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

#include <algorithm>
#include <cctype>
#include <cmath>
#include <cstring>
#include <fstream>
#include <iomanip>
#include <iostream>
#include <iterator>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <stdio.h>
#include <stdlib.h>
#include <string>
#include <time.h>
#include <tuple>
#include <vector>
using namespace std;
const double PI = 3.14159265358979323846;
const long long int MOD = 1000000000 + 7;

struct UnionFind {
  vector<int> parent;

  UnionFind(int N) : parent(N) {
    for (int i = 0; i < N; i++) {
      parent[i] = -1;
    }
  }

  int root(int i) {
    if (parent[i] < 0) {
      return i;
    }
    return (parent[i] = root(parent[i]));
  }

  bool unite(int from, int to) {
    int rx = root(from);
    int ry = root(to);
    if (rx != ry) {
      parent[ry] += parent[rx];
      parent[rx] = ry;

      return true;
    } else {
      return false;
    }
  }

  bool same(int x, int y) { return root(x) == root(y); }

  int treeSize(int x) { return -parent[root(x)]; }
};

long long int modpow(long long int base, long long int pow, long long int mod) {
  if (pow == 1) {
    return base;
  } else if (pow == 0) {
    return 1;
  }

  if (pow % 2 == 0) {
    auto temp = modpow(base, pow / 2, mod);
    return (temp * temp) % mod;
  } else {
    return (base * modpow(base, pow - 1, mod)) % mod;
  }
}

long long int moddiv(long long int X, long long int Y, long long int mod) {
  auto fermatDiv = modpow(Y, mod - 2, mod);

  return (X * fermatDiv) % mod;
}

long long modCombination(long long left, long long right, long long int mod) {
  long long answer = 1;
  if (left > right) {
    for (long long i = 0; i < right; i++) {
      answer = (answer * (left - i)) % mod;
      answer = moddiv(answer, (i + 1), mod);
    }
  }
  return answer;
}

bool IsPrime(long long N) {
  if (N == 1) {
    return false;
  }
  for (long long i = 2; i * i <= N; i++) {
    if (N % i == 0) {
      return false;
    }
  }

  return true;
}

vector<pair<long long, long long>> prime_factorize(long long N) {
  vector<pair<long long, long long>> res;
  for (long long a = 2; a * a <= N; ++a) {
    if (N % a != 0)
      continue;
    long long ex = 0; // 指数

    // 割れる限り割り続ける
    while (N % a == 0) {
      ++ex;
      N /= a;
    }

    // その結果を push
    res.push_back({a, ex});
  }

  // 最後に残った数について
  if (N != 1)
    res.push_back({N, 1});
  return res;
}

long long euclid(long long a, long long b) {
  if (a > b) {
    long long temp = b;
    b = a;
    a = temp;
  }
  if (b % a == 0) {
    return a;
  } else {
    return euclid(a, b - a);
  }
}

long long gcd(long long a, long long b) {
  if (b > a) {
    long long temp = b;
    b = a;
    a = temp;
  }
  // cout << "a:" << a << "b:" << b << endl;
  long long c = a % b;
  if (c == 0) {
    return b;
  } else {
    return gcd(b, c);
  }
}

struct State {
  long long town;
  long long money;
  long long time;

  State(long long _town, long long _money, long long _time) {
    town = _town;
    money = _money;
    time = _time;
  }

  bool operator<(const State &s) const { return this->time > s.time; }
};

struct Edge {
  long long to, time, money;
  Edge(long long _to, long long _money, long long _time) {
    to = _to;
    time = _time;
    money = _money;
  }
};

int main() {
  long long K;
  cin >> K;
  string s;
  cin >> s;
  long long originalCount = s.size();

  long long answer = 0;
  long long lastIndex = originalCount - 1;
  long long strictCount = modpow(25, lastIndex - (originalCount - 1), MOD);
  long long nonStrictCount = modpow(26, originalCount + K - 1 - lastIndex, MOD);
  long long comb = modCombination(lastIndex, originalCount - 1, MOD);
  for (long long i = lastIndex; i < originalCount + K; i++) {
    /*long long comb = modCombination(i, originalCount - 1, MOD);
    long long strictCount = i - (originalCount - 1);
    strictCount = modpow(25, strictCount, MOD);

    long long nonStrictCount = (originalCount + K - 1) - i;
    nonStrictCount = modpow(26, nonStrictCount, MOD);*/

    if (i != lastIndex) {
      comb *= i;
      comb %= MOD;

      comb = moddiv(comb, i - (originalCount - 1), MOD);

      strictCount *= 25;
      strictCount %= MOD;

      nonStrictCount = moddiv(nonStrictCount, 26, MOD);
      nonStrictCount %= MOD;
    }
    long long answerI = 1;
    answerI *= comb;
    answerI *= strictCount;
    answerI %= MOD;
    answerI *= nonStrictCount;
    answerI %= MOD;

    answer += answerI;
    answer %= MOD;
  }

  cout << answer << endl;
  return 0;
}

Error: TLE

Fixed submission:

