Coding/D_Beautiful_Graph.cpp at main · nishantlamba29/Coding · GitHub

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

const int N = 3e5 + 5;
const int mod = 998244353;
vector<int> adj[N];
int color[N];

int modpwr(long long a, int b) {
    long long res = 1;
    while(b) {
        if(b & 1) {
            res = (res * a) % mod;
        }
        a = (a * a) % mod;
        b >>= 1;
    }
    return res;
}

int c1, c2;
bool dfs(int node) {
    for(auto &j : adj[node]) {
        if(color[j] == -1) {
            color[j] = (1 ^ color[node]);
            if(color[j] == 0) c1++;
            else c2++;
            if(!dfs(j)) return false;
        }
        else if(color[j] == color[node]) {
            return false;
        }
    }
    return true;
}

void solve() {
    int n, m;
    cin >> n >> m;
    for(int i=0;i<=n;i++) {
        color[i] = -1;
        adj[i].clear();
    }
    if(m == 0) {
        cout << modpwr(3, n) << "\n";
        return;
    }
    for(int i=0;i<m;i++) {
        int u, v;
        cin >> u >> v;
        adj[u].push_back(v);
        adj[v].push_back(u);
    }

    long long ans = 1;
    for(int i=1;i<=n;i++) {
        if(color[i] == -1) {
            color[i] = 0;
            c1 = 1, c2 = 0;
            if(!dfs(i)) {
                cout << "0\n";
                return;
            }
            int ways = (modpwr(2, c1) + modpwr(2, c2)) % mod;
            ans = (ans * ways) % mod;
        }
    }

    cout << ans << "\n";

}


int32_t main(){
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    cout.tie(nullptr);

    int _;
    cin >> _;
    while (_-->0) {
        solve();
    }

    return 0;
}