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Count of different groups using Graph
  • Last Updated : 14 Jun, 2021

Given a graph with N nodes having values either P or M. Also given K pairs of integers as (x, y) representing the edges in the graph such that if a is connected to b and b is connected to c then a and c will also be connected. 

A single connected component is called a group. The group can have both P and M values. If the P values are more than the M values this group is called P influenced and similarly for M. If the number of P’s and M’s are equal then it is called a neutral group. The task is to find the number of P influenced, M influenced and, Neutral groups.

Examples:  

Input: Nodes[] = {P, M, P, M, P}, edges[][] = { 
{1, 3}, 
{4, 5}, 
{3, 5}} 
Output: 
P = 1 
M = 1 
N = 0 
There will be two groups of indexes 
{1, 3, 4, 5} and {2}. 
The first group is P influenced and 
the second one is M influenced.

Input: Nodes[] = {P, M, P, M, P}, edges[][] = { 
{1, 3}, 
{4, 5}} 
Output: 
P = 1 
M = 2 
N = 0 



Approach: It is easier to construct a graph with adjacency list and loop from 1 to N and do DFS and check the count of P and M. 
Another way is to use DSU with a little modification that size array will be of pair so that it can maintain the count of both M and P. In this approach, there is no need to construct the graph as the merge operation will take care of the connected component. Note that you should have the knowledge of DSU by size/rank for optimization.

Below is the implementation of the above approach:  

C++




// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
 
// To store the parents
// of the current node
vector<int> par;
 
// To store the size of M and P
vector<pair<int, int> > sz;
 
// Function for initialization
void init(vector<char>& nodes)
{
 
    // Size of the graph
    int n = (int)nodes.size();
 
    par.clear();
    sz.clear();
    par.resize(n + 1);
    sz.resize(n + 1);
 
    for (int i = 0; i <= n; ++i) {
        par[i] = i;
 
        if (i > 0) {
 
            // If the node is P
            if (nodes[i - 1] == 'P')
                sz[i] = { 0, 1 };
 
            // If the node is M
            else
                sz[i] = { 1, 0 };
        }
    }
}
 
// To find the parent of
// the current node
int parent(int i)
{
    while (par[i] != i)
        i = par[i];
    return i;
}
 
// Merge funtion
void unin(int a, int b)
{
    a = parent(a);
    b = parent(b);
 
    if (a == b)
        return;
 
    // Total size by adding number of M and P
    int sz_a = sz[a].first + sz[a].second;
    int sz_b = sz[b].first + sz[b].second;
 
    if (sz_a < sz_b)
        swap(a, b);
 
    par[b] = a;
    sz[a].first += sz[b].first;
    sz[a].second += sz[b].second;
    return;
}
 
// Function to calculate the influenced value
void influenced(vector<char>& nodes,
                vector<pair<int, int> > connect)
{
 
    // Number of nodes
    int n = (int)nodes.size();
 
    // Initialization function
    init(nodes);
 
    // Size of the connected vector
    int k = connect.size();
 
    // Performing union operation
    for (int i = 0; i < k; ++i) {
        unin(connect[i].first, connect[i].second);
    }
 
    // ne = Number of neutal groups
    // ma = Number of M influenced groups
    // pe = Number of P influenced groups
    int ne = 0, ma = 0, pe = 0;
 
    for (int i = 1; i <= n; ++i) {
        int x = parent(i);
 
        if (x == i) {
            if (sz[i].first == sz[i].second) {
                ne++;
            }
            else if (sz[i].first > sz[i].second) {
                ma++;
            }
            else {
                pe++;
            }
        }
    }
 
    cout << "P = " << pe << "\nM = "
         << ma << "\nN = " << ne << "\n";
}
 
// Driver code
int main()
{
 
    // Nodes at each index ( 1 - base indexing )
    vector<char> nodes = { 'P', 'M', 'P', 'M', 'P' };
 
