(string[] args)
        {
            // Initializing list of tuples
            List<Tuple<int, int>> seg = new List<Tuple<int, int>>();

            // Push segments
            seg.Add(Tuple.Create(0, 3));
            seg.Add(Tuple.Create(1, 3));
            seg.Add(Tuple.Create(3, 8));

            // Given points
            int[] point = { -1, 3, 7 };

            NumberOfSegments(seg, point);

            Console.ReadLine();
        }
    }
}

Javascript

<script>

// JavaScript program to find the number of
// segments covering each points

// Function to print an array
function PrintArray(n,arr)
{
    for(let i = 0; i < n; i++)
    {
        document.write(arr[i]," ");
    }
}

// Function prints number of segments
// covering by each points
function NumberOfSegments(segments,points,s,p)
{
let pts = [];
let seg = [];

// Pushing points and index in
// vector as a pairs
for(let i = 0; i < p; i++)
{
    pts.push([points[i], i]);
}

for(let i = 0; i < s; i++)
{
    // (l,+1)
    seg.push([segments[i][0], 1]);
    // (r+1,-1)
    seg.push([segments[i][1]+1, -1]);
}

// Sort the vectors

seg.sort((a,b) => b[0]-a[0]);
pts.sort((a,b) => a[0]-b[0]);

let count = 0;
let ans = new Array(p);

for(let i = 0; i < p; i++)
{
        let x = pts[i][0];

        while(seg.length>0 && seg[seg.length-1][0] <= x)
        {
            count+= seg[seg.length-1][1];
            seg.pop();
        }
        ans[pts[i][1]] = count;
}

// Print the answer
PrintArray(p, ans);

}

// Driver code

// Initializing vector of pairs
let seg = [];

// Push segments
seg.push([0, 3]);
seg.push([1, 3]);
seg.push([3, 8]);

// Given points
let point = [-1, 3, 7];

let s = seg.length;
let p = point.length;

NumberOfSegments(seg, point, s, p);

// This code is contributed by shinjanpatra.
</script>

Output:

0 3 1

Time Complexity: O(s*log(s) + p*log(p)), where s is the number of segments and p is the number of points.
Auxiliary Space: O(s + p).