Problem p02652 (C++) — buggy submission, verdict: Time Limit Exceeded

const int LG = 21;
const int FN = 400005;
const long long MOD = 998244353;
const long long INF = 1e9;
const long long INFLL = 1e18;

#include <bits/stdc++.h>

using namespace std;

typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef vector<int> vi;
typedef vector<ll> vll;

#define forn(i, n) for (int(i) = 0; (i) != (n); (i)++)
#define all(v) (v).begin(), (v).end()
#define rall(v) (v).rbegin(), (v).rend()
#define popcount(x) __builtin_popcount(x)
#define popcountll(x) __builtin_popcountll(x)
#define fi first
#define se second
#define re return
#define pb push_back
#define uniq(x)                                                                \\
  sort(all(x));                                                                \\
  (x).resize(unique(all(x)) - (x).begin())

#ifdef LOCAL
#define dbg(x) cerr << __LINE__ << " " << #x << " " << x << endl
#define ln cerr << __LINE__ << endl
#else
#define dbg(x) void(0)
#define ln void(0)
#endif // LOCAL

int cx[4] = {-1, 0, 1, 0};
int cy[4] = {0, -1, 0, 1};
string Yes[2] = {"No", "Yes"};
string YES[2] = {"NO", "YES"};

ll inq(ll x, ll y) {
  if (!y)
    re 1 % MOD;
  ll l = inq(x, y / 2);
  if (y % 2)
    re l *l % MOD *x % MOD;
  re l *l % MOD;
}

ll rev(ll x) { return inq(x, MOD - 2); }

bool __precomputed_combinatorics = 0;
vector<ll> __fact, __ufact, __rev;

void __precompute_combinatorics() {
  __precomputed_combinatorics = 1;
  __fact.resize(FN);
  __ufact.resize(FN);
  __rev.resize(FN);
  __rev[1] = 1;
  for (int i = 2; i < FN; i++)
    __rev[i] = MOD - __rev[MOD % i] * (MOD / i) % MOD;
  __fact[0] = 1, __ufact[0] = 1;
  for (int i = 1; i < FN; i++)
    __fact[i] = __fact[i - 1] * i % MOD,
    __ufact[i] = __ufact[i - 1] * __rev[i] % MOD;
}

ll fact(int x) {
  if (!__precomputed_combinatorics)
    __precompute_combinatorics();
  return __fact[x];
}

ll cnk(int n, int k) {
  if (k < 0 || k > n)
    return 0;
  if (!__precomputed_combinatorics)
    __precompute_combinatorics();
  return __fact[n] * __ufact[n - k] % MOD * __ufact[k] % MOD;
}

int Root(int x, vector<int> &root) {
  if (x == root[x])
    return x;
  return root[x] = Root(root[x], root);
}

void Merge(int v, int u, vector<int> &root, vector<int> &sz) {
  v = Root(v, root), u = Root(u, root);
  if (v == u)
    return;
  if (sz[v] < sz[u]) {
    sz[u] += sz[v];
    root[v] = u;
  } else {
    sz[v] += sz[u];
    root[u] = v;
  }
}

int ok(int x, int n) { return 0 <= x && x < n; }

void bfs(int v, vi &dist, vector<vi> &graph) {
  fill(all(dist), -1);
  dist[v] = 0;
  vi q = {v};
  for (int i = 0; i < q.size(); i++) {
    for (auto u : graph[q[i]]) {
      if (dist[u] == -1) {
        dist[u] = dist[q[i]] + 1;
        q.push_back(u);
      }
    }
  }
}

ll log10(ll x) {
  if (x < 10)
    re 1;
  re 1 + log10(x / 10);
}

ll sqr(ll x) { return x * x; }

int solve(int x, string s) {
  vector<int> A(s.size());
  for (int i = 0; i < s.size(); i++) {
    if (i)
      A[i] = A[i - 1];
    if (s[i] == '0')
      A[i]++;
    else
      A[i]--;
  }
  vector<int> sufmax(s.size());
  for (int i = s.size() - 1; i >= 0; i--) {
    if (i + 1 < s.size())
      sufmax[i] = sufmax[i + 1];
    else
      sufmax[i] = -1000000;
    sufmax[i] = max(sufmax[i], A[i]);
  }
  vector<int> will_go_down(s.size() + 1);
  for (int i = 0; i < s.size(); i++) {
    will_go_down[i] = max(0, sufmax[i] - (i > 0 ? A[i - 1] : 0));
  }
  /*for (int i = 0; i < s.size() + 1; i++)
  {
      cout << will_go_down[i] << " ";
  }
  cout << endl << endl;
  cout << x << endl;
  cout << will_go_down[0] << endl;*/
  assert(will_go_down[0] <= x);
  int c = 0, mx = 0, mn = 0;
  for (int i = 0; i < s.size(); i++) {
    if (s[i] == '1')
      c++;
    else if (s[i] == '0')
      c--;
    else {
      int D = -c + will_go_down[i + 1] + 1;
      if (D <= x)
        c--;
      else
        c++;
    }
    mx = max(mx, c);
    mn = min(mn, c);
  }
  // cout << endl;
  // cout << mn << " " << mx << endl;
  assert(-mn <= x);
  return mx;
}

signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  const int K = 200;

  // generator

  int n;
  // cin >> n;
  string s;
  for (int i = 0; i < n / 5; i++) {
    int x = rand() % 4;
    if (x == 0)
      s += "1?1??";
    if (2 >= x && x >= 1)
      s += "11111";
    if (x == 3)
      s += "00000";
  }
  // cout << s << "\\n";
  //  n = 5000
  //  ans = 1222

