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C++ Program to find out the super vertices in a graph
Suppose, we are given a graph that has n vertices. The vertices are numbered 1 to n, and they are connected by the edges given in the array 'edges'. Each vertex has an 'x' value within a number from 1 to n that is given in the array 'values'. Now, we have to find out the super vertices from the graph. A vertex i is called a 'super vertex' whenever the shortest path from vertex 1 to i doesn't have a vertex with the same 'x' value as the i-th vertex. We print out all the vertices satisfying this criterion.
So, if the input is like n = 5, values = {1, 2, 2, 1, 3}, edges = {{1, 2}, {2, 3}, {2, 3}, {2, 4}, {4, 5}}, then the output will be 1 3 4 5.
Every vertex except vertex 2 satisfies the criterion. So, vertex 2 is excluded.
Steps
To solve this, we will follow these steps −
Define arrays vertexVal, frq, and chk of size: 100005. Define an array vcti of size 200005. Define a function dfs(), this will take j, k, if frq[vertexVal[j]] is same as 0, then: chk[j] := 1 (increase frq[vertexVal[j]] by 1) for each value a in vcti[j], do: if a is not equal to k, then: dfs(a, j) (decrease frq[vertexVal[j]] by 1) for initialize i := 0, when i < n, update (increase i by 1), do: vertexVal[i] := values[i] for initialize i := 0, when i < n, update (increase i by 1), do: a := first value of edges[i] b := second value of edges[i] insert b at the end of vcti[a] insert a at the end of vcti[b] dfs(1, 0) for initialize i := 1, when i <= n, update (increase i by 1), do: if chk[i] is non-zero, then: print(i)
Example
Let us see the following implementation to get better understanding −
#include <bits/stdc++.h>
using namespace std;
int n;
int vertexVal[100005], frq[100005], chk[100005];
vector<int> vcti[200005];
void dfs(int j, int k){
if (frq[vertexVal[j]] == 0)
chk[j] = 1;
frq[vertexVal[j]]++;
for (auto a : vcti[j]) {
if (a != k)
dfs(a, j);
}
frq[vertexVal[j]]--;
}
void solve(int values[], vector<pair<int, int>> edges){
for (int i = 0; i < n; i++)
vertexVal[i] = values[i];
for (int i = 0; i < n; i++){
int a, b;
a = edges[i].first;
b = edges[i].second;
vcti[a].push_back(b);
vcti[b].push_back(a);
}
dfs(1, 0);
for (int i = 1;i <= n; i++){
if (chk[i]) cout<< i <<endl;
}
}
int main() {
n = 5;
int values[] = {1, 2, 2, 1, 3}; vector<pair<int, int>> edges = {{1, 2}, {2, 3}, {2, 3}, {2, 4}, {4, 5}};
solve(values, edges);
return 0;
}Input
5, {1, 2, 2, 1, 3}, {{1, 2}, {2, 3}, {2, 3}, {2, 4}, {4, 5}}Output
1 3 4 5
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