Problem p02632 (C++) — buggy submission, verdict: Time Limit Exceeded

#include <algorithm>
#include <cassert>
#include <cfloat>
#include <climits>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <deque>
#include <iostream>
#include <iterator>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

#define FOR(i, k, n) for (int(i) = (k); (i) < (n); ++(i))
#define rep(i, n) FOR(i, 0, n)
#define all(v) begin(v), end(v)
#ifdef ONLINE_JUDGE
#define debug(x)
#define debug2(x, y)
#define debug3(x, y, z)
#define assert(e)                                                              \\
  if (!(e)) {                                                                  \\
    stod("");                                                                  \\
  }
#else
#define debug(x) std::cerr << #x << ": " << x << "\\n"
#define debug2(x, y)                                                           \\
  std::cerr << #x << ": " << x << ", " << #y << ": " << y << "\\n"
#define debug3(x, y, z)                                                        \\
  std::cerr << #x << ": " << x << ", " << #y << ": " << y << ", " << #z        \\
            << ": " << z << "\\n"
#endif

using ll = long long;
using vi = std::vector<int>;
using vvi = std::vector<vi>;
using vll = std::vector<ll>;
using vvll = std::vector<vll>;
template <typename T> using vvec = std::vector<std::vector<T>>;
template <typename T> auto make_v(size_t sz) { return std::vector<T>(sz); }
template <typename T, typename... Ts> auto make_v(size_t sz, Ts... ts) {
  return std::vector<decltype(make_v<T>(ts...))>(sz, make_v<T>(ts...));
}
template <typename T> void fill_v(T &var, const T &x) { var = x; }
template <typename V, typename T> void fill_v(V &v, const T &x) {
  for (auto &&w : v) {
    fill_v(w, x);
  }
}

template <typename T>
std::ostream &operator<<(std::ostream &s, const std::vector<T> &v) {
  int sz = v.size();
  s << "\\n";
  rep(i, sz) {
    s << v[i];
    if (i < sz - 1) {
      s << "\\t";
    }
  }
  s << "\\n";
  return s;
}
template <typename T>
std::ostream &operator<<(std::ostream &s,
                         const std::vector<std::vector<T>> &v) {
  for (auto &&w : v) {
    s << w;
  }
  return s;
}
template <typename T>
std::ostream &operator<<(std::ostream &s, const std::deque<T> &v) {
  int sz = v.size();
  s << "\\n";
  rep(i, sz) {
    s << v[i];
    if (i < sz - 1) {
      s << "\\t";
    }
  }
  s << "\\n";
  return s;
}
template <typename T>
std::ostream &operator<<(std::ostream &s, const std::deque<std::deque<T>> &v) {
  for (auto &&w : v) {
    s << w;
  }
  return s;
}
template <typename T>
std::ostream &operator<<(std::ostream &s, const std::set<T> &v) {
  s << "\\n";
  for (auto &&elm : v) {
    s << elm << "\\t";
  }
  s << "\\n";
  return s;
}

inline void scan(int &a) { scanf("%d", &a); }
inline void scan(ll &a) { scanf("%lld", &a); }
inline void scan(char &a) { scanf(" %c", &a); }
inline void scan(double &a) { scanf("%lf", &a); }
template <typename T> inline void scan(std::vector<T> &v) {
  for (auto &&sv : v) {
    scan(sv);
  }
}
template <typename First, typename... Args>
inline void scan(First &f, Args &...args) {
  scan(f);
  scan(args...);
}
inline void scan(std::string &s) {
  char BUF[3000000];
  scanf(" %s", BUF);
  s = std::string(BUF);
}
inline void print(int a) { printf("%d\\n", a); }
inline void print(ll a) { printf("%lld\\n", a); }
inline void print(double a) { printf("%.12f\\n", a); }
inline void print(std::string s) { std::cout << s << "\\n"; }

using namespace std;

/*
k = 1, s = "aa"
aaa ... aaz 26
aba ... aza 25
baa ... zaa 25
-> 76
k = 1, s = "ab"
aba ... abz 26
aab, acb ... azb 25
bab ... zab
-> 76
*/

ll mod = 1000000007;

ll po(ll k, ll x) {
  if (x == 0) {
    return 1;
  }
  if (x == 1) {
    return k % mod;
  }
  ll y = po(k, x / 2);
  y = y * y % mod;
  if (x % 2 == 1) {
    y = y * k % mod;
  }
  return y;
}

ll combination(ll n, ll k, const vll &frac) {
  k = min(k, n - k);
  if (k == 0) {
    return 1;
  }
  ll ret = frac.at(n);
  ll denomi = frac.at(k) * frac.at(n - k) % mod;
  ret = ret * po(denomi, mod - 2) % mod;
  return ret;
}

ll mod_mult(vll &a) {
  ll ret = 1;
  for (ll x : a) {
    ret = ret * x % mod;
  }
  return ret;
}

ll calc(ll k, string &s) {
  ll m = s.length();
  ll n = k + m;
  ll ans = 0;
  vll po25(n + 1), po26(n + 1), frac(n + 1);
  po25.at(0) = 1;
  po26.at(0) = 1;
  frac.at(0) = 1;
  rep(i, n) {
    po25.at(i + 1) = po25.at(i) * 25 % mod;
    po26.at(i + 1) = po26.at(i) * 26 % mod;
    frac.at(i + 1) = frac.at(i) * (i + 1) % mod;
  }
  FOR(i, m - 1, n) {
    vll a = {combination(i, m - 1, frac), po(25, i - (m - 1)),
             po(26, n - 1 - i)};
    ans = (ans + mod_mult(a)) % mod;
  }
  return ans;
}

void solve() {
  ll k;
  scan(k);
  string s;
  scan(s);
  ll ans = calc(k, s);
  print(ans);
}

int main() {
  solve();
  return 0;
}


Error: TLE

Fixed submission:

