Problem p02736 (C++)

Buggy submission (status: Time Limit Exceeded):
#include <bits/stdc++.h>
#ifdef LOCAL_DEBUG
#define DEBUG 1
#define CERR                                                                   \
  if (DEBUG)                                                                   \
  cerr
#define MACRO(_1, _2, _3, _4, _5, _6, _7, _8, _9, _10, NAME, ...) NAME
#define pr(...)                                                                \
  CERR << MACRO(__VA_ARGS__, pr10, pr9, pr8, pr7, pr6, pr5, pr4, pr3, pr2,     \
                pr1)(__VA_ARGS__)                                              \
       << endl
#define pr1(a) (#a) << "=" << (a) << " "
#define pr2(a, b) pr1(a) << pr1(b)
#define pr3(a, b, c) pr1(a) << pr2(b, c)
#define pr4(a, b, c, d) pr1(a) << pr3(b, c, d)
#define pr5(a, b, c, d, e) pr1(a) << pr4(b, c, d, e)
#define pr6(a, b, c, d, e, f) pr1(a) << pr5(b, c, d, e, f)
#define pr7(a, b, c, d, e, f, g) pr1(a) << pr6(b, c, d, e, f, g)
#define pr8(a, b, c, d, e, f, g, h) pr1(a) << pr7(b, c, d, e, f, g, h)
#define pr9(a, b, c, d, e, f, g, h, i) pr1(a) << pr8(b, c, d, e, f, g, h, i)
#define pr10(a, b, c, d, e, f, g, h, i, j)                                     \
  pr1(a) << pr9(b, c, d, e, f, g, h, i, j)
#define prArr(a)                                                               \
  {                                                                            \
    CERR << (#a) << "={";                                                      \
    int i = 0;                                                                 \
    for (auto t : (a))                                                         \
      CERR << (i++ ? ", " : "") << t;                                          \
    CERR << "}" << endl;                                                       \
  }
#else
#define DEBUG 0
#define pr(...)
#define prArr(a)
#endif
using namespace std;
using Int = long long;
using _int = int;
using ll = long long;
using Double = long double;
const Int INF = (1LL << 60) + 1e9; // ~ 1.15 * 1e18
const Int mod = (1e9) + 7;
const Double EPS = 1e-8;
const Double PI = 6.0 * asin((Double)0.5);
using P = pair<Int, Int>;
template <class T> T Max(T &a, T b) { return a = max(a, b); }
template <class T> T Min(T &a, T b) { return a = min(a, b); }
template <class T1, class T2> ostream &operator<<(ostream &o, pair<T1, T2> p) {
  return o << "(" << p.first << "," << p.second << ")";
}
template <class T1, class T2, class T3>
ostream &operator<<(ostream &o, tuple<T1, T2, T3> t) {
  return o << "(" << get<0>(t) << "," << get<1>(t) << "," << get<2>(t) << ")";
}
template <class T1, class T2> istream &operator>>(istream &i, pair<T1, T2> &p) {
  return i >> p.first >> p.second;
}
template <class T> ostream &operator<<(ostream &o, vector<T> a) {
  Int i = 0;
  for (T t : a)
    o << (i++ ? " " : "") << t;
  return o;
}
template <class T> istream &operator>>(istream &i, vector<T> &a) {
  for (T &t : a)
    i >> t;
  return i;
}

template <typename T> class CumulativeSum {
public:
  Int n;
  vector<T> sum;
  vector<T> A;
  Int added;
  CumulativeSum() : n(-1), added(0) {}
  CumulativeSum(Int n) : n(n), sum(n + 1), A(n + 1), added(0) {}
  CumulativeSum(const vector<T> &B)
      : n(B.size()), sum(n + 1), A(n + 1), added(0) {
    for (Int i = 1; i <= n; i++)
      sum[i] = sum[i - 1] + B[i - 1];
  }

  void apply() {
    for (Int i = 1; i <= n; i++)
      A[i] = A[i] + A[i - 1];
    for (Int i = 1; i <= n; i++)
      A[i] = A[i] + A[i - 1];
    for (Int i = 1; i <= n; i++)
      sum[i] = sum[i] + A[i - 1];
    added = 0;
    A.clear();
    A.resize(n + 1);
  }

  //[l, r)にxを加算
  void add(Int l, Int r, T x) {
    added = 1;
    assert(l <= r && 0 <= l && r <= n);
    A[l] = A[l] + x;
    A[r] = A[r] - x;
  }

  //[l, r)の和を得る
  T get(Int l, Int r) {
    assert(l <= r && 0 <= l && r <= n);
    if (added)
      apply();
    return sum[r] - sum[l];
  }
};