#include <algorithm>
#include <cctype>
#include <cmath>
#include <cstring>
#include <fstream>
#include <iomanip>
#include <iostream>
#include <iterator>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <stdio.h>
#include <stdlib.h>
#include <string>
#include <time.h>
#include <tuple>
#include <vector>
using namespace std;
const double PI = 3.14159265358979323846;
const long long int MOD = 1000000000 + 7;

struct UnionFind {
  vector<int> parent;

  UnionFind(int N) : parent(N) {
    for (int i = 0; i < N; i++) {
      parent[i] = -1;
    }
  }

  int root(int i) {
    if (parent[i] < 0) {
      return i;
    }
    return (parent[i] = root(parent[i]));
  }

  bool unite(int from, int to) {
    int rx = root(from);
    int ry = root(to);
    if (rx != ry) {
      parent[ry] += parent[rx];
      parent[rx] = ry;

      return true;
    } else {
      return false;
    }
  }

  bool same(int x, int y) { return root(x) == root(y); }

  int treeSize(int x) { return -parent[root(x)]; }
};

long long int modpow(long long int base, long long int pow, long long int mod) {
  if (pow == 1) {
    return base;
  } else if (pow == 0) {
    return 1;
  }

  if (pow % 2 == 0) {
    auto temp = modpow(base, pow / 2, mod);
    return (temp * temp) % mod;
  } else {
    return (base * modpow(base, pow - 1, mod)) % mod;
  }
}

long long int moddiv(long long int X, long long int Y, long long int mod) {
  auto fermatDiv = modpow(Y, mod - 2, mod);

  return (X * fermatDiv) % mod;
}

long long modCombination(long long left, long long right, long long int mod) {
  long long answer = 1;
  if (left > right) {
    for (long long i = 0; i < right; i++) {
      answer = (answer * (left - i)) % mod;
      answer = moddiv(answer, (i + 1), mod);
    }
  }
  return answer;
}

bool IsPrime(long long N) {
  if (N == 1) {
    return false;
  }
  for (long long i = 2; i * i <= N; i++) {
    if (N % i == 0) {
      return false;
    }
  }

  return true;
}

vector<pair<long long, long long>> prime_factorize(long long N) {
  vector<pair<long long, long long>> res;
  for (long long a = 2; a * a <= N; ++a) {
    if (N % a != 0)
      continue;
    long long ex = 0; // 指数

    // 割れる限り割り続ける
    while (N % a == 0) {
      ++ex;
      N /= a;
    }

    // その結果を push
    res.push_back({a, ex});
  }

  // 最後に残った数について
  if (N != 1)
    res.push_back({N, 1});
  return res;
}

long long euclid(long long a, long long b) {
  if (a > b) {
    long long temp = b;
    b = a;
    a = temp;
  }
  if (b % a == 0) {
    return a;
  } else {
    return euclid(a, b - a);
  }
}

long long gcd(long long a, long long b) {
  if (b > a) {
    long long temp = b;
    b = a;
    a = temp;
  }
  // cout << "a:" << a << "b:" << b << endl;
  long long c = a % b;
  if (c == 0) {
    return b;
  } else {
    return gcd(b, c);
  }
}

struct State {
  long long town;
  long long money;
  long long time;

  State(long long _town, long long _money, long long _time) {
    town = _town;
    money = _money;
    time = _time;
  }

  bool operator<(const State &s) const { return this->time > s.time; }
};

struct Edge {
  long long to, time, money;
  Edge(long long _to, long long _money, long long _time) {
    to = _to;
    time = _time;
    money = _money;
  }
};

int main() {
  long long K;
  cin >> K;
  string s;
  cin >> s;
  long long originalCount = s.size();

  long long answer = 0;
  long long lastIndex = originalCount - 1;
  for (long long i = lastIndex; i < originalCount + K; i++) {
    long long comb = modCombination(i, originalCount - 1, MOD);
    long long strictCount = i - (originalCount - 1);
    strictCount = modpow(25, strictCount, MOD);

    long long nonStrictCount = (originalCount + K - 1) - i;
    nonStrictCount = modpow(26, nonStrictCount, MOD);

    long long answerI = 1;
    answerI *= comb;
    answerI *= strictCount;
    answerI %= MOD;
    answerI *= nonStrictCount;
    answerI %= MOD;

    answer += answerI;
    answer %= MOD;
  }

  cout << answer << endl;
  return 0;
}