Problem p02651 (C++) — buggy submission, verdict: Time Limit Exceeded

#include <algorithm>
#include <cassert>
#include <cmath>
#include <fstream>
#include <iostream>
#include <list>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <stdio.h>
#include <stdlib.h>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

//....................................................................................................................//

using std::cin;
using std::cout;
using std::deque;
using std::get;
using std::greater;
using std::ifstream;
using std::ios_base;
using std::less;
using std::list;
using std::lower_bound;
using std::make_pair;
using std::make_tuple;
using std::map;
using std::max;
using std::max_element;
using std::min;
using std::min_element;
using std::multimap;
using std::multiset;
using std::ofstream;
using std::pair;
using std::priority_queue;
using std::queue;
using std::set;
using std::stack;
using std::string;
using std::swap;
using std::tuple;
using std::unordered_map;
using std::unordered_multimap;
using std::unordered_set;
using std::upper_bound;
using std::vector;
// using std::endl;

//....................................................................................................................//

typedef long long ll;
typedef unsigned long long ull;

[[maybe_unused]] const string endl = "\\n";
[[maybe_unused]] const string sep = " ";
[[maybe_unused]] const string yes = "YES\\n";
[[maybe_unused]] const string no = "NO\\n";
[[maybe_unused]] const string ng = "NG\\n";
[[maybe_unused]] const string ok = "OK\\n";
[[maybe_unused]] const double pi = acos(-1);
[[maybe_unused]] const ull modular = 1e9 + 7;

//....................................................................................................................//

template <class T> T min(const T &a, const T &b, const T &c) {
  return min(a, min(b, c));
}

template <class T> T max(const T &a, const T &b, const T &c) {
  return max(a, max(b, c));
}

typedef vector<vector<ll>> graph;

vector<ll> lca_h, lca_dfs_list, lca_first, lca_tree;
vector<char> lca_dfs_used;

void lca_dfs(const graph &g, ll v, ll h = 1) {
  lca_dfs_used[v] = true;
  lca_h[v] = h;
  lca_dfs_list.push_back(v);
  for (auto i = g[v].begin(); i != g[v].end(); ++i)
    if (!lca_dfs_used[*i]) {
      lca_dfs(g, *i, h + 1);
      lca_dfs_list.push_back(v);
    }
}

void lca_build_tree(ll i, ll l, ll r) {
  if (l == r)
    lca_tree[i] = lca_dfs_list[l];
  else {
    ll m = (l + r) >> 1;
    lca_build_tree(i + i, l, m);
    lca_build_tree(i + i + 1, m + 1, r);
    if (lca_h[lca_tree[i + i]] < lca_h[lca_tree[i + i + 1]])
      lca_tree[i] = lca_tree[i + i];
    else
      lca_tree[i] = lca_tree[i + i + 1];
  }
}

void lca_prepare(const graph &g, ll root) {
  ll n = (ll)g.size();
  lca_h.resize(n);
  lca_dfs_list.reserve(n * 2);
  lca_dfs_used.assign(n, 0);

  lca_dfs(g, root);

  ll m = (ll)lca_dfs_list.size();
  lca_tree.assign(lca_dfs_list.size() * 4 + 1, -1);
  lca_build_tree(1, 0, m - 1);

  lca_first.assign(n, -1);
  for (ll i = 0; i < m; ++i) {
    ll v = lca_dfs_list[i];
    if (lca_first[v] == -1)
      lca_first[v] = i;
  }
}

ll lca_tree_min(ll i, ll sl, ll sr, ll l, ll r) {
  if (sl == l && sr == r)
    return lca_tree[i];
  ll sm = (sl + sr) >> 1;
  if (r <= sm)
    return lca_tree_min(i + i, sl, sm, l, r);
  if (l > sm)
    return lca_tree_min(i + i + 1, sm + 1, sr, l, r);
  ll ans1 = lca_tree_min(i + i, sl, sm, l, sm);
  ll ans2 = lca_tree_min(i + i + 1, sm + 1, sr, sm + 1, r);
  return lca_h[ans1] < lca_h[ans2] ? ans1 : ans2;
}

ll lca(ll a, ll b) {
  ll left = lca_first[a], right = lca_first[b];
  if (left > right)
    swap(left, right);
  return lca_tree_min(1, 0, (ll)lca_dfs_list.size() - 1, left, right);
}