// INSERT ABOVE HERE
//  0 0 -> 0
//  1 1 -> 0
//  2 2 -> 0

// 0 1 -> 1
// 1 0 -> 1
// 1 2 -> 1
// 2 1 -> 1

// 0 2 -> 2
// 2 0 -> 2

CumulativeSum<Int> S;
Int nCr(Int n, Int r) {
  if (S.n == -1) {
    S = CumulativeSum<Int>(2e6);
    for (Int i = 0; i < 2e6; i++) {
      Int c = 0;
      Int t = i;
      while (t && t % 2 == 0)
        t /= 2, c++;
      S.add(i, i + 1, c);
    }
  }
  if (n < r)
    return 0;
  if (r == 0)
    return 1;
  if (n == r)
    return 1;
  Int a = S.get(0, r + 1);         // r!
  Int b = S.get(n - r + 1, n + 1); // (n!) / (n-r)!
  // pr(n, r, a, b);
  if (b > a)
    return 0;
  return 1;
}
Int solve_(Int N, vector<Int> A, Int flag = 0) {

  for (Int i = 0; i < N - 1; i++) {
    if (i == 0 && flag)
      pr(i, A);
    vector<Int> nA;
    for (Int i = 0; i < (Int)A.size() - 1; i++) {
      nA.push_back(abs(A[i] - A[i + 1]));
    }
    A = nA;
    if (flag)
      pr(i, A);
  }
  assert(A.size() == 1);
  return A[0];
}

Int solve2(Int N, vector<Int> A, Int flag) {
  Int sum = 0;
  for (Int i = 0; i < (Int)A.size(); i++) {
    Int a = A[i];
    Int num = nCr(((Int)A.size() - 1), i);
    pr(a, num, A.size(), i);
    if (a == 2)
      sum ^= num % 2;
  }
  pr(sum);
  return sum ? 2 : 0;
}

Int solve3(Int N, vector<Int> A, Int flag) {
  Int sum = 0;
  for (Int i = 0; i < (Int)A.size(); i++) {
    Int a = A[i];
    Int num = nCr(((Int)A.size() - 1), i);
    pr(a, num, A.size(), i);
    if (a == 3)
      sum ^= num % 2;
  }
  pr(sum);
  return sum ? 3 : 0;
}

Int solve(Int, vector<Int>, Int);
Int solve13(Int N, vector<Int> A, Int flag) {
  if (A.size() == 1)
    return A[0];
  vector<Int> nA;
  for (Int i = 0; i < (Int)A.size() - 1; i++) {
    nA.push_back(abs(A[i] - A[i + 1]));
  }
  A = nA;
  return solve(A.size(), A, flag);
}

Int solve(Int N, vector<Int> A, Int flag = 0) {
  if (A == vector<Int>({3}))
    return 3;
  Int all02 = 1, all03 = 1, all13 = 1;
  for (Int i = 0; i < N; i++)
    if (!(A[i] == 0 || A[i] == 2))
      all02 = 0;
  for (Int i = 0; i < N; i++)
    if (!(A[i] == 0 || A[i] == 3))
      all03 = 0;
  for (Int i = 0; i < N; i++)
    if (!(A[i] == 1 || A[i] == 3))
      all13 = 0;
  Int one = 0, thr = 0;
  for (Int i = 0; i < N; i++)
    if (A[i] == 1)
      one = 1;
  for (Int i = 0; i < N; i++)
    if (A[i] == 3)
      thr = 1;

  if (all02)
    return solve2(N, A, flag);
  if (all03)
    return solve3(N, A, flag);
  if (one && thr && all13)
    return solve13(N, A, flag);

  for (Int &a : A)
    a %= 2;
  if (A.size() == 1)
    return A[0];
  if (flag)
    pr(A);
  Int sum = 0;
  for (Int i = 0; i < (Int)A.size(); i++) {
    Int a = A[i];
    Int num = nCr(((Int)A.size() - 1), i);
    if (flag)
      pr(a, num, A.size(), i);
    sum ^= a * num % 2;
  }
  return sum;
}

void test() {
  while (1) {
    Int N = rand() % 5 + 1;
    vector<Int> A(N);
    for (Int &a : A)
      a = rand() % 3 + 1;
    Int a = solve_(N, A);
    // if(a == 0 || a == 1) continue;
    Int b = solve(N, A);
    pr(N, A, a, b);
    assert(a == b);
    // return;
  }
}

signed main() {
  srand((unsigned)time(NULL));
  cin.tie(0);
  ios_base::sync_with_stdio(0);
  cout << fixed << setprecision(12);
  // test();

  Int N;
  cin >> N;
  string s;
  cin >> s;
  N = s.size();

  vector<Int> A;
  for (Int i = 0; i < N; i++)
    A.push_back(s[i] - '0');
  // Int ans = solve(N, A);
  Int ans = solve_(N, A, 1);
  cout << ans << endl;
  return 0;
}