    // Connected Pairs
    vector<pair<int, int> > connect = {
        { 1, 3 },
        { 3, 5 },
        { 4, 5 }
    };
 
    influenced(nodes, connect);
 
    return 0;
}

Java




// Java implementation of the approach
import java.io.*;
import java.util.*;
 
class GFG{
     
// To store the parents
// of the current node
static ArrayList<Integer> par = new ArrayList<Integer>();
 
// To store the size of M and P
static ArrayList<
       ArrayList<Integer>> sz = new ArrayList<
                                    ArrayList<Integer>>();
                                     
// Function for initialization
static void init(ArrayList<Character> nodes)
{
     
    // Size of the graph
    int n = nodes.size();
    for(int i = 0; i <= n; ++i)
    {
        par.add(i);
         
        if (i == 0)
        {
            sz.add(new ArrayList<Integer>(
                Arrays.asList(0, 0)));
        }
         
        if (i > 0)
        {
             
            // If the node is P
            if (nodes.get(i - 1) == 'P')
            {
                sz.add(new ArrayList<Integer>(
                    Arrays.asList(0, 1)));
            }
             
            // If the node is M
            else
            {
                sz.add(new ArrayList<Integer>(
                    Arrays.asList(1, 0)));
            }
        }
    }
}
 
// To find the parent of
// the current node
static int parent(int i)
{
    while (par.get(i) != i)
    {
        i = par.get(i);
    }
    return i;
}
 
// Merge funtion
static void unin(int a, int b)
{
    a = parent(a);
    b = parent(b);
     
    if (a == b)
    {
        return;
    }
     
    // Total size by adding number
    // of M and P
    int sz_a = sz.get(a).get(0) +
               sz.get(a).get(1);
    int sz_b = sz.get(b).get(0) +
               sz.get(b).get(1);
                
    if (sz_a < sz_b)
    {
        int temp = a;
        a = b;
        b = temp;
    }
    par.set(b, a);
     
    sz.get(a).set(0, sz.get(a).get(0) +
                     sz.get(b).get(0));
    sz.get(a).set(1, sz.get(a).get(1) +
                     sz.get(b).get(1));
    return;
}
 
// Function to calculate the influenced value
static void influenced(ArrayList<Character> nodes,
             ArrayList<ArrayList<Integer>> connect)
{
     
    // Number of nodes
    int n = nodes.size();
     
    // Initialization function
    init(nodes);
     
    // Size of the connected vector
    int k = connect.size();
     
    // Performing union operation
    for(int i = 0; i < k; ++i)
    {
        unin(connect.get(i).get(0),
             connect.get(i).get(1));
    }
     
    // ne = Number of neutal groups
    // ma = Number of M influenced groups
    // pe = Number of P influenced groups
    int ne = 0, ma = 0, pe = 0;
    for(int i = 1; i <= n; ++i)
    {
        int x = parent(i);
         
        if (x == i)
        {
            if (sz.get(i).get(0) ==
                sz.get(i).get(1))
            {
                ne++;
            }
            else if (sz.get(i).get(0) >
                     sz.get(i).get(1))
            {
                ma++;
            }
            else
            {
                pe++;
            }
        }
    }
    System.out.println("P = " + pe +
                     "\nM = " + ma +
                     "\nN = " + ne);
}
 
// Driver code
public static void main(String[] args)
{
     
    // Nodes at each index ( 1 - base indexing )
    ArrayList<Character> nodes = new ArrayList<Character>();
    nodes.add('P');
    nodes.add('M');
    nodes.add('P');
    nodes.add('M');
    nodes.add('P');
     
    // Connected Pairs
    ArrayList<
    ArrayList<Integer>> connect = new ArrayList<
                                      ArrayList<Integer>>();
    connect.add(new ArrayList<Integer>(
        Arrays.asList(1, 3)));
    connect.add(new ArrayList<Integer>(
        Arrays.asList(3, 5)));
    connect.add(new ArrayList<Integer>(
        Arrays.asList(4, 5)));
         
    influenced(nodes, connect);
}
}
 
// This code is contributed by avanitrachhadiya2155

Python3




# Python3 implementation of the approach
 
# To store the parents
# of the current node
par = []
 
# To store the size of M and P
sz = []
 
# Function for initialization
def init(nodes):
 
    # Size of the graph
    n = len(nodes)
    for i in range(n + 1):
        par.append(0)
        sz.append(0)
 
    for i in range(n + 1):
        par[i] = i
 
        if (i > 0):
 
