# Count of different groups using Graph

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

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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:

## CPP

 `// C++ implementation of the approach ` `#include ` `using` `namespace` `std; ` ` `  `// To store the parents ` `// of the current node ` `vector<``int``> par; ` ` `  `// To store the size of M and P ` `vector > 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 > 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 > connect = { ` `        ``{ 1, 3 }, ` `        ``{ 3, 5 }, ` `        ``{ 4, 5 } ` `    ``}; ` ` `  `    ``influenced(nodes, connect); ` ` `  `    ``return` `0; ` `} `

## 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 `

Output:

```P = 1
M = 1
N = 0
```

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