Fixed submission:
#include <bits/stdc++.h>
#ifdef LOCAL_DEBUG
#define DEBUG 1
#define CERR                                                                   \
  if (DEBUG)                                                                   \
  cerr
#define MACRO(_1, _2, _3, _4, _5, _6, _7, _8, _9, _10, NAME, ...) NAME
#define pr(...)                                                                \
  CERR << MACRO(__VA_ARGS__, pr10, pr9, pr8, pr7, pr6, pr5, pr4, pr3, pr2,     \
                pr1)(__VA_ARGS__)                                              \
       << endl
#define pr1(a) (#a) << "=" << (a) << " "
#define pr2(a, b) pr1(a) << pr1(b)
#define pr3(a, b, c) pr1(a) << pr2(b, c)
#define pr4(a, b, c, d) pr1(a) << pr3(b, c, d)
#define pr5(a, b, c, d, e) pr1(a) << pr4(b, c, d, e)
#define pr6(a, b, c, d, e, f) pr1(a) << pr5(b, c, d, e, f)
#define pr7(a, b, c, d, e, f, g) pr1(a) << pr6(b, c, d, e, f, g)
#define pr8(a, b, c, d, e, f, g, h) pr1(a) << pr7(b, c, d, e, f, g, h)
#define pr9(a, b, c, d, e, f, g, h, i) pr1(a) << pr8(b, c, d, e, f, g, h, i)
#define pr10(a, b, c, d, e, f, g, h, i, j)                                     \
  pr1(a) << pr9(b, c, d, e, f, g, h, i, j)
#define prArr(a)                                                               \
  {                                                                            \
    CERR << (#a) << "={";                                                      \
    int i = 0;                                                                 \
    for (auto t : (a))                                                         \
      CERR << (i++ ? ", " : "") << t;                                          \
    CERR << "}" << endl;                                                       \
  }
#else
#define DEBUG 0
#define pr(...)
#define prArr(a)
#endif
using namespace std;
using Int = long long;
using _int = int;
using ll = long long;
using Double = long double;
const Int INF = (1LL << 60) + 1e9; // ~ 1.15 * 1e18
const Int mod = (1e9) + 7;
const Double EPS = 1e-8;
const Double PI = 6.0 * asin((Double)0.5);
using P = pair<Int, Int>;
template <class T> T Max(T &a, T b) { return a = max(a, b); }
template <class T> T Min(T &a, T b) { return a = min(a, b); }
template <class T1, class T2> ostream &operator<<(ostream &o, pair<T1, T2> p) {
  return o << "(" << p.first << "," << p.second << ")";
}
template <class T1, class T2, class T3>
ostream &operator<<(ostream &o, tuple<T1, T2, T3> t) {
  return o << "(" << get<0>(t) << "," << get<1>(t) << "," << get<2>(t) << ")";
}
template <class T1, class T2> istream &operator>>(istream &i, pair<T1, T2> &p) {
  return i >> p.first >> p.second;
}
template <class T> ostream &operator<<(ostream &o, vector<T> a) {
  Int i = 0;
  for (T t : a)
    o << (i++ ? " " : "") << t;
  return o;
}
template <class T> istream &operator>>(istream &i, vector<T> &a) {
  for (T &t : a)
    i >> t;
  return i;
}

template <typename T> class CumulativeSum {
public:
  Int n;
  vector<T> sum;
  vector<T> A;
  Int added;
  CumulativeSum() : n(-1), added(0) {}
  CumulativeSum(Int n) : n(n), sum(n + 1), A(n + 1), added(0) {}
  CumulativeSum(const vector<T> &B)
      : n(B.size()), sum(n + 1), A(n + 1), added(0) {
    for (Int i = 1; i <= n; i++)
      sum[i] = sum[i - 1] + B[i - 1];
  }

  void apply() {
    for (Int i = 1; i <= n; i++)
      A[i] = A[i] + A[i - 1];
    for (Int i = 1; i <= n; i++)
      A[i] = A[i] + A[i - 1];
    for (Int i = 1; i <= n; i++)
      sum[i] = sum[i] + A[i - 1];
    added = 0;
    A.clear();
    A.resize(n + 1);
  }

  //[l, r)にxを加算
  void add(Int l, Int r, T x) {
    added = 1;
    assert(l <= r && 0 <= l && r <= n);
    A[l] = A[l] + x;
    A[r] = A[r] - x;
  }

  //[l, r)の和を得る
  T get(Int l, Int r) {
    assert(l <= r && 0 <= l && r <= n);
    if (added)
      apply();
    return sum[r] - sum[l];
  }
};