  // input

  cin >> s;
  int w = 0, z = 0;
  for (int i = 0; i < s.size(); i++) {
    if (s[i] == '1' || s[i] == '?')
      w--;
    else
      w++;
    z = max(z, w);
  }
  // cout << z << endl;
  int x = solve(z, s), y = solve(z + 1, s);
  cout << min(z + x, z + 1 + y);
}

/* Note:
Check constants at the beginning of the code.
    N is set to 4e5 but be careful in problems with large constant factor.
    Setting N in every problem is more effective.
Check corner cases.
    N = 1
No def int long long for now.
Add something here.
*/


Error: TLE

Fixed submission:

const int LG = 21;
const int FN = 400005;
const long long MOD = 998244353;
const long long INF = 1e9;
const long long INFLL = 1e18;

#include <bits/stdc++.h>

using namespace std;

typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef vector<int> vi;
typedef vector<ll> vll;

#define forn(i, n) for (int(i) = 0; (i) != (n); (i)++)
#define all(v) (v).begin(), (v).end()
#define rall(v) (v).rbegin(), (v).rend()
#define popcount(x) __builtin_popcount(x)
#define popcountll(x) __builtin_popcountll(x)
#define fi first
#define se second
#define re return
#define pb push_back
#define uniq(x)                                                                \\
  sort(all(x));                                                                \\
  (x).resize(unique(all(x)) - (x).begin())

#ifdef LOCAL
#define dbg(x) cerr << __LINE__ << " " << #x << " " << x << endl
#define ln cerr << __LINE__ << endl
#else
#define dbg(x) void(0)
#define ln void(0)
#endif // LOCAL

int cx[4] = {-1, 0, 1, 0};
int cy[4] = {0, -1, 0, 1};
string Yes[2] = {"No", "Yes"};
string YES[2] = {"NO", "YES"};

ll inq(ll x, ll y) {
  if (!y)
    re 1 % MOD;
  ll l = inq(x, y / 2);
  if (y % 2)
    re l *l % MOD *x % MOD;
  re l *l % MOD;
}

ll rev(ll x) { return inq(x, MOD - 2); }

bool __precomputed_combinatorics = 0;
vector<ll> __fact, __ufact, __rev;

void __precompute_combinatorics() {
  __precomputed_combinatorics = 1;
  __fact.resize(FN);
  __ufact.resize(FN);
  __rev.resize(FN);
  __rev[1] = 1;
  for (int i = 2; i < FN; i++)
    __rev[i] = MOD - __rev[MOD % i] * (MOD / i) % MOD;
  __fact[0] = 1, __ufact[0] = 1;
  for (int i = 1; i < FN; i++)
    __fact[i] = __fact[i - 1] * i % MOD,
    __ufact[i] = __ufact[i - 1] * __rev[i] % MOD;
}

ll fact(int x) {
  if (!__precomputed_combinatorics)
    __precompute_combinatorics();
  return __fact[x];
}

ll cnk(int n, int k) {
  if (k < 0 || k > n)
    return 0;
  if (!__precomputed_combinatorics)
    __precompute_combinatorics();
  return __fact[n] * __ufact[n - k] % MOD * __ufact[k] % MOD;
}

int Root(int x, vector<int> &root) {
  if (x == root[x])
    return x;
  return root[x] = Root(root[x], root);
}

void Merge(int v, int u, vector<int> &root, vector<int> &sz) {
  v = Root(v, root), u = Root(u, root);
  if (v == u)
    return;
  if (sz[v] < sz[u]) {
    sz[u] += sz[v];
    root[v] = u;
  } else {
    sz[v] += sz[u];
    root[u] = v;
  }
}

int ok(int x, int n) { return 0 <= x && x < n; }

void bfs(int v, vi &dist, vector<vi> &graph) {
  fill(all(dist), -1);
  dist[v] = 0;
  vi q = {v};
  for (int i = 0; i < q.size(); i++) {
    for (auto u : graph[q[i]]) {
      if (dist[u] == -1) {
        dist[u] = dist[q[i]] + 1;
        q.push_back(u);
      }
    }
  }
}

ll log10(ll x) {
  if (x < 10)
    re 1;
  re 1 + log10(x / 10);
}

ll sqr(ll x) { return x * x; }

signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  const int K = 200;

  // generator

  int n;
  // cin >> n;
  string s;
  for (int i = 0; i < n / 5; i++) {
    int x = rand() % 4;
    if (x == 0)
      s += "1?1??";
    if (2 >= x && x >= 1)
      s += "11111";
    if (x == 3)
      s += "00000";
  }
  // cout << s << "\\n";
  //  n = 5000
  //  ans = 1222

  // input

  cin >> s;
  vector<int> dp(s.size() + 5, INF);
  dp[0] = 0;
  for (int i = s.size() - 1; i >= 0; i--) {
    vector<int> dp0(dp.size(), INF), dp1(dp.size(), INF);
    if (s[i] != '0') {
      // up
      for (int then_down = 1; then_down < dp.size(); then_down++) {
        dp1[then_down - 1] = dp[then_down] + 1;
      }
      dp1[0] = min(dp1[0], dp[0] + 1);
    }
    if (s[i] != '1') {
      // down
      for (int then_down = 0; then_down < dp.size() - 1; then_down++) {
        dp0[then_down + 1] = dp[then_down] - 1;
      }
    }
    for (int j = 0; j < dp.size(); j++)
      dp[j] = min(max(dp0[j], 0), dp1[j]);
  }
  int ans = INF;
  for (int i = 0; i <= s.size(); i++) {
    ans = min(ans, i + dp[i]);
  }
  cout << ans;
}

/* Note:
Check constants at the beginning of the code.
    N is set to 4e5 but be careful in problems with large constant factor.
    Setting N in every problem is more effective.
Check corner cases.
    N = 1
No def int long long for now.
Add something here.
*/