Problem p02100 (C++) — buggy submission, verdict: Runtime Error

// need
#include <algorithm>
#include <iostream>

// data structure
#include <bitset>
// #include <list>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <utility>
#include <vector>
// #include <array>
// #include <tuple>
#include <complex>
#include <unordered_map>
#include <unordered_set>
// #include <deque>
#include <valarray>

// stream
// #include <istream>
// #include <sstream>
// #include <ostream>

// etc
#include <cassert>
#include <functional>
#include <iomanip>
// #include <typeinfo>
#include <chrono>
#include <numeric>
#include <random>

#define INIT                                                                   \\
  std::ios::sync_with_stdio(false);                                            \\
  std::cin.tie(0);
#define VAR(type, ...)                                                         \\
  type __VA_ARGS__;                                                            \\
  MACRO_VAR_Scan(__VA_ARGS__);
template <typename T> void MACRO_VAR_Scan(T &t) { std::cin >> t; }
template <typename First, typename... Rest>
void MACRO_VAR_Scan(First &first, Rest &...rest) {
  std::cin >> first;
  MACRO_VAR_Scan(rest...);
}
#define VEC_ROW(type, n, ...)                                                  \\
  std::vector<type> __VA_ARGS__;                                               \\
  MACRO_VEC_ROW_Init(n, __VA_ARGS__);                                          \\
  for (int i = 0; i < n; ++i) {                                                \\
    MACRO_VEC_ROW_Scan(i, __VA_ARGS__);                                        \\
  }
template <typename T> void MACRO_VEC_ROW_Init(int n, T &t) { t.resize(n); }
template <typename First, typename... Rest>
void MACRO_VEC_ROW_Init(int n, First &first, Rest &...rest) {
  first.resize(n);
  MACRO_VEC_ROW_Init(n, rest...);
}
template <typename T> void MACRO_VEC_ROW_Scan(int p, T &t) { std::cin >> t[p]; }
template <typename First, typename... Rest>
void MACRO_VEC_ROW_Scan(int p, First &first, Rest &...rest) {
  std::cin >> first[p];
  MACRO_VEC_ROW_Scan(p, rest...);
}
#define OUT(d) std::cout << d;
#define FOUT(n, d) std::cout << std::fixed << std::setprecision(n) << d;
#define SOUT(n, c, d) std::cout << std::setw(n) << std::setfill(c) << d;
#define SP std::cout << " ";
#define TAB std::cout << "\\t";
#define BR std::cout << "\\n";
#define ENDL std::cout << std::endl;
#define FLUSH std::cout << std::flush;
#define VEC(type, c, n)                                                        \\
  std::vector<type> c(n);                                                      \\
  for (auto &i : c)                                                            \\
    std::cin >> i;
#define MAT(type, c, m, n)                                                     \\
  std::vector<std::vector<type>> c(m, std::vector<type>(n));                   \\
  for (auto &r : c)                                                            \\
    for (auto &i : r)                                                          \\
      std::cin >> i;
#define ALL(a) (a).begin(), (a).end()
#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
#define RFOR(i, a, b) for (int i = (b)-1; i >= (a); --i)
#define REP(i, n) for (int i = 0; i < int(n); ++i)
#define RREP(i, n) for (int i = (n)-1; i >= 0; --i)
#define FORLL(i, a, b) for (ll i = ll(a); i < ll(b); ++i)
#define RFORLL(i, a, b) for (ll i = ll(b) - 1; i >= ll(a); --i)
#define REPLL(i, n) for (ll i = 0; i < ll(n); ++i)
#define RREPLL(i, n) for (ll i = ll(n) - 1; i >= 0; --i)
#define PAIR std::pair<int, int>
#define PAIRLL std::pair<ll, ll>
#define IN(a, x, b) (a <= x && x < b)
#define SHOW(d)                                                                \\
  { std::cerr << #d << "\\t:" << d << "\\n"; }
#define SHOWVECTOR(v)                                                          \\
  {                                                                            \\
    std::cerr << #v << "\\t:";                                                  \\
    for (const auto &xxx : v) {                                                \\
      std::cerr << xxx << " ";                                                 \\
    }                                                                          \\
    std::cerr << "\\n";                                                         \\
  }
#define SHOWVECTOR2(v)                                                         \\
  {                                                                            \\
    std::cerr << #v << "\\t:\\n";                                                \\
    for (const auto &xxx : v) {                                                \\
      for (const auto &yyy : xxx) {                                            \\
        std::cerr << yyy << " ";                                               \\
      }                                                                        \\
      std::cerr << "\\n";                                                       \\
    }                                                                          \\
  }
#define SHOWPAIR(p)                                                            \\
  { std::cerr << #p << "\\t:(" << p.first << ",\\t" << p.second << ")\\n"; }
#define SHOWPAIRVECTOR2(v)                                                     \\
  {                                                                            \\
    std::cerr << #v << "\\t:\\n";                                                \\
    for (const auto &xxx : v) {                                                \\
      for (const auto &yyy : xxx) {                                            \\
        std::cerr << '(' << yyy.first << ", " << yyy.second << ") ";           \\
      }                                                                        \\
      std::cerr << "\\n";                                                       \\
    }                                                                          \\
  }
#define SHOWPAIRVECTOR(v)                                                      \\
  {                                                                            \\
    for (const auto &xxx : v) {                                                \\
      std::cerr << '(' << xxx.first << ", " << xxx.second << ") ";             \\
    }                                                                          \\
    std::cerr << "\\n";                                                         \\
  }
#define SHOWQUEUE(a)                                                           \\
  {                                                                            \\
    std::queue<decltype(a.front())> tmp(a);                                    \\
    std::cerr << #a << "\\t:";                                                  \\
    for (int i = 0; i < static_cast<int>(a.size()); ++i) {                     \\
      std::cerr << tmp.front() << "\\n";                                        \\
      tmp.pop();                                                               \\
    }                                                                          \\
    std::cerr << "\\n";                                                         \\
  }
template <typename T> inline T CHMAX(T &a, const T b) {
  return a = (a < b) ? b : a;
}
template <typename T> inline T CHMIN(T &a, const T b) {
  return a = (a > b) ? b : a;
}
#define EXCEPTION(msg)                                                         \\
  throw std::string("Exception : " msg " [ in ") + __func__ + " : " +          \\
      std::to_string(__LINE__) + " lines ]"
#define TRY(cond, msg)                                                         \\
  try {                                                                        \\
    if (cond)                                                                  \\
      EXCEPTION(msg);                                                          \\
  } catch (std::string s) {                                                    \\
    std::cerr << s << std::endl;                                               \\
  }
void CHECKTIME(std::function<void()> f) {
  auto start = std::chrono::system_clock::now();
  f();
  auto end = std::chrono::system_clock::now();
  auto res = std::chrono::duration_cast<std::chrono::nanoseconds>((end - start))
                 .count();
  std::cerr << "[Time:" << res << "ns  (" << res / (1.0e9) << "s)]\\n";
}

