Find Minimum and Maximum distinct persons entering or leaving the room

Given a binary string persons where '1' and '0' represent people entering and leaving a room respectively. The task is to find the Minimum and Maximum Distinct Persons entering or leaving the building.

Examples:

Input: "000"
Output: Minimum Persons: 3
Maximum Persons: 3
Explanation: 3 distinct persons left the building.

Input: "111"
Output: Minimum Persons: 3
Maximum Persons: 3
Explanation: 3 distinct persons entered the building.

Input: "110011"
Output: Minimum Persons: 2
Maximum Persons: 6
Explanation: 2 persons entered->those 2 persons left->same 2 persons entered 
to account for minimum 2 persons.
All persons entered or left are distinct to account for maximum 6 persons.

Input: "10101"
Output: Minimum Persons: 1
Maximum Persons: 5
Explanation:  1 person entered- > he left -> again entered -> again left -> and again entered 
to account for minimum 1 person.
All persons entered or left are distinct to account for maximum 5 persons.

Approach: The problem can be solved based on the following observation:

• Each person entering or leaving the room can be a unique person. This will give the maximum number of persons that can enter a room. This will be equal to the total number of times a leaving or entering operation is performed,
• Each time the same persons who are leaving the room are entering the room next time. So the maximum among the people leaving at a time or entering at a time is the minimum possible number of unique persons.

Follow the below illustration for a better understanding.

Illustration:

Consider persons = "10101"

For finding the maximum:

        => At first, first person (say P1) enters the room
        => Then, second person (say P2) exits the room
        => Then, third person (say P3) enters the room
        => Then, fourth person (say P4) exits the room
        => At last, fifth person (say P5) enters the room

Total 5 persons enter or leave the room at most.

For finding the minimum possible persons:

        => At first, first person (say P1) enters the room.
        => Then P1 exits the room.
        => Then P1 again enters the room.
        => Then again P1 exits the room.
        => At last P1 again enters the room.

So at least one person enters or leaves the room.

Follow the below steps to implement the above observation:

• Start traversing the whole string persons.
• If persons[i] = '1' then increment entered else decrement entered.
• Store the maximum value of entered and N (size of string persons) as the first and second value of the pair result.
• In that loop, if at anytime entered becomes negative then re-initialize it to 0 and increment the first value of the pair result.
• Return result as the final pair containing minimum and maximum distinct persons as first and second value respectively.

Below is the implementation of the above approach:

// C++ code to implement the approach

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

// Function to find the minimum and
// maximum number of possible persons
// entering or leaving the room
pair<int,int> minDistPersons(string& persons)
{
   int N=persons.length(),entered=0;
   pair<int,int>result={0,N};
   
   for(int i=0;i<N;i++)
   {
       if(persons[i]=='1')
       entered++;
       else entered--;
       
       result.first=max(result.first,entered);
       
       if(entered<0)
       {
         entered=0;
           result.first++;
       }
   }
   
   return result;
}

// Driver code
int main()
{
    string persons = "10101";

    // Function call
    pair<int, int> ans = minDistPersons(persons);
    cout << "Minimum Persons: " << ans.first
         << "\n";
    cout << "Maximum Persons: " << ans.second;
    return 0;
}
// this code is contributed by prophet1999

// Java code to implement the approach
import java.io.*;

class GFG
{

  // Function to find the minimum and
  // maximum number of possible persons
  // entering or leaving the room
  public static int[] minDistPersons(String persons)
  {
    int N = persons.length();
    int entered = 0;
    int result[] = new int[2];
    result[1] = N;
    for (int i = 0; i < N; i++) {
        
      if (persons.charAt(i) == '1')
        entered++;
      else entered--;
      
      result[0] = Math.max(result[0],entered);
      
      if(entered<0)
      {
          entered=0;
          result[0]++;
      }
      
    }

    return result;
  }

  // Driver Code
  public static void main(String[] args)
  {
    String persons = "10101";

    // Function call
    int ans[] = minDistPersons(persons);
    System.out.println("Minimum Persons: " + ans[0]);
    System.out.print("Maximum Persons: " + ans[1]);
  }
}

// this code is contributed by prophet1999

# Python3 code for the above approach

# Function to find the minimum and
# maximum number of positive persons
# entering or leaving the room
def minDistPersons(persons):
    N = len(persons)
    entered, exited = 0, 0
    result = [0, N]

    for i in range(N):
        if persons[i] == "1":
            entered+=1
        else:
            entered-=1
        result[0] = max(result[0], entered)
        if(entered<0):
            entered=0
            result[0]+=1

    return result

# Driver Code
persons = "10101"

# Function call
ans = minDistPersons(persons)

print("Minimum Persons: " + str(ans[0]))
print("Maximum Persons: " + str(ans[1]))

# this code is contributed by prophet1999

// C# program for above approach
using System;
class GFG
{

  
  // Function to find the minimum and
  // maximum number of possible persons
  // entering or leaving the room
  public static int[] minDistPersons(string persons)
  {
    int N = persons.Length;
    int entered = 0;
    int[] result = new int[2];
    result[1] = N;
    for (int i = 0; i < N; i++) {
        
      if (persons[i] == '1')
        entered++;
      else entered--;
      
      result[0] = Math.Max(result[0],entered);
      
      if(entered<0)
      {
          entered=0;
          result[0]++;
      }
      
    }

    return result;
  }

// Driver Code
public static void Main()
{
    string persons = "10101";

    // Function call
    int[] ans = minDistPersons(persons);
    Console.WriteLine("Minimum Persons: " + ans[0]);
    Console.Write("Maximum Persons: " + ans[1]);
}
}

// This code is contributed by code_hunt.

 <script>
        // JavaScript code for the above approach

        // Function to find the minimum and
        // maximum number of possible persons
        // entering or leaving the room
        function minDistPersons(persons) {
            let N = persons.length;
            let entered = 0;
            let result = [0, N];

            for (let i = 0; i < N; i++) {
                if (persons[i] == '1')
                    entered++;
                else
                    entered--;
                    
                result[0] = Math.max(...[result[0], entered]);
                
                if(entered<0)
                {
                    entered=0;
                    result[0]++;
                }
            }

            return result;
        }

        // Driver code
        let persons = "10101";

        // Function call
        let ans = minDistPersons(persons);
        document.write("Minimum Persons: " + ans[0] + '<br>');
        document.write("Maximum Persons: " + ans[1]);

    // this code is contributed by prophet1999
    </script>

Minimum Persons: 1
Maximum Persons: 5

Time Complexity: O(N), where N is the length of the string persons.
Auxiliary Space: O(1)