ll gcd(ll a, ll b) {
  if (a == 0) {
    return b;
  }
  return gcd(b % a, a);
}

ll fast_power(ll a, ll pow) {
  if (pow == 0) {
    return 1;
  }
  if (pow % 2 == 0) {
    auto x = fast_power(a, pow / 2);
    return (x * x);
  } else {
    auto x = fast_power(a, pow - 1);
    return (a * x);
  }
}

ll fast_power(ll a, ll pow, ll mod) {
  if (pow == 0) {
    return 1;
  }
  if (pow % 2 == 0) {
    auto x = fast_power(a, pow / 2, mod);
    return (x * x) % mod;
  } else {
    auto x = fast_power(a, pow - 1, mod);
    return (a * x) % mod;
  }
}

void getFactorialsModular(const ll n, const ll mod, vector<ll> &F) {
  F.resize(n + 1);
  F[0] = 1;
  for (ll i = 1; i <= n; ++i) {
    F[i] = (F[i - 1] * i) % mod;
  }
}

void getFactorialsAndInverseModular(const ll n, const ll mod, vector<ll> &F,
                                    vector<ll> &I) {
  getFactorialsModular(n, mod, F);
  I.resize(n + 1);
  I[0] = 1;
  for (ll i = 1; i <= n; ++i) {
    I[i] = fast_power(F[i], mod - 2, mod);
  }
}

ll CnkMod(ll n, ll k, ll mod, vector<ll> &F, vector<ll> &I) {
  return (((F[n] * I[k]) % mod) * I[n - k]) % mod;
}

ll CnkWithRepetitionMod(ll n, ll k, ll mod, vector<ll> &F, vector<ll> &I) {
  return CnkMod(n + k - 1, k - 1, mod, F, I);
}

/*
MIT License
Copyright (c) 2019 ouuan
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
*/

// for further information and bug tracking,
// please visit https://github.com/ouuan/segmentTree

template <typename valueType, typename tagType> class segmentTreeNode {
public:
  int id, left, right;
  valueType val;
  tagType tag;
};

template <typename valueType, typename tagType,
          valueType (*merge)(valueType, valueType),
          void (*update)(segmentTreeNode<valueType, tagType> &, tagType)>
class segmentTree {
private:
  std::vector<segmentTreeNode<valueType, tagType>> nodes;
  int leftRange, rightRange;
  valueType valueZero;
  tagType tagZero;

  void push_up(int cur) {
    nodes[cur].val = merge(nodes[cur << 1].val, nodes[cur << 1 | 1].val);
  }

  void push_down(int cur) {
    update(nodes[cur << 1], nodes[cur].tag);
    update(nodes[cur << 1 | 1], nodes[cur].tag);
    nodes[cur].tag = tagZero;
  }

  void build(int cur, int l, int r, const std::vector<valueType> &initValue) {
    nodes[cur].id = cur;
    nodes[cur].left = l;
    nodes[cur].right = r;
    nodes[cur].tag = tagZero;
    if (l == r - 1)
      nodes[cur].val = initValue[l - leftRange];
    else {
      build(cur << 1, l, (l + r) >> 1, initValue);
      build(cur << 1 | 1, (l + r) >> 1, r, initValue);
      push_up(cur);
    }
  }

  void init(const std::vector<valueType> &_initValue,
            const valueType &_valueZero, const tagType &_tagZero) {
    valueZero = _valueZero;
    tagZero = _tagZero;
    nodes.resize((rightRange - leftRange) << 2);
    build(1, leftRange, rightRange, _initValue);
  }

  void modify(int cur, int l, int r, int L, int R, const tagType &tag) {
    if (l >= R || r <= L)
      return;
    if (L <= l && r <= R)
      update(nodes[cur], tag);
    else {
      push_down(cur);
      modify(cur << 1, l, (l + r) >> 1, L, R, tag);
      modify(cur << 1 | 1, (l + r) >> 1, r, L, R, tag);
      push_up(cur);
    }
  }

  valueType query(int cur, int l, int r, int L, int R) {
    if (l >= R || r <= L)
      return valueZero;
    if (L <= l && r <= R)
      return nodes[cur].val;
    push_down(cur);
    return merge(query(cur << 1, l, (l + r) >> 1, L, R),
                 query(cur << 1 | 1, (l + r) >> 1, r, L, R));
  }

public:
  segmentTree() {}

  segmentTree(int _leftRange, int _rightRange,
              const std::vector<valueType> &_initValue,
              const valueType &_valueZero, const tagType &_tagZero) {
    leftRange = _leftRange;
    rightRange = _rightRange;
    init(_initValue, _valueZero, _tagZero);
  }

  segmentTree(int size, const std::vector<valueType> &_initValue,
              const valueType &_valueZero, const tagType &_tagZero) {
    leftRange = 1;
    rightRange = size + 1;
    init(_initValue, _valueZero, _tagZero);
  }

  void modify(int l, int r, const tagType &tag) {
    modify(1, leftRange, rightRange, l, r, tag);
  }

  void modify(int p, const tagType &tag) { modify(p, p + 1, tag); }

  valueType query(int l, int r) {
    return query(1, leftRange, rightRange, l, r);
  }

  valueType query(int p) { return query(p, p + 1); }
};