#define int ll
using ll = long long;
using ull = unsigned long long;
constexpr int INFINT = 1 << 30;                         // 1.07x10^ 9
constexpr int INFINT_LIM = (1LL << 31) - 1;             // 2.15x10^ 9
constexpr ll INFLL = 1LL << 60;                         // 1.15x10^18
constexpr ll INFLL_LIM = (1LL << 62) - 1 + (1LL << 62); // 9.22x10^18
constexpr double EPS = 1e-7;
constexpr int MOD = 1000000007;
constexpr double PI = 3.141592653589793238462643383279;

using State = std::string::const_iterator;

int number(State &it) {
  int res = 0;
  bool minus = false;
  if (*it == '+') {
    ++it;
  } else if (*it == '-') {
    minus = true;
    ++it;
  }
  if (*it != 'x') {
    while (isdigit(*it)) {
      res *= 10;
      res += *it - '0';
      ++it;
    }
  } else {
    res = 1;
  }
  if (minus) {
    res *= -1;
  }
  return res;
}

PAIR term(State &it) {
  int t = number(it);
  if (*it != 'x') {
    return PAIR(0, t);
  }
  ++it; // x
  if (*it != '^') {
    return PAIR(1, t);
  }
  ++it; // ^
  int p = number(it);
  return PAIR(p, t);
}

std::vector<PAIR> expression(State &it) {
  std::vector<PAIR> res;
  do {
    res.emplace_back(term(it));
  } while (*it == '+' || *it == '-');
  return res;
}

ll mypow(ll n, ll p) {
  ll res = 1;
  while (p) {
    if (p & 1)
      res *= n;
    n *= n;
    p >>= 1;
  }
  return res;
}

signed main() {
  INIT;
  VAR(std::string, s);
  s = '+' + s + '$';
  auto it = s.cbegin();
  auto exp(expression(it));
  std::string res;
  RFOR(i, -2001, 2001) {
    ll t = 0;
    for (const auto &x : exp) {
      t += x.second * mypow(i, x.first);
    }
    if (t == 0) {
      res += "(x";
      if (i < 0)
        res += "+";
      res += std::to_string(-i);
      res += ")";
    }
  }
  OUT(res) BR;
  return 0;
}

Error: 0
(2, 1) (1, 3) (0, 2) 