            # If the node is P
            if (nodes[i - 1] == 'P'):
                sz[i] = [0, 1]
 
            # If the node is M
            else:
                sz[i] = [1, 0]
 
# To find the parent of
# the current node
def parent(i):
    while (par[i] != i):
        i = par[i]
    return i
 
# Merge funtion
def unin(a, b):
    a = parent(a)
    b = parent(b)
 
    if (a == b):
        return
 
    # Total size by adding number of M and P
    sz_a = sz[a][0] + sz[a][1]
    sz_b = sz[b][0] + sz[b][1]
 
    if (sz_a < sz_b):
        a, b = b, a
 
    par[b] = a
    sz[a][0] += sz[b][0]
    sz[a][1] += sz[b][1]
    return
 
# Function to calculate the influenced value
def influenced(nodes,connect):
 
    # Number of nodes
    n = len(nodes)
 
    # Initialization function
    init(nodes)
 
    # Size of the connected vector
    k = len(connect)
 
    # Performing union operation
    for i in range(k):
        unin(connect[i][0], connect[i][1])
 
    # ne = Number of neutal groups
    # ma = Number of M influenced groups
    # pe = Number of P influenced groups
    ne = 0
    ma = 0
    pe = 0
 
    for i in range(1, n + 1):
        x = parent(i)
 
        if (x == i):
            if (sz[i][0] == sz[i][1]):
                ne += 1
            elif (sz[i][0] > sz[i][1]):
                ma += 1
            else:
                pe += 1
 
    print("P =",pe,"\nM =",ma,"\nN =",ne)
 
# Driver code
 
# Nodes at each index ( 1 - base indexing )
nodes = [ 'P', 'M', 'P', 'M', 'P' ]
 
# Connected Pairs
connect = [ [ 1, 3 ],
            [ 3, 5 ],
            [ 4, 5 ] ]
 
influenced(nodes, connect)
 
# This code is contributed by mohit kumar 29

C#




// C# implementation of the approach
using System;
using System.Collections.Generic;
 
class GFG{
     
// To store the parents
// of the current node
static List<int> par = new List<int>();
 
// To store the size of M and P
static List<List<int>> sz = new List<List<int>>();
 
// Function for initialization
static void init(List<char> nodes)
{
     
    // Size of the graph
    int n = nodes.Count;
    for(int i = 0; i <= n; ++i)
    {
        par.Add(i);
         
        if (i == 0)
        {
            sz.Add(new List<int>(){0, 0});
        }
         
        if (i > 0)
        {
             
            // If the node is P
            if (nodes[i - 1] == 'P')
            {
                sz.Add(new List<int>(){0, 1});
                 
            }
             
            // If the node is M
            else
            {
                sz.Add(new List<int>(){1, 0});
            }
        }
    }
}
 
// To find the parent of
// the current node
static int parent(int i)
{
    while (par[i] != i)
    {
        i = par[i];
    }
    return i;
}
 
// Merge funtion
static void unin(int a, int b)
{
    a = parent(a);
    b = parent(b);
     
    if (a == b)
    {
        return;
    }
     
    // Total size by adding number
    // of M and P
    int sz_a = sz[a][0] + sz[a][1];
    int sz_b = sz[b][0] + sz[b][1];
     
    if (sz_a < sz_b)
    {
        int temp = a;
        a = b;
        b = temp;
    }
     
    par[b] = a;
    sz[a][0] += sz[b][0];
    sz[a][1] += sz[b][1];
    return;
}
 
// Function to calculate the influenced value
static void influenced(List<char> nodes,
                       List<List<int>> connect)
{
     
    // Number of nodes
    int n = nodes.Count;
     
    // Initialization function
    init(nodes);
     
    // Size of the connected vector
    int k = connect.Count;
     