// template<class T, class Compare= less<typename
// std::iterator_traits<T>::value_type>> void merge(T begin, T middle, T end,
// Compare cmp = less<typename std::iterator_traits<T>::value_type>()) {
//     vector<typename std::iterator_traits<T>::value_type> Temp(end - begin);
//     auto it_1 = begin;
//     auto it_2 = middle;
//     while (it_1 < middle && it_2 < end) {
//         if (cmp(*it_1, *it_2)) {
//             Temp[(it_1 - begin) + (it_2 - middle)] = *it_1;
//             ++it_1;
//         } else {
//             Temp[(it_1 - begin) + (it_2 - middle)] = *it_2;
//             ++it_2;
//         }
//     }
//     while (it_1 < middle) {
//         Temp[(it_1 - begin) + (it_2 - middle)] = *it_1;
//         ++it_1;
//     }
//     while (it_2 < end) {
//         Temp[(it_1 - begin) + (it_2 - middle)] = *it_2;
//         ++it_2;
//     }
//     for (auto it = begin; it != end; ++it) {
//         *it = Temp[it - begin];
//     }
// }
//
// template<class T, class Compare = less<typename
// std::iterator_traits<T>::value_type>> void merge_sort(T begin, T end, Compare
// cmp = less<typename std::iterator_traits<T>::value_type>()) {
//     auto middle = begin + (end - begin) / 2;
//     if (end - begin <= 1) {
//         return;
//     }
//     merge_sort(begin, middle, cmp);
//     merge_sort(middle, end, cmp);
//     merge(begin, middle, end, cmp);
// }
//
// template<class T, class Compare = less<typename
// std::iterator_traits<T>::value_type>> T Partition(T begin, T end, Compare cmp
// = less<typename std::iterator_traits<T>::value_type>()) {
//     typename std::iterator_traits<T>::value_type x = *(begin + (end - begin)
//     / 2); T left = begin; T right = end - 1; while (left <= right) {
//         while (cmp(*left, x)) {
//             ++left;
//         }
//         while (cmp(x, *right)) {
//             --right;
//         }
//         if (left >= right) {
//             break;
//         }
//         swap(*left, *right);
//         ++left;
//         --right;
//     }
//     return left;
// }
//
// template<class T, class Compare = less<typename
// std::iterator_traits<T>::value_type>> void qsort(T begin, T end, Compare cmp
// = less<typename std::iterator_traits<T>::value_type>()) {
//     if (end - begin <= 1) {
//         return;
//     }
//     T border = Partition(begin, end, cmp);
//     qsort(begin, border, cmp);
//     qsort(border, end, cmp);
// }
//
// template<class T, class Compare = less<T>>
// class Heap {
// public:
//     Heap() {};
//
//     Heap(vector<T> &&__Array) : Array(std::move(__Array)) {
//
//     }
//
//     T getMinimum const() {
//
//     }
//
//     size_t size() const { return Array.size(); }
//
//     vector<T> Array;
//
// };

int main() {
  cin.tie(nullptr);
  cout.tie(nullptr);
  std::ios_base::sync_with_stdio(false);
  cout.precision(15);
  ll tests;
  cin >> tests;
  while (tests--) {
    ll n;
    cin >> n;
    vector<ll> A(n);
    for (int i = 0; i < n; ++i) {
      cin >> A[i];
    }
    string s;
    cin >> s;
    vector<ll> D;
    for (int i = n - 1; i >= 0; --i) {
      if (s[i] == '1') {
        ll v = A[i];
        for (auto &t : D) {
          v = min(v, v ^ t);
        }
        if (v) {
          D.clear();
          break;
        }
      } else {
        ll v = A[i];
        for (auto &t : D) {
          v = min(v, v ^ t);
        }
        D.push_back(v);
      }
    }
    if (D.empty()) {
      cout << 1 << endl;
    } else {
      cout << 0 << endl;
    }
  }
}