// INSERT ABOVE HERE
//  0 0 -> 0
//  1 1 -> 0
//  2 2 -> 0

// 0 1 -> 1
// 1 0 -> 1
// 1 2 -> 1
// 2 1 -> 1

// 0 2 -> 2
// 2 0 -> 2

CumulativeSum<Int> S;
Int nCr(Int n, Int r) {
  if (S.n == -1) {
    S = CumulativeSum<Int>(2e6);
    for (Int i = 0; i < 2e6; i++) {
      Int c = 0;
      Int t = i;
      while (t && t % 2 == 0)
        t /= 2, c++;
      S.add(i, i + 1, c);
    }
  }
  if (n < r)
    return 0;
  if (r == 0)
    return 1;
  if (n == r)
    return 1;
  Int a = S.get(0, r + 1);         // r!
  Int b = S.get(n - r + 1, n + 1); // (n!) / (n-r)!
  // pr(n, r, a, b);
  if (b > a)
    return 0;
  return 1;
}
Int solve_(Int N, vector<Int> A, Int flag = 0) {

  for (Int i = 0; i < N - 1; i++) {
    if (i == 0 && flag)
      pr(i, A);
    vector<Int> nA;
    for (Int i = 0; i < (Int)A.size() - 1; i++) {
      nA.push_back(abs(A[i] - A[i + 1]));
    }
    A = nA;
    if (flag)
      pr(i, A);
  }
  assert(A.size() == 1);
  return A[0];
}

Int solve2(Int N, vector<Int> A, Int flag) {
  Int sum = 0;
  for (Int i = 0; i < (Int)A.size(); i++) {
    Int a = A[i];
    Int num = nCr(((Int)A.size() - 1), i);
    pr(a, num, A.size(), i);
    if (a == 2)
      sum ^= num % 2;
  }
  pr(sum);
  return sum ? 2 : 0;
}

Int solve3(Int N, vector<Int> A, Int flag) {
  Int sum = 0;
  for (Int i = 0; i < (Int)A.size(); i++) {
    Int a = A[i];
    Int num = nCr(((Int)A.size() - 1), i);
    pr(a, num, A.size(), i);
    if (a == 3)
      sum ^= num % 2;
  }
  pr(sum);
  return sum ? 3 : 0;
}

Int solve(Int, vector<Int>, Int);
Int solve13(Int N, vector<Int> A, Int flag) {
  if (A.size() == 1)
    return A[0];
  vector<Int> nA;
  for (Int i = 0; i < (Int)A.size() - 1; i++) {
    nA.push_back(abs(A[i] - A[i + 1]));
  }
  A = nA;
  return solve(A.size(), A, flag);
}

Int solve(Int N, vector<Int> A, Int flag = 0) {
  if (A == vector<Int>({3}))
    return 3;
  Int all02 = 1, all03 = 1, all13 = 1;
  for (Int i = 0; i < N; i++)
    if (!(A[i] == 0 || A[i] == 2))
      all02 = 0;
  for (Int i = 0; i < N; i++)
    if (!(A[i] == 0 || A[i] == 3))
      all03 = 0;
  for (Int i = 0; i < N; i++)
    if (!(A[i] == 1 || A[i] == 3))
      all13 = 0;
  Int one = 0, thr = 0;
  for (Int i = 0; i < N; i++)
    if (A[i] == 1)
      one = 1;
  for (Int i = 0; i < N; i++)
    if (A[i] == 3)
      thr = 1;

  if (all02)
    return solve2(N, A, flag);
  if (all03)
    return solve3(N, A, flag);
  if (one && thr && all13)
    return solve13(N, A, flag);

  for (Int &a : A)
    a %= 2;
  if (A.size() == 1)
    return A[0];
  if (flag)
    pr(A);
  Int sum = 0;
  for (Int i = 0; i < (Int)A.size(); i++) {
    Int a = A[i];
    Int num = nCr(((Int)A.size() - 1), i);
    if (flag)
      pr(a, num, A.size(), i);
    sum ^= a * num % 2;
  }
  return sum;
}

void test() {
  while (1) {
    Int N = rand() % 5 + 1;
    vector<Int> A(N);
    for (Int &a : A)
      a = rand() % 3 + 1;
    Int a = solve_(N, A);
    // if(a == 0 || a == 1) continue;
    Int b = solve(N, A);
    pr(N, A, a, b);
    assert(a == b);
    // return;
  }
}

signed main() {
  srand((unsigned)time(NULL));
  cin.tie(0);
  ios_base::sync_with_stdio(0);
  cout << fixed << setprecision(12);
  // test();

  Int N;
  cin >> N;
  string s;
  cin >> s;
  N = s.size();

  vector<Int> A;
  for (Int i = 0; i < N; i++)
    A.push_back(s[i] - '0');
  Int ans = solve(N, A);
  // Int ans = solve_(N, A, 1);
  cout << ans << endl;
  return 0;
}