Fixed submission:

// need
#include <algorithm>
#include <iostream>

// data structure
#include <bitset>
// #include <list>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <utility>
#include <vector>
// #include <array>
// #include <tuple>
#include <complex>
#include <unordered_map>
#include <unordered_set>
// #include <deque>
#include <valarray>

// stream
// #include <istream>
// #include <sstream>
// #include <ostream>

// etc
#include <cassert>
#include <functional>
#include <iomanip>
// #include <typeinfo>
#include <chrono>
#include <numeric>
#include <random>

#define INIT                                                                   \\
  std::ios::sync_with_stdio(false);                                            \\
  std::cin.tie(0);
#define VAR(type, ...)                                                         \\
  type __VA_ARGS__;                                                            \\
  MACRO_VAR_Scan(__VA_ARGS__);
template <typename T> void MACRO_VAR_Scan(T &t) { std::cin >> t; }
template <typename First, typename... Rest>
void MACRO_VAR_Scan(First &first, Rest &...rest) {
  std::cin >> first;
  MACRO_VAR_Scan(rest...);
}
#define VEC_ROW(type, n, ...)                                                  \\
  std::vector<type> __VA_ARGS__;                                               \\
  MACRO_VEC_ROW_Init(n, __VA_ARGS__);                                          \\
  for (int i = 0; i < n; ++i) {                                                \\
    MACRO_VEC_ROW_Scan(i, __VA_ARGS__);                                        \\
  }
template <typename T> void MACRO_VEC_ROW_Init(int n, T &t) { t.resize(n); }
template <typename First, typename... Rest>
void MACRO_VEC_ROW_Init(int n, First &first, Rest &...rest) {
  first.resize(n);
  MACRO_VEC_ROW_Init(n, rest...);
}
template <typename T> void MACRO_VEC_ROW_Scan(int p, T &t) { std::cin >> t[p]; }
template <typename First, typename... Rest>
void MACRO_VEC_ROW_Scan(int p, First &first, Rest &...rest) {
  std::cin >> first[p];
  MACRO_VEC_ROW_Scan(p, rest...);
}
#define OUT(d) std::cout << d;
#define FOUT(n, d) std::cout << std::fixed << std::setprecision(n) << d;
#define SOUT(n, c, d) std::cout << std::setw(n) << std::setfill(c) << d;
#define SP std::cout << " ";
#define TAB std::cout << "\\t";
#define BR std::cout << "\\n";
#define ENDL std::cout << std::endl;
#define FLUSH std::cout << std::flush;
#define VEC(type, c, n)                                                        \\
  std::vector<type> c(n);                                                      \\
  for (auto &i : c)                                                            \\
    std::cin >> i;
#define MAT(type, c, m, n)                                                     \\
  std::vector<std::vector<type>> c(m, std::vector<type>(n));                   \\
  for (auto &r : c)                                                            \\
    for (auto &i : r)                                                          \\
      std::cin >> i;
#define ALL(a) (a).begin(), (a).end()
#define FOR(i, a, b) for (int i = (a); i < (b); ++i)
#define RFOR(i, a, b) for (int i = (b)-1; i >= (a); --i)
#define REP(i, n) for (int i = 0; i < int(n); ++i)
#define RREP(i, n) for (int i = (n)-1; i >= 0; --i)
#define FORLL(i, a, b) for (ll i = ll(a); i < ll(b); ++i)
#define RFORLL(i, a, b) for (ll i = ll(b) - 1; i >= ll(a); --i)
#define REPLL(i, n) for (ll i = 0; i < ll(n); ++i)
#define RREPLL(i, n) for (ll i = ll(n) - 1; i >= 0; --i)
#define PAIR std::pair<int, int>
#define PAIRLL std::pair<ll, ll>
#define IN(a, x, b) (a <= x && x < b)
#define SHOW(d)                                                                \\
  { std::cerr << #d << "\\t:" << d << "\\n"; }
#define SHOWVECTOR(v)                                                          \\
  {                                                                            \\
    std::cerr << #v << "\\t:";                                                  \\
    for (const auto &xxx : v) {                                                \\
      std::cerr << xxx << " ";                                                 \\
    }                                                                          \\
    std::cerr << "\\n";                                                         \\
  }
#define SHOWVECTOR2(v)                                                         \\
  {                                                                            \\
    std::cerr << #v << "\\t:\\n";                                                \\
    for (const auto &xxx : v) {                                                \\
      for (const auto &yyy : xxx) {                                            \\
        std::cerr << yyy << " ";                                               \\
      }                                                                        \\
      std::cerr << "\\n";                                                       \\
    }                                                                          \\
  }
#define SHOWPAIR(p)                                                            \\
  { std::cerr << #p << "\\t:(" << p.first << ",\\t" << p.second << ")\\n"; }
#define SHOWPAIRVECTOR2(v)                                                     \\
  {                                                                            \\
    std::cerr << #v << "\\t:\\n";                                                \\
    for (const auto &xxx : v) {                                                \\
      for (const auto &yyy : xxx) {                                            \\
        std::cerr << '(' << yyy.first << ", " << yyy.second << ") ";           \\
      }                                                                        \\
      std::cerr << "\\n";                                                       \\
    }                                                                          \\
  }
#define SHOWPAIRVECTOR(v)                                                      \\
  {                                                                            \\
    for (const auto &xxx : v) {                                                \\
      std::cerr << '(' << xxx.first << ", " << xxx.second << ") ";             \\
    }                                                                          \\
    std::cerr << "\\n";                                                         \\
  }
#define SHOWQUEUE(a)                                                           \\
  {                                                                            \\
    std::queue<decltype(a.front())> tmp(a);                                    \\
    std::cerr << #a << "\\t:";                                                  \\
    for (int i = 0; i < static_cast<int>(a.size()); ++i) {                     \\
      std::cerr << tmp.front() << "\\n";                                        \\
      tmp.pop();                                                               \\
    }                                                                          \\
    std::cerr << "\\n";                                                         \\
  }
template <typename T> inline T CHMAX(T &a, const T b) {
  return a = (a < b) ? b : a;
}
template <typename T> inline T CHMIN(T &a, const T b) {
  return a = (a > b) ? b : a;
}
#define EXCEPTION(msg)                                                         \\
  throw std::string("Exception : " msg " [ in ") + __func__ + " : " +          \\
      std::to_string(__LINE__) + " lines ]"
#define TRY(cond, msg)                                                         \\
  try {                                                                        \\
    if (cond)                                                                  \\
      EXCEPTION(msg);                                                          \\
  } catch (std::string s) {                                                    \\
    std::cerr << s << std::endl;                                               \\
  }
void CHECKTIME(std::function<void()> f) {
  auto start = std::chrono::system_clock::now();
  f();
  auto end = std::chrono::system_clock::now();
  auto res = std::chrono::duration_cast<std::chrono::nanoseconds>((end - start))
                 .count();
  std::cerr << "[Time:" << res << "ns  (" << res / (1.0e9) << "s)]\\n";
}