Error: TLE

Fixed submission:

#include <algorithm>
#include <cassert>
#include <cmath>
#include <fstream>
#include <iostream>
#include <list>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <stdio.h>
#include <stdlib.h>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

//....................................................................................................................//

using std::cin;
using std::cout;
using std::deque;
using std::get;
using std::greater;
using std::ifstream;
using std::ios_base;
using std::less;
using std::list;
using std::lower_bound;
using std::make_pair;
using std::make_tuple;
using std::map;
using std::max;
using std::max_element;
using std::min;
using std::min_element;
using std::multimap;
using std::multiset;
using std::ofstream;
using std::pair;
using std::priority_queue;
using std::queue;
using std::set;
using std::stack;
using std::string;
using std::swap;
using std::tuple;
using std::unordered_map;
using std::unordered_multimap;
using std::unordered_set;
using std::upper_bound;
using std::vector;
// using std::endl;

//....................................................................................................................//

typedef long long ll;
typedef unsigned long long ull;

[[maybe_unused]] const string endl = "\\n";
[[maybe_unused]] const string sep = " ";
[[maybe_unused]] const string yes = "YES\\n";
[[maybe_unused]] const string no = "NO\\n";
[[maybe_unused]] const string ng = "NG\\n";
[[maybe_unused]] const string ok = "OK\\n";
[[maybe_unused]] const double pi = acos(-1);
[[maybe_unused]] const ull modular = 1e9 + 7;

//....................................................................................................................//

template <class T> T min(const T &a, const T &b, const T &c) {
  return min(a, min(b, c));
}

template <class T> T max(const T &a, const T &b, const T &c) {
  return max(a, max(b, c));
}

typedef vector<vector<ll>> graph;

vector<ll> lca_h, lca_dfs_list, lca_first, lca_tree;
vector<char> lca_dfs_used;

void lca_dfs(const graph &g, ll v, ll h = 1) {
  lca_dfs_used[v] = true;
  lca_h[v] = h;
  lca_dfs_list.push_back(v);
  for (auto i = g[v].begin(); i != g[v].end(); ++i)
    if (!lca_dfs_used[*i]) {
      lca_dfs(g, *i, h + 1);
      lca_dfs_list.push_back(v);
    }
}

void lca_build_tree(ll i, ll l, ll r) {
  if (l == r)
    lca_tree[i] = lca_dfs_list[l];
  else {
    ll m = (l + r) >> 1;
    lca_build_tree(i + i, l, m);
    lca_build_tree(i + i + 1, m + 1, r);
    if (lca_h[lca_tree[i + i]] < lca_h[lca_tree[i + i + 1]])
      lca_tree[i] = lca_tree[i + i];
    else
      lca_tree[i] = lca_tree[i + i + 1];
  }
}

void lca_prepare(const graph &g, ll root) {
  ll n = (ll)g.size();
  lca_h.resize(n);
  lca_dfs_list.reserve(n * 2);
  lca_dfs_used.assign(n, 0);

  lca_dfs(g, root);

  ll m = (ll)lca_dfs_list.size();
  lca_tree.assign(lca_dfs_list.size() * 4 + 1, -1);
  lca_build_tree(1, 0, m - 1);

  lca_first.assign(n, -1);
  for (ll i = 0; i < m; ++i) {
    ll v = lca_dfs_list[i];
    if (lca_first[v] == -1)
      lca_first[v] = i;
  }
}

ll lca_tree_min(ll i, ll sl, ll sr, ll l, ll r) {
  if (sl == l && sr == r)
    return lca_tree[i];
  ll sm = (sl + sr) >> 1;
  if (r <= sm)
    return lca_tree_min(i + i, sl, sm, l, r);
  if (l > sm)
    return lca_tree_min(i + i + 1, sm + 1, sr, l, r);
  ll ans1 = lca_tree_min(i + i, sl, sm, l, sm);
  ll ans2 = lca_tree_min(i + i + 1, sm + 1, sr, sm + 1, r);
  return lca_h[ans1] < lca_h[ans2] ? ans1 : ans2;
}

ll lca(ll a, ll b) {
  ll left = lca_first[a], right = lca_first[b];
  if (left > right)
    swap(left, right);
  return lca_tree_min(1, 0, (ll)lca_dfs_list.size() - 1, left, right);
}

