In this HackerEarth Components of Graph <Airbus> problem solution You are given a directed network of flights i.e. N cities and M one-directional flights. Each city has a particular air quality index value associated with it. Now, your task is to determine the maximum threshold value X such that if the flights incident to or from the cities with air quality index values less than X is canceled then there should exist a reachable component of cities in the network of size at least K. A subcomponent of a flight network is considered to be a reachable component if all the cities in that component are connected, this implies that all the flights are reachable from each other via direct or connecting flights.


HackerEarth Components of Graph <Airbus> problem solution


HackerEarth Components of Graph <Airbus> problem solution.

#include<bits/stdc++.h>
#define LL long long int
#define M 1000000007
#define endl "\n"
#define eps 0.00000001
LL pow(LL a,LL b,LL m){ a%=m;LL x=1,y=a;while(b > 0){if(b%2 == 1){x=(x*y);if(x>m) x%=m;}y = (y*y);if(y>m) y%=m;b /= 2;}return x%m;}
LL gcd(LL a,LL b){if(b==0) return a; else return gcd(b,a%b);}
LL gen(LL start,LL end){LL diff = end-start;LL temp = rand()%start;return temp+diff;}
using namespace std;
int u[100001];
int v[100001];
int val[100001];
int n, m, k;
vector<int> graph[100001];
stack<int> scc_stack;
bool visit[100001];
int components_sz[100001];
int components_count = 0;
void dfs(int node) {
visit[node] = 1;
for(int i: graph[node]) {
if(visit[i] == 0) {
visit[i] = 1;
dfs(i);
}
}
scc_stack.push(node);
}


void dfs2(int node) {
components_sz[components_count]++;
visit[node] = 1;
for(int i: graph[node]) {
if(visit[i] == 1)
continue;
visit[i] = 1;
dfs2(i);
}
}

bool check(int limit) {
components_count = 0;
memset(visit, 0, sizeof(visit));
while(!scc_stack.empty()) {
scc_stack.pop();
}
for(int i = 1; i <= n; i++) {
graph[i].clear();
}
for(int i = 1; i <= m; i++) {
int a = u[i], b = v[i];
if(val[a] >= limit && val[b] >= limit) {
graph[a].push_back(b);
}
}
for(int i = 1; i <= n; i++) {
if(visit[i] == 0) {
dfs(i);
}
}
for(int i = 1; i <= n; i++)
graph[i].clear();
memset(visit, 0, sizeof(visit));
for(int i = 1; i <= m; i++) {
int a = u[i], b = v[i];
if(val[a] >= limit && val[b] >= limit) {
graph[b].push_back(a);
}
}
while(scc_stack.size()) {
int cur = scc_stack.top();
scc_stack.pop();
if(visit[cur] == 1)
continue;
++components_count;
dfs2(cur);
}
int ans = 0;
for(int i = 1; i <= components_count; i++) {
ans = max(ans , components_sz[i]);
components_sz[i] = 0;
}
components_count = 0;
if(ans >= k)
return 1;
else
return 0;
}
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
assert(cin >> n >> m >> k);

for(int i = 1; i <= n; i++)
assert(cin >> val[i]);
for(int i = 1; i <= m; i++) {
assert(cin >> u[i] >> v[i]);
}
int l = 1, r = 1000000000;
int ans = -1;
while(l <= r) {
int mid = (l + r) / 2;
if(check(mid) == 1) {
ans = mid;
l = mid + 1;
}
else {
r = mid - 1;
}
}
assert(ans != -1);
cout << ans << endl;
}