Problem p01680 (C++) — buggy submission, verdict: Time Limit Exceeded

#include <bits/stdc++.h>

using namespace std;

inline int toInt(string s) {
  int v;
  istringstream sin(s);
  sin >> v;
  return v;
}
template <class T> inline string toString(T x) {
  ostringstream sout;
  sout << x;
  return sout.str();
}
template <class T> inline T sqr(T x) { return x * x; }

typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<string> vs;
typedef pair<int, int> pii;
typedef long long ll;

#define all(a) (a).begin(), (a).end()
#define rall(a) (a).rbegin(), (a).rend()
#define pb push_back
#define mp make_pair
#define each(i, c)                                                             \\
  for (typeof((c).begin()) i = (c).begin(); i != (c).end(); ++i)
#define exist(s, e) ((s).find(e) != (s).end())
#define range(i, a, b) for (int i = (a); i < (b); ++i)
#define rep(i, n) range(i, 0, n)
#define clr(a, b) memset((a), (b), sizeof(a))
#define dump(x) cerr << #x << " = " << (x) << endl;
#define debug(x)                                                               \\
  cerr << #x << " = " << (x) << " (L" << __LINE__ << ")"                       \\
       << " " << __FILE__ << endl;

const double eps = 1e-10;
const double pi = acos(-1.0);
const ll INF = 1LL << 62;
const int inf = 1 << 29;

const int nmax = 100010;
const ll mod = 1000000007;
bool used[nmax];

ll power(ll a, ll n) {
  ll b = 1LL;
  while (n) {
    if (n & 1)
      b = b * a % mod;
    a = a * a % mod;
    n >>= 1;
  }
  return b % mod;
}

int par[nmax], ranks[nmax], sz[nmax];

void init(int n) { rep(i, n) par[i] = i, ranks[i] = sz[i] = 0; }
int find(int x) { return (x == par[x]) ? x : par[x] = find(par[x]); }
void unite(int a, int b) {
  a = find(a), b = find(b);
  if (ranks[a] < ranks[b])
    par[a] = b;
  else {
    par[b] = a;
    if (ranks[a] == ranks[b])
      ranks[a]++;
  }
  return;
}
bool same(int a, int b) { return find(a) == find(b); }

int main(void) {
  int n, m;
  while (cin >> n >> m) {
    if (n == 0 && m == 0)
      break;
    rep(i, n) used[i] = false;
    init(n);

    rep(i, m) {
      int a, b;
      cin >> a >> b;
      a--, b--;
      unite(a, b);
    }

    rep(i, n) sz[find(i)]++;

    if (m == 0)
      cout << power(2, n) << endl;
    else {
      ll ans = 1LL, num = 0, res = 0;
      rep(i, n) {
        if (sz[i] >= 2)
          num++;
        if (sz[i] == 1)
          res++;
      }
      ans *= power(2, res);
      ans %= mod;
      ans *= power(2, num);
      ans %= mod;
      ans = (ans + 1) % mod;
      cout << ans << endl;
    }
  }
  return 0;
}

Error: TLE

Fixed submission:

#include <bits/stdc++.h>

using namespace std;

inline int toInt(string s) {
  int v;
  istringstream sin(s);
  sin >> v;
  return v;
}
template <class T> inline string toString(T x) {
  ostringstream sout;
  sout << x;
  return sout.str();
}
template <class T> inline T sqr(T x) { return x * x; }

typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<string> vs;
typedef pair<int, int> pii;
typedef long long ll;

#define all(a) (a).begin(), (a).end()
#define rall(a) (a).rbegin(), (a).rend()
#define pb push_back
#define mp make_pair
#define each(i, c)                                                             \\
  for (typeof((c).begin()) i = (c).begin(); i != (c).end(); ++i)
#define exist(s, e) ((s).find(e) != (s).end())
#define range(i, a, b) for (int i = (a); i < (b); ++i)
#define rep(i, n) range(i, 0, n)
#define clr(a, b) memset((a), (b), sizeof(a))
#define dump(x) cerr << #x << " = " << (x) << endl;
#define debug(x)                                                               \\
  cerr << #x << " = " << (x) << " (L" << __LINE__ << ")"                       \\
       << " " << __FILE__ << endl;

const double eps = 1e-10;
const double pi = acos(-1.0);
const ll INF = 1LL << 62;
const int inf = 1 << 29;

const int nmax = 100010;
const ll mod = 1000000007;
bool used[nmax];

ll power(ll a, ll n) {
  ll b = 1LL;
  while (n) {
    if (n & 1)
      b = b * a % mod;
    a = a * a % mod;
    n >>= 1;
  }
  return b % mod;
}

int par[nmax], ranks[nmax], sz[nmax];

void init() { rep(i, nmax) par[i] = i, ranks[i] = sz[i] = 0; }
int find(int x) { return (x == par[x]) ? x : find(par[x]); }
void unite(int a, int b) {
  a = find(a), b = find(b);
  if (ranks[a] < ranks[b])
    par[b] = a;
  else {
    par[a] = b;
    if (ranks[a] == ranks[b])
      ranks[a]++;
  }
  return;
}
bool same(int a, int b) { return find(a) == find(b); }

int main(void) {
  int n, m;
  while (cin >> n >> m) {
    if (n == 0 && m == 0)
      break;
    rep(i, n) used[i] = false;
    init();

    rep(i, m) {
      int a, b;
      cin >> a >> b;
      a--, b--;
      unite(a, b);
    }

    rep(i, n) sz[find(i)]++;

    if (m == 0)
      cout << power(2, n) << endl;
    else {
      ll ans = 1LL, num = 0, res = 0;
      rep(i, n) {
        if (sz[i] >= 2)
          num++;
        if (sz[i] == 1)
          res++;
      }
      ans *= power(2, res);
      ans %= mod;
      ans *= power(2, num);
      ans %= mod;
      ans = (ans + 1) % mod;
      cout << ans << endl;
    }
  }
  return 0;
}