ll gcd(ll a, ll b) {
  if (a == 0) {
    return b;
  }
  return gcd(b % a, a);
}

ll fast_power(ll a, ll pow) {
  if (pow == 0) {
    return 1;
  }
  if (pow % 2 == 0) {
    auto x = fast_power(a, pow / 2);
    return (x * x);
  } else {
    auto x = fast_power(a, pow - 1);
    return (a * x);
  }
}

ll fast_power(ll a, ll pow, ll mod) {
  if (pow == 0) {
    return 1;
  }
  if (pow % 2 == 0) {
    auto x = fast_power(a, pow / 2, mod);
    return (x * x) % mod;
  } else {
    auto x = fast_power(a, pow - 1, mod);
    return (a * x) % mod;
  }
}

void getFactorialsModular(const ll n, const ll mod, vector<ll> &F) {
  F.resize(n + 1);
  F[0] = 1;
  for (ll i = 1; i <= n; ++i) {
    F[i] = (F[i - 1] * i) % mod;
  }
}

void getFactorialsAndInverseModular(const ll n, const ll mod, vector<ll> &F,
                                    vector<ll> &I) {
  getFactorialsModular(n, mod, F);
  I.resize(n + 1);
  I[0] = 1;
  for (ll i = 1; i <= n; ++i) {
    I[i] = fast_power(F[i], mod - 2, mod);
  }
}

ll CnkMod(ll n, ll k, ll mod, vector<ll> &F, vector<ll> &I) {
  return (((F[n] * I[k]) % mod) * I[n - k]) % mod;
}

ll CnkWithRepetitionMod(ll n, ll k, ll mod, vector<ll> &F, vector<ll> &I) {
  return CnkMod(n + k - 1, k - 1, mod, F, I);
}

/*
MIT License
Copyright (c) 2019 ouuan
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
*/

// for further information and bug tracking,
// please visit https://github.com/ouuan/segmentTree

template <typename valueType, typename tagType> class segmentTreeNode {
public:
  int id, left, right;
  valueType val;
  tagType tag;
};

template <typename valueType, typename tagType,
          valueType (*merge)(valueType, valueType),
          void (*update)(segmentTreeNode<valueType, tagType> &, tagType)>
class segmentTree {
private:
  std::vector<segmentTreeNode<valueType, tagType>> nodes;
  int leftRange, rightRange;
  valueType valueZero;
  tagType tagZero;

  void push_up(int cur) {
    nodes[cur].val = merge(nodes[cur << 1].val, nodes[cur << 1 | 1].val);
  }

  void push_down(int cur) {
    update(nodes[cur << 1], nodes[cur].tag);
    update(nodes[cur << 1 | 1], nodes[cur].tag);
    nodes[cur].tag = tagZero;
  }

  void build(int cur, int l, int r, const std::vector<valueType> &initValue) {
    nodes[cur].id = cur;
    nodes[cur].left = l;
    nodes[cur].right = r;
    nodes[cur].tag = tagZero;
    if (l == r - 1)
      nodes[cur].val = initValue[l - leftRange];
    else {
      build(cur << 1, l, (l + r) >> 1, initValue);
      build(cur << 1 | 1, (l + r) >> 1, r, initValue);
      push_up(cur);
    }
  }

  void init(const std::vector<valueType> &_initValue,
            const valueType &_valueZero, const tagType &_tagZero) {
    valueZero = _valueZero;
    tagZero = _tagZero;
    nodes.resize((rightRange - leftRange) << 2);
    build(1, leftRange, rightRange, _initValue);
  }

  void modify(int cur, int l, int r, int L, int R, const tagType &tag) {
    if (l >= R || r <= L)
      return;
    if (L <= l && r <= R)
      update(nodes[cur], tag);
    else {
      push_down(cur);
      modify(cur << 1, l, (l + r) >> 1, L, R, tag);
      modify(cur << 1 | 1, (l + r) >> 1, r, L, R, tag);
      push_up(cur);
    }
  }

  valueType query(int cur, int l, int r, int L, int R) {
    if (l >= R || r <= L)
      return valueZero;
    if (L <= l && r <= R)
      return nodes[cur].val;
    push_down(cur);
    return merge(query(cur << 1, l, (l + r) >> 1, L, R),
                 query(cur << 1 | 1, (l + r) >> 1, r, L, R));
  }

public:
  segmentTree() {}

  segmentTree(int _leftRange, int _rightRange,
              const std::vector<valueType> &_initValue,
              const valueType &_valueZero, const tagType &_tagZero) {
    leftRange = _leftRange;
    rightRange = _rightRange;
    init(_initValue, _valueZero, _tagZero);
  }

  segmentTree(int size, const std::vector<valueType> &_initValue,
              const valueType &_valueZero, const tagType &_tagZero) {
    leftRange = 1;
    rightRange = size + 1;
    init(_initValue, _valueZero, _tagZero);
  }

  void modify(int l, int r, const tagType &tag) {
    modify(1, leftRange, rightRange, l, r, tag);
  }

  void modify(int p, const tagType &tag) { modify(p, p + 1, tag); }

  valueType query(int l, int r) {
    return query(1, leftRange, rightRange, l, r);
  }

  valueType query(int p) { return query(p, p + 1); }
};