#define int ll
using ll = long long;
using ull = unsigned long long;
constexpr int INFINT = 1 << 30;                         // 1.07x10^ 9
constexpr int INFINT_LIM = (1LL << 31) - 1;             // 2.15x10^ 9
constexpr ll INFLL = 1LL << 60;                         // 1.15x10^18
constexpr ll INFLL_LIM = (1LL << 62) - 1 + (1LL << 62); // 9.22x10^18
constexpr double EPS = 1e-7;
constexpr int MOD = 1000000007;
constexpr double PI = 3.141592653589793238462643383279;

using State = std::string::const_iterator;

int number(State &it) {
  int res = 0;
  bool minus = false;
  if (*it == '+') {
    ++it;
  } else if (*it == '-') {
    minus = true;
    ++it;
  }
  if (*it != 'x') {
    while (isdigit(*it)) {
      res *= 10;
      res += *it - '0';
      ++it;
    }
  } else {
    res = 1;
  }
  if (minus) {
    res *= -1;
  }
  return res;
}

PAIR term(State &it) {
  int t = number(it);
  if (*it != 'x') {
    return PAIR(0, t);
  }
  ++it; // x
  if (*it != '^') {
    return PAIR(1, t);
  }
  ++it; // ^
  int p = number(it);
  return PAIR(p, t);
}

std::vector<PAIR> expression(State &it) {
  std::vector<PAIR> res;
  do {
    res.emplace_back(term(it));
  } while (*it == '+' || *it == '-');
  return res;
}

ll mypow(ll n, ll p) {
  ll res = 1;
  while (p) {
    if (p & 1)
      res *= n;
    n *= n;
    p >>= 1;
  }
  return res;
}

signed main() {
  INIT;
  VAR(std::string, s);
  s = '+' + s + '$';
  auto it = s.cbegin();
  auto exp(expression(it));
  SHOWPAIRVECTOR(exp);
  std::string res;
  RFOR(i, -2001, 2001) {
    ll t = 0;
    for (const auto &x : exp) {
      t += x.second * mypow(i, x.first);
    }
    if (t == 0) {
      res += "(x";
      if (i < 0)
        res += "+";
      res += std::to_string(-i);
      res += ")";
    }
  }
  OUT(res) BR;
  return 0;
}