#include <algorithm>
#include <cassert>
#include <cfloat>
#include <climits>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <deque>
#include <iostream>
#include <iterator>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

#define FOR(i, k, n) for (int(i) = (k); (i) < (n); ++(i))
#define rep(i, n) FOR(i, 0, n)
#define all(v) begin(v), end(v)
#ifdef ONLINE_JUDGE
#define debug(x)
#define debug2(x, y)
#define debug3(x, y, z)
#define assert(e)                                                              \\
  if (!(e)) {                                                                  \\
    stod("");                                                                  \\
  }
#else
#define debug(x) std::cerr << #x << ": " << x << "\\n"
#define debug2(x, y)                                                           \\
  std::cerr << #x << ": " << x << ", " << #y << ": " << y << "\\n"
#define debug3(x, y, z)                                                        \\
  std::cerr << #x << ": " << x << ", " << #y << ": " << y << ", " << #z        \\
            << ": " << z << "\\n"
#endif

using ll = long long;
using vi = std::vector<int>;
using vvi = std::vector<vi>;
using vll = std::vector<ll>;
using vvll = std::vector<vll>;
template <typename T> using vvec = std::vector<std::vector<T>>;
template <typename T> auto make_v(size_t sz) { return std::vector<T>(sz); }
template <typename T, typename... Ts> auto make_v(size_t sz, Ts... ts) {
  return std::vector<decltype(make_v<T>(ts...))>(sz, make_v<T>(ts...));
}
template <typename T> void fill_v(T &var, const T &x) { var = x; }
template <typename V, typename T> void fill_v(V &v, const T &x) {
  for (auto &&w : v) {
    fill_v(w, x);
  }
}

template <typename T>
std::ostream &operator<<(std::ostream &s, const std::vector<T> &v) {
  int sz = v.size();
  s << "\\n";
  rep(i, sz) {
    s << v[i];
    if (i < sz - 1) {
      s << "\\t";
    }
  }
  s << "\\n";
  return s;
}
template <typename T>
std::ostream &operator<<(std::ostream &s,
                         const std::vector<std::vector<T>> &v) {
  for (auto &&w : v) {
    s << w;
  }
  return s;
}
template <typename T>
std::ostream &operator<<(std::ostream &s, const std::deque<T> &v) {
  int sz = v.size();
  s << "\\n";
  rep(i, sz) {
    s << v[i];
    if (i < sz - 1) {
      s << "\\t";
    }
  }
  s << "\\n";
  return s;
}
template <typename T>
std::ostream &operator<<(std::ostream &s, const std::deque<std::deque<T>> &v) {
  for (auto &&w : v) {
    s << w;
  }
  return s;
}
template <typename T>
std::ostream &operator<<(std::ostream &s, const std::set<T> &v) {
  s << "\\n";
  for (auto &&elm : v) {
    s << elm << "\\t";
  }
  s << "\\n";
  return s;
}

inline void scan(int &a) { scanf("%d", &a); }
inline void scan(ll &a) { scanf("%lld", &a); }
inline void scan(char &a) { scanf(" %c", &a); }
inline void scan(double &a) { scanf("%lf", &a); }
template <typename T> inline void scan(std::vector<T> &v) {
  for (auto &&sv : v) {
    scan(sv);
  }
}
template <typename First, typename... Args>
inline void scan(First &f, Args &...args) {
  scan(f);
  scan(args...);
}
inline void scan(std::string &s) {
  char BUF[3000000];
  scanf(" %s", BUF);
  s = std::string(BUF);
}
inline void print(int a) { printf("%d\\n", a); }
inline void print(ll a) { printf("%lld\\n", a); }
inline void print(double a) { printf("%.12f\\n", a); }
inline void print(std::string s) { std::cout << s << "\\n"; }

using namespace std;

/*
k = 1, s = "aa"
aaa ... aaz 26
aba ... aza 25
baa ... zaa 25
-> 76
k = 1, s = "ab"
aba ... abz 26
aab, acb ... azb 25
bab ... zab
-> 76
*/

ll mod = 1000000007;

ll po(ll k, ll x) {
  if (x == 0) {
    return 1;
  }
  if (x == 1) {
    return k % mod;
  }
  ll y = po(k, x / 2);
  y = y * y % mod;
  if (x % 2 == 1) {
    y = y * k % mod;
  }
  return y;
}

ll combination(ll n, ll k) {
  k = min(k, n - k);
  if (k == 0) {
    return 1;
  }
  ll ret = 1;
  FOR(i, n - k + 1, n + 1) { ret = ret * i % mod; }
  ll denomi = 1; // denominator
  FOR(i, 1, k + 1) { denomi = denomi * i % mod; }
  ret = ret * po(denomi, mod - 2) % mod; // inverse
  return ret;
}

ll calc(ll k, string &s) {
  ll m = s.length();
  ll n = k + m;
  ll ans = 0;
  FOR(i, m - 1, n) {
    ans = (ans + combination(i, m - 1) * po(25, i - (m - 1)) % mod *
                     po(26, n - 1 - i)) %
          mod;
  }
  return ans;
}

void solve() {
  ll k;
  scan(k);
  string s;
  scan(s);
  ll ans = calc(k, s);
  print(ans);
}

int main() {
  solve();
  return 0;
}