// template<class T, class Compare= less<typename
// std::iterator_traits<T>::value_type>> void merge(T begin, T middle, T end,
// Compare cmp = less<typename std::iterator_traits<T>::value_type>()) {
//     vector<typename std::iterator_traits<T>::value_type> Temp(end - begin);
//     auto it_1 = begin;
//     auto it_2 = middle;
//     while (it_1 < middle && it_2 < end) {
//         if (cmp(*it_1, *it_2)) {
//             Temp[(it_1 - begin) + (it_2 - middle)] = *it_1;
//             ++it_1;
//         } else {
//             Temp[(it_1 - begin) + (it_2 - middle)] = *it_2;
//             ++it_2;
//         }
//     }
//     while (it_1 < middle) {
//         Temp[(it_1 - begin) + (it_2 - middle)] = *it_1;
//         ++it_1;
//     }
//     while (it_2 < end) {
//         Temp[(it_1 - begin) + (it_2 - middle)] = *it_2;
//         ++it_2;
//     }
//     for (auto it = begin; it != end; ++it) {
//         *it = Temp[it - begin];
//     }
// }
//
// template<class T, class Compare = less<typename
// std::iterator_traits<T>::value_type>> void merge_sort(T begin, T end, Compare
// cmp = less<typename std::iterator_traits<T>::value_type>()) {
//     auto middle = begin + (end - begin) / 2;
//     if (end - begin <= 1) {
//         return;
//     }
//     merge_sort(begin, middle, cmp);
//     merge_sort(middle, end, cmp);
//     merge(begin, middle, end, cmp);
// }
//
// template<class T, class Compare = less<typename
// std::iterator_traits<T>::value_type>> T Partition(T begin, T end, Compare cmp
// = less<typename std::iterator_traits<T>::value_type>()) {
//     typename std::iterator_traits<T>::value_type x = *(begin + (end - begin)
//     / 2); T left = begin; T right = end - 1; while (left <= right) {
//         while (cmp(*left, x)) {
//             ++left;
//         }
//         while (cmp(x, *right)) {
//             --right;
//         }
//         if (left >= right) {
//             break;
//         }
//         swap(*left, *right);
//         ++left;
//         --right;
//     }
//     return left;
// }
//
// template<class T, class Compare = less<typename
// std::iterator_traits<T>::value_type>> void qsort(T begin, T end, Compare cmp
// = less<typename std::iterator_traits<T>::value_type>()) {
//     if (end - begin <= 1) {
//         return;
//     }
//     T border = Partition(begin, end, cmp);
//     qsort(begin, border, cmp);
//     qsort(border, end, cmp);
// }
//
// template<class T, class Compare = less<T>>
// class Heap {
// public:
//     Heap() {};
//
//     Heap(vector<T> &&__Array) : Array(std::move(__Array)) {
//
//     }
//
//     T getMinimum const() {
//
//     }
//
//     size_t size() const { return Array.size(); }
//
//     vector<T> Array;
//
// };

int main() {
  cin.tie(nullptr);
  cout.tie(nullptr);
  std::ios_base::sync_with_stdio(false);
  cout.precision(15);
  ll tests;
  cin >> tests;
  while (tests--) {
    ll n;
    cin >> n;
    vector<ll> A(n);
    for (int i = 0; i < n; ++i) {
      cin >> A[i];
    }
    string s;
    cin >> s;
    set<ll> D = {0};
    for (int i = n - 1; i >= 0; --i) {
      if (s[i] == '1') {
        if (!D.count(A[i])) {
          D.clear();
        }
      } else {
        set<ll> T;
        for (auto &t : D) {
          T.insert(t);
          T.insert(t ^ A[i]);
        }
        D = T;
      }
    }
    if (D.empty()) {
      cout << 1 << endl;
    } else {
      cout << 0 << endl;
    }
  }
}