    // Performing union operation
    for(int i = 0; i < k; ++i)
    {
        unin(connect[i][0], connect[i][1]);
    }
     
    // ne = Number of neutal groups
    // ma = Number of M influenced groups
    // pe = Number of P influenced groups
    int ne = 0, ma = 0, pe = 0;
    for(int i = 1; i <= n; ++i)
    {
        int x = parent(i);
         
        if (x == i)
        {
            if (sz[i][0] == sz[i][1])
            {
                ne++;
            }
            else if (sz[i][0] > sz[i][1])
            {
                ma++;
            }
            else
            {
                pe++;
            }
        }
    }
    Console.WriteLine("P = " + pe + "\nM = " +
                      ma + "\nN = " + ne);
}
 
// Driver code
static public void Main()
{
     
    // Nodes at each index ( 1 - base indexing )
    List<char> nodes = new List<char>(){'P', 'M', 'P', 'M', 'P'};
     
    // Connected Pairs
    List<List<int>> connect = new List<List<int>>();
    connect.Add(new List<int>(){1, 3});
    connect.Add(new List<int>(){3, 5});
    connect.Add(new List<int>(){4, 5});
     
    influenced(nodes, connect);
}
}
 
// This code is contributed by rag2127

Javascript




<script>
// Javascript implementation of the approach
 
// To store the parents
// of the current node
let par = [];
 
// To store the size of M and P
let sz = [];
 
// Function for initialization
function init(nodes)
{
    // Size of the graph
    let n = nodes.length;
    for(let i = 0; i <= n; ++i)
    {
        par.push(i);
          
        if (i == 0)
        {
            sz.push([0,0]);
        }
          
        if (i > 0)
        {
              
            // If the node is P
            if (nodes[i - 1] == 'P')
            {
                sz.push([0,1]);
            }
              
            // If the node is M
            else
            {
                sz.push([1,0]);
            }
        }
    }
}
 
// To find the parent of
// the current node
function parent(i)
{
    while (par[i] != i)
    {
        i = par[i];
    }
    return i;
}
 
// Merge funtion
function unin(a,b)
{
    a = parent(a);
    b = parent(b);
      
    if (a == b)
    {
        return;
    }
      
    // Total size by adding number
    // of M and P
    let sz_a = sz[a][0] +
               sz[a][1];
    let sz_b = sz[b][0] +
               sz[b][1];
                 
    if (sz_a < sz_b)
    {
        let temp = a;
        a = b;
        b = temp;
    }
    par[b] = a;
      
    sz[a][0] = sz[a][0] +
                     sz[b][0];
    sz[a][1] = sz[a][1] +
                     sz[b][1];
    return;
}
 
// Function to calculate the influenced value
function influenced(nodes,connect)
{
    // Number of nodes
    let n = nodes.length;
      
    // Initialization function
    init(nodes);
      
    // Size of the connected vector
    let k = connect.length;
      
    // Performing union operation
    for(let i = 0; i < k; ++i)
    {
        unin(connect[i][0],
             connect[i][1]);
    }
      
    // ne = Number of neutal groups
    // ma = Number of M influenced groups
    // pe = Number of P influenced groups
    let ne = 0, ma = 0, pe = 0;
    for(let i = 1; i <= n; ++i)
    {
        let x = parent(i);
          
        if (x == i)
        {
            if (sz[i][0] ==
                sz[i][1])
            {
                ne++;
            }
            else if (sz[i][0] >
                     sz[i][1])
            {
                ma++;
            }
            else
            {
                pe++;
            }
        }
    }
    document.write("P = " + pe +
                     "<br>M = " + ma +
                     "<br>N = " + ne);
}
 
// Driver code
// Nodes at each index ( 1 - base indexing )
let nodes =[];
nodes.push('P');
nodes.push('M');
nodes.push('P');
nodes.push('M');
nodes.push('P');
 
// Connected Pairs
let connect = [];
connect.push([1,3]);
connect.push([3,5]);
connect.push([4,5]);
 
influenced(nodes, connect);
 
// This code is contributed by patel2127
</script>
Output: 
P = 1
M = 1
N = 0

 

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